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CAMPG Tutorial - California State University, Sacramento

1. M LO aam aama amama amaaa aaa amaaa Yk k k k k k k k k k k k k k k k k k k k k kkkkkkkkkkkkkkkkkkkk DR I NE BOND GRAPH ANALYSIS SSYSTEM DESCRIPTION POWER FLOW BOND FROM TO 1 SF 1 01 2 5 2 0 1 2 5 1234 3 12 34 3 4 1 2 3 4 RA 5 0 1 2 5 1567 6 15 6 7 I6 7 15 6 7 07 8 11 8 0 78 11 1_8_9_10 9 1 8 9 10 c 9 10 1 989 10 R 10 lr 0 7 8 11 I CAUSALITY FLOW NOTE FROM TO BOND FROM TO 1 0 1 2 5 SF 1 2 1234 0 1 2 5 3 c 3 12 34 4 RA 1 2 3 4 5 0125 1567 6 15 6 7 I_6 7 0 7 8 11 1 5 6 7 8 1 8 9 10 0 78 11 9 C_9 1 8 9 10 10 R_10 1 8 9 10 11 0 7 8 11 I 11 End of model 54 What follows is the same file seen above but this time the file has been broken down into easier to see sections Some of the file was excluded from this second listing This was done because the only parts that are going to be show here are the parts that the user may have to change Initial Conditions lll Initial conditions Q9IN Q3IN P11IN P6IN initial Q9IN Q3IN P11IN P6IN System Physical Parameters ee System Physical Parameters global C3 R4 I6 C9 R10 111 c3 02 R4 I6 C9 2 R10 I11 External Inputs llllz External inputs se t sf t global SF1 SF1 Simulation Tim
2. 174 ACSL gt A lt invokes procedure to plot forces see file below ACSL gt B lt invokes procedure to plot velocities See file below The last two commands contain just the letter A and the letter B This means execute the commands contained in the SETUP file that are describer under the procedure A The procedure A is defined by the keyword PROCEED and the label which is this case 1s the letter A Then execute the commands contained in the SETUP file under the procedure B These procedures are displayed in the SETUP file example shown below For example the PREPAR and OUTPUT statements and the different PLOT statements can be generated by using a SETUP file like the one below SET TITLE DAMPED OSCILLATOR PREPAR T ELE2 E3 F3 Q3 OUTPUT T ELE2 E3 F3 Q3 SET TCWPRN 72 START PROCED A SET TITLE SPRING DAMPER AND MASS FORCES PLOT ELE2 E3 END PROCED B SET TITLE VELOCITY OF THE MASS PLOT F3 END PROCED C SET TITLE DISPLACEMENT OF THE MASS PLOT Q3 END SET CALPLT TRUE PRNPLT FALSE PLT 6 SET CMD DIS 175 This SETUP file sets up the initial TITLE which will appear in the respective plots The commands in this example do the following PREPAR OUTPUT TCWPRN CALPLT PRNPLT FALSE PLT Prepares the calculation tables for plotting Requests a display of the calculated values on the screen as the simulation executes If the output is large and a listing on the screen
3. Solution of system equations using Matlab ode23 function The campgequ m function contains the system differential equations in state variable form It returns the vector t p q where t time and p q vector of state variables For matlab version 4 2 use t p dq ode23 campgequ t0 tf initial 127 status odeset outputfcn esandfs t p_q ode23 campgequ tspan initial status P11 p q 1 Q10 p q 2 P8 p q 3 P2 p q 4 Q5 p q 5 State variables vector p_q P11 Q10 P8 P2 Q5 radeg 360 2 pi Sample Matlab structure for plotting simulation results Figure with the Theta s figure 1 subplot 311 plot t p_q 6 radeg r grid title Theta 1 subplot 312 plot t p_q 7 radeg b grid title Theta 2 subplot 313 plot t p_q 8 radeg r grid title Theta 3 New figure with W s figure 2 subplot 311 plot t Efforts 2 r grid title W 1 subplot 312 plot t Efforts 3 b grid title W 2 subplot 313 plot t Efforts 4 r grid title W 3 New figure with accellerations figure 3 subplot 311 plot t Efforts 5 radeg I2 r grid title WD1 subplot 312 plot t Efforts 5 radeg I8 b grid title WD2 subplot 313 plot t Efforts 7 radeg I11 r grid title WD3 New figure with Twist Force and Input torque figure 4 subplot 311 plot t p q 2 radeg
4. Force Acting on the Dummy 5000 5000 10000 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 Time seconds 241 242 Technical References BOOKS l J J Granda and F E Cellier eds Proceedings of ICBGM 2007 8th International Conference on Bond Graph Modeling and Simulation Simulation Series Vol 39 Nr 1 SCS Publishing ISBN 1 56555 310 1 January 2007 Karnopp D Rosenberg R SYSTEM DYNAMICS Modeling and Simulation of Mechatronics Systems Wiley and Sons New York 2006 MATLAB User s Manual The Mathworks 2007 ADVANCED CONTINUOUS SIMULATION LANGUAGE ACSL User Guide Reference Manual AEgis Technologies 2006 SYSQUAKE User s Manual Calerga Switzerland 2007 J J Granda and F E Cellier eds Proceedings of ICBGM 2005 7h International Conference on Bond Graph Modeling and Simulation Simulation Series Vol 37 Nr 1 SCS Publishing ISBN 1 56555 287 3 January 2005 J J Granda and F E Cellier eds Proceedings of ICBGM 2003 6h International Conference on Bond Graph Modeling and Simulation simulation Series Vol 35 Nr 2 SCS Publishing ISBN 1 56555 257 1 January 2003 J J Granda and G Dauphin Tanguy eds Proceedings of ICBGM 2001 5th International Conference on Bond Graph Modeling and Simulation Simulation Series Vol 33 Nr 1 SCS Publishing ISBN 1 56555 103 6 January 2001 243 10 11 12 13 14 Granda J J ADVANCES
5. Computer Aided Modeling Program with Graphical Input Version 5 5 WINDOWS XP USER S MANUAL Cadsim Engineering P O Box 4083 Davis Ca 95617 http www bondgraph com Copyright 2007 All Rights Reserved CAMPG Computer Aided Modeling Program with Graphical Input Windows XP USER S MANUAL The Universal Bond Graph Modeling Preprocessor for Dynamic and Mechatronics Systems Cadsim Engineering P O Box 4083 Davis Ca 95617 U S A http www bondgraph com Copyright 2000 2007 All rights Reserved Contents Chapter 1 CAMPG QUICK START hio SINS TARGA TION 3S2 eteterevbeo e eoa pee a RE E RER aan sheet 1 t2 MAM PG ICONS SEC ese rescue t esas Rer ORNA dE TREE EARN 2 1 3 Bond Graph Model Entry cree ced reet eoe ett 4 1 4 CAMPG ACSL INTERFACE eee 6 1 5 CAMPG MATLAB Interface esses 9 1 6 The CAMPG SIMULINK interface esee 11 1 7 The CAMPG SYSQUAKE interface cece cece cence es 14 Chapter 2 CAMPG Basics 2 L antroduetiOle s uos novaxces tud evo awe ur EE tapes Eyed uo nene e deis 17 Purpose of this manual cep rey on dees ones 17 Description of C AMPG decies eek Iva I ere dE Pda 17 CAMP and CAMPGT iieisttsb e tei Ped eate kiii 18 2 2 HOw to Use CAMBDOGI i etse otseo ERR RR PEN EERARERDUFPR VE TERRE E Vid qos 19 Starting CAMPG one tt dtt x oa E 19 Creating a bond graph ccc cece cece nee e cence nee ee en eee 19
6. 1 kh SE T CERE I ES AS MGY MGY MGY SE j 1 MGY 1 SE
7. 13 0 8 1b sec 2 in SINUSOIDAL DRIVING TORQUE T 100 SIN 20 THETA 2 I2 0 01 Ib sec in R2 1 0in K TORSIONAL SPRING STIFFNESS OF SHAFT 4000 in Ib rad SCHEMATIC OF GEAR TRAIN SYSTEM THETA 3 Fig 4 18 Physical System Model of Drive Train Backlash 0 2 in The contact force between the gear teeth is defined by a dead space non linear function The force increases linearly when the gears are in contact but is zero when they are not Since the input torque is a harmonic function the teeth are not always in contact and therefore a nonlinear model exists The diagram of this function is shown in Fig 4 9 seen below The position of the gears forces and velocities are of interest in the design of the gear train Nonlinear Dead Space Contact F b d Force between geer teeth slope BACKLASH IN GEAR TEETH Fig 4 19 Mathematical functions of backlash OBJECTIVES 1 Generate an engineering model of the gear train shown in Fig 4 18 2 Transform the engineering model of the real system into a computer model for simulation using the Computer Aided Modeling Program CAMPG Using computer simulation in an interactive way generate numerical and graphical output using the Advanced Continuous Simulation Language ACSL Interpret the results and make design decisions 201 200000 1b in PROCEDURE FOR SOLUTION 1 GENERATE AN ENGINEERING MODEL The system shown in Fig
8. amp C 2 0 1 3 0 0 D 0 f6 P6 I6 C 0 0 0 1 16 D 0 7 P6 16 C 0 0 0 1 16 D 0 e9 09 C9 C 1 C9 0 0 0 D 0 f11 P11 I11 C 0 0 1 111 0 D 0 This section is where the C and D matrices are created These matrices are created in the same fashion that the A and B matrices are created with one exception These matrices are created by the user and the user decides which outputs to initialize This is done by removing the from in front of the line that needs to be initialized and then inserting a number in place of The number that is inserted is going to be the row of the matrix that output will occupy As seen here this is not the entire C and D matrix creation section 65 This was done because the entire listing can be seed above under CAMPGSYM M Listing Creating an Identity Matrix Find the size of A and then figure out I I eye 4 This is where the identity matrix is created that will be used in the calculation of the transfer functions This section needs no changes to be made CAMPG automatically creates this section and sets the size of it equal to the number of states Creation of the Transfer Function Matrix Transfer Functions Matrix H H C inv s I A B D pretty H collect H This is where the actual matrix that contains the transfer functions is created and then
9. first order differential equations campgsym m gt m file containing system matrices in symbolic form For simulation and control edit these files Enter values for physical parameters initial conditions inputs and time controls in places where the marks appear Standard generalized variables in Bond Graph notation used Sagre CAMPGMOD M MATLAB MODEL INPUT FILE clear all 4 A pi r 2 ep Initial conditions P9IN 0 P12IN 0 Q11IN 0 Q14IN O initial Q11IN Q14IN P9IN P12IN o eo System Physical Parameters global I9 R10 C11 I12 R13 C14 Efforts counter I9 1000 50 1 R10 100000 C11 A 1000 9 8 112 1000 50 1 R13 100000 C14 A 1000 9 8 E ce External inputs se t sf t global SE1 SE2 SE3 SF8 SE1 1000 9 8 20 SE2 1000 9 8 30 SE3 1000 9 8 30 SF8 Gate hed Simulation Time Control t02 0 Initial Time tf 200 Final Time tspan tO tf B 2usmes Computer Simulation counter 1 151 AP de oe oe oe oe oe oe de oe oe oe Solution of system equations using Matlab ode23 function The campgequ m function contains the system differential equations in state variable form It returns the vector t p q where t time and p q vector of state variables For matlab version 4 2 use t p dq ode23 campgequ t0 tf initial status odeset outputfcn esandfs t p_q ode23
10. 4 18 is the engineering model of the real system The stiffness elements are the shafts the inertia element is the flywheel and the gears GENERATE THE CORRESPONDING BOND GRAPH Make a Bond Graph model of the gear train Consider the inertia of the gears and the flywheel the compliance effect of the drive shaft and the slack between the gear teeth Fig 4 20 shows this model The backlash is modeled as a nonlinear compliant element C because the constitutive relation between contact force and the relative displacement is defined in Fig ure 132 The force function is directly related to the relative displacement between the teeth This relative displacement at the gear teeth point of contact is calculated by the integration of the relative velocity between the two gears The relative tangential velocity is obtained by multiplying the angular velocity of the gear by their respective radius and finding the difference in tangential velocities a the point where the gears are in contact This is accomplished by the TF elements that make this transformation between the angular velocity and the tangential velocity The C element performs the integration and controls also the force using the defined DEAD SPACE function that represents the time the gears are in contact as well as when they are not CAMPG Generate a description of the graph using the graphics capabilities of the Computer Aided Modeling Program with Graphical input CAMPG This model
11. Fluid Mechanics Institute California State University Sacramento June 1987 Granda J J Ferner E Computer Simulation of a Hydraulic Four Way Control Valve TRANSACTIONS Journal of the Society for Computer Simulation January 1987 Granda J J Analysis of an Aircraft Landing Mechanism Using Computer Graphics and an Automatic Model Generator Proceedings of the Summer Computer Simulation Conference Reno Nevada July 28 30 1986 Granda J J Modeling and Simulation of Electromechanical Systems using Computer Graphics Proceedings of the Conference on Computer Graphics California State University Sacramento Ca March 1986 Granda J J Ferner E Computer Aided Simulation of a Hydraulic Four Way Valve Proceedings of the Multiconference on Languages for Continuous Systems Simulation San Diego Ca January 1986 Granda J J Computer Simulation of a Hydraulic Power Steering System with Mechanical Feedback Proceedings of the 29th Heat Transfer and Fluid Mechanics Institute CSU Sacramento Sacramento Ca June 1985 Granda J J Computer Aided Control System Design using Bond Graph Modeling Abstract Proceedings of the IEEE Control Systems Society 2nd Symposium on Computer Aided Control System Design CACSD Santa Barbara California March 1985 Granda J J Computer Graphics Techniques for the Generation and Analysis of Physical System Models Proceedings of the Multiconference on Artificial Intelligence Graphics
12. Fig 4 23 Angles Response Fig 4 24 Angle flywheel Angle of Twist THETA2 102 THETAS 102 8 ANGLES OF ROTATION GEAR 1 AND GEAR 2 20 0 00 THETAL 10 0 1 00 ANGLE FLYWHEEL ANGLE OF TWIST SHRFT ere i 0 0 75 1 00 0 50 220 Fig 4 22 Fig 4 23 Since the input is a torque a causal effect is the acceleration and velocity of the gears These variables are affected by de discontinuity of the contact made among the gear teeth The plot at the bottom of Fig 4 22 shows that gear 1 is accelerating under a basic harmonic function but the positive and negative peaks are accelerations of decelerations due to the dynamics of the gear train The figure in the middle is an order of magnitude bigger and contains higher peeks of acceleration and deceleration This can be explained due to several factors The most influential ones are the gear ratio and the separations and sudden contact that the gears experience at a high frequency The acceleration at the flywheel is affected by the stiffness of the shaft it is lower in this case because the shaft is flexible This figure shows the angular velocity of the gears and also of the flywheel The bottom figure shows a nonlinear function while the flywheel velocity appears as a periodic function The changes in velocity of gear 2 occur at a high frequency This is due to the vibration of the gear train on both sides of gear 3 Rapid changes in the
13. Normally the user would have to create duplicate parts of the bond graph manually When using CAMPG the user has the option of simply copying and or flipping selected segments of elements junctions and or bonds This shortens the time required to create the bond graph An example of this can been seen in Fig 5 8 232 CAMP G c XcampgXbgmodels engparts Lene rae ntentose aranea ociera moros TT 18 AR AR 59 adi se zn rp E E an SE gil n 53 5 55 In is SE 62 57 c s osx TF 58 R 9 1 o IG gt amp n Sir o D delete single I done delete single BOND 29 done delete single BOND 36 done BOND FROM bond from 1 27 28 to TF bond 29 Fig 5 8 Complex system components SUBSYSTEMS Several Bond Graph models can be created independently on the same screen or subsystems existing on bg files on disk can be imported into the working screen Subsystems can be numbered differently using the renumber option on the EDIT menu SIMULTANEOUS SIMULATIONS Using CAMPG s ability to create separate bond graphs is the same session window it is possible to run simultaneous simulations This can be useful if the user needs to compare the simulation results of two 233 AAA systems that are being compared To illustrate this technique two completely unrelated systems will be modeled simultaneously this will help to demonstrate the flexibility of this
14. Placing elements osii n Seed See ete eee 21 Bondi estesa er yid Pod yep Re r M eR rd eUs 21 2 3 CAMPG Features And Menus Lecce 21 Dialogue BOR eateries sits iee lees Mt sae ette 22 SEES o Locis seb a aE E cU Su E E e he soak iR te V LUC 22 Quick Delete rsi e Doe o ss 22 Pull Down Menus x52 55 ceca puede A dt Bur pua SEC He UNA PS Ue 22 Scroll Bars ccm 31 Undo remiten e veso ee eh ea eh E E ET E ET Scuba es 31 2 4 Generating Bond Graph Models eese 3l Systematic Method Of Bond Graph Construction Sequential Method Of Bond Graph Construction Quick Delete dde ER Edit Delete soenoe enee euo Peer HUMOUR IE vos bes 2 5 Interfacing with a Digital Simulation Language ACSL input file preparation sese CAMPG simulation language interface menu EXILCAMDPG 4 eia patema um EUH Ed eu RUN ACSL with CAMPSL CSL sees Chapter 3 CAMPG and MATLAB 2 1 AntroduCtlOti us certe c e edet s 32 Interfacing CAMPG with MATLAB sese CAMPG Executable Icons ence e e 3 3 Files Created During Interfacing and Descriptions CAMPGMOD Mocs eee eet pare ELA AAAA ERE E RR ELA UE Initial Conditions eee eee ee ee ee System Physical Parameters External Inputs HR EE Simulation Time Control Defining Outpu
15. SYSTEMATIC method In the case of the gear teeth the SEQUENTIAL method is used to generate the bond graph and demonstrate how to construct bond graph models using this method and CAMPG Just as a brief reminder the SEQUENTIAL method consists 120 of assembling of all bonds immediately following the placement of the elements and 0 or 1 junctions This method helps to illustrate other editing features of CAMPG such as the moving of whole bond graphs or parts of them to other parts of the screen The bond graph of Fig 3 27 was constructed using the following steps CAMPG CR Start CAMPG and brings up the logo containing the user name and the license number Please refer to this number for maintenance and updates space bar CR This clears the screen preparing it for a drawing Any other character or movement of the mouse will do the same EDIT CUR The next three steps clear the session file If you have no previous SESSION BG file These steps are not necessary DELETE CUR ALL CUR YES CUR SE CUR There is a box on the left icon menu which has the SE symbol in it This is the SOURCE EFFORT element in the bond graph Pick the SE with the mouse Left of screen CUR Place the SE on the screen by moving the cursor to the middle of the vertical left edge of the drawing screen and a couple of grids to the right and clicking the left button of the mouse The model can start in any location of the screen 12
16. The Advanced Continuous Simulation Language ACSL is a program developed for modeling and evaluating the performance of continuous systems described by time dependent linear or non linear differential equations These equations can be expressed as block diagrams transfer functions graphical representations i e bond graphs and of course algebraic expressions The input format for the models allows the specification of the block diagram equations in any sequence This means that as long as all variables are defined to the left of all equal signs they could appear in any order The computer will perform a logical variables sort prior to the computations Some of the most important features of the program are free form input flexibility for plotting many simulation oriented operators any FORTRAN function or user created subroutine may be used It is this flexibility that allows a simulation language such ACSL to be a universal tool and describe just about any system nonlinearity or special function used to describe it 155 Explicit Structure of a Simulation Model A complete simulation model is stored in a disk file that can be used as ACSL input It must include the physical parameters initial conditions differential equations and time control statements These items are organized in a structured and organized way An ACSL input file created by the user or by CAMPG contains these in the form of an explicit structure Groups of st
17. and Simulation San Diego Ca January 1985 250 39 60 61 62 63 64 Granda J J Computer Generation of Physical System Differential Equations using Bond Graphs Journal of the Franklin Institute January February Issue 1985 Granda J Computer Aided Design of Dynamic Systems Proceedings of the Summer Computer Simulation Conference Boston Mass July 23 25 1984 Granda J Modeling and Simulation in a Computer Aided Design Curriculum Annual Meeting of the American Society for Engineering Education University of Utah June 24 28 1984 Granda J Bond Graph Modeling Solutions of Algebraic Loops and Differential Causality in Mechanical and Electrical Systems Proceedings of the Tenth International Association of Science and Technology for Development IASTED International Conference Applied Simulation and Modeling ASM 84 San FranciscoJune 4 6 1984 Granda J J Computer Generation of Mechanical Systems Differential Equations NATO National Science Foundation Advanced Study Institute on Computer Aided Analysis and Optimization of Mechanical System Dynamics The University of Iowa August 1983 Granda J J A guide to Using the Computer Aided Modeling Program Department of Mechanical Engineering California State University Sacramento June 1983 251 CAMPG The Universal Bond Graph Modeling Preprocessor for Dynamic and Mechatronics Systems I j AS MGY MGY MGY I SE j 1 MGYs
18. called Y against the values in the vector called X These vectors need to be the same length These vectors can be called anything FPRINTF Used to display numbers or strings in a formatted style DISP Used to display what ever is enclosed in the single quotes in the brackets 68 SYMS GLOBAL XLABEL YLABEL TITLE LEGEND ZOOM GRID Usually used to send text messages to the screen Used to declare variables ie R2 I12 C5 etc as being symbolic Good for using when getting transfer functions Used to declare a variable as global between the workspace and a function or M file or between two or more files Simply make the GLOBAL statement in each file where the variable is to be used and the variable only needs to be defined once Allows the user to label the x axis of a graph Allows the user to label the y axis of a graph Allows the user to create a title for a graph Allows the user to create a legend for a graph Allows the user to set the graph to zoom mode When a graph is in zoom mode the user can zoom in on a particular area of the graph to get a better feel for what is going on Also allows the user to Zoom out Allows the user to set grid lines on the graph 69 CLEAR SIZE FORMAT WHILE FOR IF ELSE END Allows the user to clear the variables that have been declared Very useful in the beginning of an M file Without this command the user may be usin
19. campgs ym m Symbolic State Space Model Matrices Transfer Functions campgnum m Numerical State Space Model Transfer Functions Matrices These will open automatically when MATLAB starts You can also open them indepedently by entering campgmatlab cag2mat at the MATLAB prompt or by clicking the MATLAB icon on the CAMPG icons group to continue Fig 1 9 CAMPG MATLAB message console display CAMPG MATLAB will automatically interface to MATLAB and will open the MATLAB command console ant the MATLAB input files in the form of m files input to MATLAB These four files are displayed in a window with tabs The files generated will be campgmod m Model Parameter Initialization Plot control campgequ m Model Differential Equations Non linear simulation Campgsym m Symbolic State Space Model Matrices Transfer Functions Campgnum m Numerical State Space Model Transfer Functions Matrices These will open automatically when MATLAB starts The user can also open them independently by entering campgmatlab or cag2mat at the MATLAB prompt or by clicking the MATLAB icon on the CAMPG icons group The display will look like illustrated in the figure below S Editor C Campg working campgnum m File Edit Text Cell Tools Debug Desktop Window Help Da EM X m o c 6 MF OHH 88i mp8 Stack Base 1 CAMP G MATLAB Numeric State Space Model campgnum m CAMP G MATLAB function Generates Numeric A B C D matrices Numeric Tranfer F
20. done previons session loaded from session and placed can t locate from element for bond BOND FROM cfstoring to engineS8c bg done nt Fig 5 5 Eight cylinder engine CAMPG model MULTIPORT ELEMENTS CAMPG allows the user to create multiport elements and use these elements in bond graphs This is also a very useful feature in many real world applications in that many bond graphs of real world applications make use of multiport elements CAMPG has the ability to display them and when an interface has been selected it also has the ability to compute the equations for them A few examples of the multiport element can be seen in Fig 5 6 along with the complex equations for one of the multiport elements 228 CAMP G session P rie eait inarroce anciven options meme T SUA n do UY t 3 2 gt 7o o 20 1 1 e7 E e8 e9 e10 ell e12 P7 174P8 I7x84PO I7XO4P 10 I7X 104P 1 1 I7X 1 14P 12 1 7x 12 P7 I8x74P8 IS4POQ ISxQ4P 10 18x 104P 11 I8x 11 4P 12 I8x 12 P7 10x74PB IOxS84PO IO4P 10 IOx104P11 IOx114P 12 I0x 12 P7 110x74P8 I10x84PO I10xO4P10 I104P11 I110x114P12 I10x12 P7 I11x74PB I11x84PO I11xXO4P10 I11X104P11 I114P12 111x12 P7 I12x74P8 I12x84POQ I12XO4P 10 I 12x 104P 11 I 12x 11 4P 12 112 G EE previons session loaded from session and placed can t locate element or bond sts Bmove segment 1 12 marked done Jreove segment 1 7
21. would be too long and the output therefore is not desired the command can be suppressed if previously set Use OUTPUT CLEAR and there will be no output to the screen A B and C define different procedures specifying different plots Forces three column output width 72 characters per line Implies a line plot practical while using a graphics terminal Turns off printer plots This is particularly useful if the user is not using a graphics terminal Directs the plot to the screen The procedures A B C can be executed just by entering one of those letters in which case they act as labels or names for that procedure defined in the SETUP file and delimited by each label A B C and an END statement Note that other names besides A B C could be used as labels The user may choose to name the procedures with any name The name of those procedures are entered at runtime to execute the commands that are within them 176 4 7 Important ACSL Features ACSL contains many useful features and commands which assist the user in the analysis and simulation of a dynamic system A summary of these follows A more detailed explanation of the features can be found in the ACSL manual PROCEDURAL FORM PROCEDURAL output list input list where output list 2 v1 v2 vn input list el e2 en vi are non subscripted variable names while e may be variables or expressions The PROCEDURAL header must be paired with a
22. 1 111 R10 1 16 R4 1 16 R10 B 4 1 R4 Generate C and D matrices correspoding to outputs e s and f s 1 SF1 C D 0 0 0 0 1 95 e3 93 C3 C 0 1 C3 0 0 D 0 f6 P6 I6 C 0 0 0 1 16 D 0 7 P6 16 C 0 0 0 1 16 D 0 e9 909 C9 C 2 1 C9 0 0 0 D 2 0 f11 P11 I11 C 0 0 1 111 0 D 0 5 P6 16 C 0 0 0 1 16 D 0 f8 P6 I6 P11 I11 C 0 0 1 111 1 16 D 0 f9 P6 I6 P11 I11 C 0 0 1 111 1 16 D 0 f10 P6 I6 P11 I11 C 0 0 1 111 1 16 D 0 f2 SF1 P6 16 C 0 0 0 1 16 D 1 3 SF1 P6 16 C d 0 0 0 1 16 D 1 4 SF1 P6 16 C 0 0 0 1 16 D 1 elO P6 1lI6 R10 P11 I11 R10 C 0 0 1 I11 R10 1 I6 R10 D 0 e4 SF1 R4 P6 16 R4 C 0 0 0 1 16 R4 D 1 R4 e8 09 C9 P6 16 R10 P11 111 R10 C 1 C9 0 1 111 R10 1 16 R10 96 D 0 e11 99 C9 P6 16 R10 P11 1I11 R10 C 1 1 C9 0 1 I11 R10 41 I6 R10 D 1 0 e2 03 C3 SF1 R4 P6 16 R4 C 0 1 C3 0 1 16 R4 D 1 R4 e5 03 C34SF1 RA P6 16 RA C 0 1 C3 0 1 I6 RA4 D 1 R4 e7 09 C9 P6 16 R10 P11 111 R10 C 1 C9 0 1 111 R10 1 16 R
23. 3 40 Water 40 Height 20 0 0 50 100 150 200 Height in taller Surge Tank 148 Pressure in Stand Pipes with Surge Tank Radius of 3 meters x 107 Pressure in upper segment of standpipe Fig 3 41 2 Pressure Plots 0 50 100 150 200 x 10 Pressure in upper segment of standpipe 0 50 100 150 200 Water Height in Surge Tanks with Radius of 2 meters Fig 3 42 Height in shorter Surge Tank Waterr Height Plots 0 50 100 150 200 Pressure in Stand Pipes with Surge Tank Radius of 2 meters X 10 Pressure in upper segment of standpipe Fig 3 43 Pressure 0 Plots 0 50 100 150 200 x 10 Pressure in upper segment of standpipe 4 0 50 100 150 200 Results It seems as though 4 meters for a radius of the surge tanks would be pretty good There is no over flow of the water and the pressures in the stand pipes are not very high The data for 5 meters is better but for all the additional water that would be required and the additional cost it is not that good of an improvement Fig 3 38 to Fig 3 43 shows the water height in the surge tanks and the pressure in the stand pipes for radii of the surge tanks ranging from 2 to 4 meters 150 Listing of Campgmod CAMPG MATLAB GENERATED MODEL DESCRIPTION The following files have been generated campgmod m gt m file containing model parameters intial conditions sources and simulation controls campgequ m gt m function containing the system
24. Continuous Simulation Language ACSL 4 Interpret the results make design decisions and perform simulation of several models in an interactive way 186 PROCEDURE FOR SOLUTION Construct an engineering model of the crash test and consider only the time when the bumper is in contact with the wall Fig 4 11 seen above shows the engineering model of the crash test 2 Generate a bond graph model Fig 4 2 seen below shows the bond graph model for this dynamic system 3 Enter the Bond Graph description into the CAMPG program Fig 4 13 seen below shows the CAMPG screen that was generated after entering the bond graph model Bond Graph Model Car I M W Vw 0 6 7 Wall op 1 9 gt 1L 5 0 H tem Dummy BE 1 A i C lk R b C 1 k R b Bumper Seat Belts Fig 4 12 Vehicle and seat belts Bond Graph Model 187 Bond Graph as Created in CAMPG CAMP G session ELHEEN BITTE FRETI ee EE 3 E a F1 o HH move segment 0 marked move segment 1 marked Mmove segment t oes marked BOND FROM cRfundo Fig 4 13 Bond Graph Model Generated in CAMPG The SYSTEMATIC method was used to enter the bond graph model shown in Fig 4 13 seen above Below is a detailed description how this was done The symbol CUR means to select with the cursor The symbol lt CR gt means to enter from the keyboard kk seo 28 28 KE K K K K K K K K K K K K K K K K K K K K KK ee K K KK K
25. DOS environment The user may select the appropriate button that corresponds to that language or to DOS Regardless of the selection CAMPG saves the bond graph model drawing to a file called SESSION BG before exits the program TO ACSL CUR clicking the mouse on this button will cause the computer to generate an ACSL input file CAMPSL CSL is the ACSL input file Upon completion and saving of the bond graph file the computer will print a menu that gives the user selections to how to proceed 41 The computer will display a message like WORKING ONE MOMENT PLEASE EDIT FILE CAMPSL CSL And then will display The CAMPG ACSL model files have been succesfully generated and written in the working directory Edit file campsl csl1 to complete the input model to ACSL Use Windows Notepad or other editor canpsl csl is the model input to ACSL ress any key to continue Fig 2 5 CAMPG ACSL message display 42 The message reminds the user that CAMPSL CSL is the ACSL input file generated by CAMPG This file needs to be edited to enter parameter values non linearities and simulation control statements Edit CAMPSL CSL This option will automatically place the user on the editor of choice This can be EDT the VAX editor running on the PC it can be a word processor with ASCII files editing capability such as Wordperfect Microsoft Word and others The different editors for a particular system co
26. E F Several cases were simulated at different speeds and with different parameter values SET TITLE SEAT BELT TEST PREPAR T E3 F4 E6 F6 Q3 E9 E10 E11 F11 Q9 OUTPUT T E3 F4 E6 F6 Q3 E9 E10 E11 F11 Q9 NCIOUT 10 SET TCWPRN 72 START PROCED A SET TITLE SPRING FORCE E3 DAMPER FORCE E4 SET CALPLT TRUE STRPLT F GRDSPL F PLOT XHI FINTIM XTAG SEC E3 E4 END PROCED B SET TITLE FORCE ACTING ON THE CAR E6 AND DISPLACEMENT Q3 SET CALPLT TRUE STRPLT T GRDSPL T PLOT XHI FINTIM XTAG SEC E6 Q3 END PROCED C SET TITLE SPRING FORCE E9 AND DAMPER FORCE E10 SET CALPLT TRUE STRPLT F GRDSPL F PLOT XHI FINTIM XTAG SEC E9 E10 END PROCED E SET TITLE FORCE ACTING ON THE PASSENGER E11 DISPLACEMENT Q9 AT SPEED 25 MILE H SET CALPLT TRUE STRPLT F GRDSPL F PLOT XHI FINTIM XTAG SEC E11 Q9 END PROCEDF SET TITLE FORCE ACTING ON THE PASSENGER E11 DISPLACEMENT Q9 AT SPEED 25 MILE H 195 SET CALPLT F STRPLT T Y ASSPL 1 0 GRDSPL T PLOT XHI FINTIM XTAG SEC E11 Q9 END SET PRNPLT FALSE PLT 6 SET CMD 5 DESIGN CRITERIA The simulation must produce a design of the seat belts and the bumper so that it satisfies the following conditions 1 He doesn t hit the windshield if he travels at 25 and at 55 mph 2 What is the force acting on his chest and waist at 25 mph and at 55 mph Compare the data on injuries and determine
27. INTEGER FUNCTION Joe ere GER oc ER Oo s n LOGICAL FUNCTION ith e ped ete e t etl SUBROUTINE Ascote tex DR IU ENT C St D d ORIS BUNC TION d tet bieuesed ovt seno repe bie n EUR Cena i RCRAAN PROGRAM 5 rac evi ee Nets ME e imis os 4 8 CAMPG ACSL Tutorial o ee corau eee reino vec b apes rone toa ets Generate the Bond Graph in CAMPG eee eee eee Generate an AGSL Input Elle oci E ER IR Enter Parameter Values 22e e RD ose ep ore DA R n AC SI indes HE ERI TEENIE REETU rede Optimize Simulation 26s Atsa4 eed atev uses ies c eee LE Me 4 9 Linear System Example Vehicle Crash Test OBICCHIVES zese a ess b cues beue cem Pete E derer ate odd Procedure For Solution uon OI INIM OR IRR EE NNNEM RESUS Yor ie os eA ecoute cx err uu M dune EAE ads 4 10 Nonlinear System Example Gear Train with Backlash Problem Objectives 5o e tesetui oe ver cosas ncasseaGheakeedeseee Procedure for Solution ooo LE E RE E A E EC RUE Generate an Engineering Model eee eee eens Generate the corresponding Bond Graph in CAMPG Generate an ACSL Input File cece eee eee eee eens Entering Parameter Values sceee eee ene ence eee enees vi Use of Setup Files in Simulation sseusessese 216 Desion Catena xsqenve erst ese rdv ieda oe TUNV RUPEE S MU AE 218 Results Sobre e ind xi RD PERIERE RUE Sia luvs teva RN IPIE EUN
28. K K K K K K KK KK K K K K CAMPG lt CR gt This brings up the CAMPG screen with a logo Any movement of the mouse or typing any 188 EDIT CUR DELETE CUR ALL CUR YES CUR OPTIONS CUR STICKY CUR ON CUR 1 CUR CUR CUR CUR 0 CUR CUR character will clear the logo and show a blank screen or will bring up the latest model generated and stored in the SESSION BG file These next three steps clear the screen if there is an existing session file If there is no previous SESSION BG file these steps are not necessary This pull down menu selection will be used to turn on the STICKY function so that all the similar elements can be placed all at once This step allows the SYSTEMATIC METHOD of building the bond graph model Select the 1 from the menu on the left to place the ONE JUNCTIONS Move the cursor and click in the middle of the screen Move the cursor 4 grids to the right and 4 grids down and click again to place the second 1 Move the cursor 8 grids to the left and click to put the third 1 on the screen Select the 0 from the left hand menu to place the ZERO JUNCTIONS on the screen 189 CUR C CUR CUR CUR R CUR CUR CUR I CUR CUR CUR SF CUR CUR bond symbol CUR Click the cursor at 4 grids to the left of the 1 middle of screen and at 4 grids to the right of it Select C from the menu in order to place the cap
29. P6 1lI6 R10 P11 I11 R10 C 0 0 1 I11 R10 1 I6 R10 D 0 e4 SF1 R4 P6 16 R4 C 0 0 0 1 16 R4 D 1 R4 e8 09 C9 P6 16 R10 P11 111 R10 C 1 C9 0 1 111 R10 1 16 R10 62 D 0 e11 99 C9 P6 I6 R10 P11 111 R10 C 1 C9 0 1 I11 R10 41 I6 R10 D 0 e2 03 C34SF1 RA4 P6 I6 RA C 0 1 C3 0 1 I6 RA4 D 1 R4 e5 03 C34SF1 RA P6 16 RA C 0 1 C3 0 1 I6 RA4 D 1 R4 e7 09 C94 P6 I6 R10 P11 I11 R10 C 1 C9 0 1 I11 R10 41 I6 R10 D 0 el Q3 C34SFl1 RA P6 I6 RA C 0 1 C3 0 1 I6 RA4 D 1 R4 e6 Q3 C3 SF1 R4 P6 16 R4 Q9 C9 P6 I6 R10 P11 111 R10 C 1 C9 1 C3 1 I11 R10 1 1I6 RA4 1 16 R10 D 1 R4 A B C D Generate vector of transfer functions Example e3 s SE1 s 4 s SF10 s q4 s SE1 s Define SI matrix syms s Find the size of A and then figure out I I eye 4 Use Matlab Symbolic Tool Box to do symbolic matrix operations leading to the calculation of symbolic transfer functions Transfer Functions Matrix H H C inv s I A B D pretty collect H Frequency Response Sample structures num den H bode num den 63 Frequency Response Bode Plots num den 2ss2tf A B C D 1 bode num den What follows is the same file seen above but this time the fi
30. START 1 1 INSTALLATION Using Windows Explorer point to the directory of the CAMPG CD Open the file listing on the CD and click on the SetupWindows XP bat file CAMPG will install on your computer and will create a c Campg Working directory CAMPG folder on your desktop and a CAMPG entry on your Start Programs listing The CAMPG folder on your desktop and the CAMPG entry on the START ALL Programs listing contain the following icons C Documents and Settings All Users Desktop CAMPG File Edit View Favorites Tools Help amp Search lg Folders lly Address C Documents and Settings All Users Desktop CAMPG gt E Em Ia File and Folder Tasks Y E s D ME p Bond Graph CAMP G Campg CAMPG New CAMPG CAMPG Other Places i Examples TUTORIAL Manual Project Di SCREEN WINDOW ume m p E My Documents Shared Documents P My Computer 3 My Network Places Examples Examples MATLAB Technical Working ACSL MATLAB 7 0 1 References Directory 1 My Computer Fig 1 1 CAMPG icons set 1 2 CAMPG ICONS SET CAMPG Li CAMPG WINDOW CAMPG SCREEN CAMPG New Project Directory pp Campg Manual This icon is used to run CAMPG in full screen and also in a Window If you double click on this icon CAMPG will start in full screen but if you enter Alt Enter it will run in a window This icon is used to run CAMPG exclusively in full screen You may see some messages that are un
31. SYSQUAKE AA EASYS R VISIM Cea FORTRAN UNIVERSAL loading from session bg done t Bprevions session loaded from session and placed BOND FROM Fig 2 4 CAMPG Simulation Language Interface Menu EXIT CAMPG Once a simulation language is selected CAMPG will proceed to generate the necessary files to produce an interface to the Simulation Language and it will continue with a menu that allows the user to edit and complete the input file and other options discussed below However the user may want to exit CAMPG without creating an input file to a digital simulation language select EXIT in the upper left 40 corner This will automatically save the current bond graph to a session file named by default as SESSION BG The user can save the file under another name This is done using the FILES menu and entering the file name under the STORE button The file will be saved with another name This is useful also to save a session file for use in the future The process is change the name either outside of CAMPG at the Command prompt or by using the STORE button under the FILES menu CAMPG can generate input files for ACSL and other simulation languages after the selection is made from the EXIT menu Once the file generation takes place a menu will be displayed Shown below is a summary of these steps EXIT CUR this button will allow the generation of the input files for a simulation language as well as exiting to the
32. State Spe campgnum m Numeric State Sp Address C Documents and Settings All Users Desktop CAMPG nemesa eee M Bond Graph CAMP G Campg CAMPGNew CAMPG Other Places Examples TUTORIAL Manual Project Di SCREEN B desktop a i wy 71 start a EG 2 Ge ATLAB v CAMPG WIN DOSBox 0 7 Ola on QS gt Fig 1 11 CAMPG MATLAB interface with Bond Graph Window 1 10 The CAMPG SIMULINK interface CAMPG interface to SIMULINK follows the same format as the one for MATLAB The user enters a Bond Graph model utilizing the mention of the left and at the top and then chooses the SIMULINK interface under the INTERFACE menu The following files will be generated 11 campgini m Model Parameter and A B C D matrices Initialization campgnum m Matrices and Transfer Functions Initialization campgtfn mdl CAMPG SIMULINK transfer function campgsst m CAMPG SIMULINK State Space Form These will open automatically when SIMULINK starts The user can also open them independently by entering campgsimulink cag2sim at the MATLAB prompt CAMPG WINDOW The CAMP G SIMULINK model files have been succesfully generated and written to files in the working directory Modify the files named below to complete model Use the MATLAB Editor Windows Notepad or other editor campgini m Model Parameter and A B C D matrices Initialization campgnun m Matrices and Tranfer Functions Initialization camp
33. Time seconds Listing of CAMPGEQU M function p qdot campgequ t p q i gates ete campgequ m CAMPG MATLAB function System differential equations state Vectors global I9 R10 C11 I12 R13 C14 1102 1104 C107 R108 C109 R110 global SE1 SE2 SE3 SF8 SF100 vect out if t 100 SF8 1 elseif t gt 100 amp t lt 100 1 SF8 10 t41000 else SF8 0 end System Differential Equations First Order Form Se arate Define State Variables Q11 p q 1 Q14 p q 2 Q109 p q 3 0107 p q 4 P9 p q 5 P12 p q 6 P104 p q 7 P102 p q 8 State variables vector pq O11 O14 Q109 Q107 P9 P12 P104 P102 bs Define derivatives dp dq and output variables e f e1 SE1 e2 SE2 238 f9 P9 I9 e3 SE3 12 P12 112 e4 el el1 011 C11 f5 f9 e6 ell f6 f12 el4 2014 C14 f7 f12 e8 el4 8 SF8 10 f9 fll f5 f6 13 f12 fl4 f7 f8 100 SF100 102 P102 1102 103 102 104 P104 1104 e107 Q107 C107 e109 9109 C109 106 103 104 109 106 110 106 dQll1 f11 dO14 f14 dQ109 109 4 9 f2 f9 f3 f12 e5 ell e7 el4 e10 10 R10 el3 f13 R13 101 102 105 100 101 e110 f110 R110 107 105 108 105 dQ107 107 fl f4 e9 e2 e4 e5 e10 e12 e3 e6 e7 el3 e106 e109 e110 e104 e106 el08 f108 R108 dP9 e9 dP12 ze12 dP104ze104 e105 e107 e108 e101 e105 e103 e106 e100 e105 e102 e101
34. causality algebraic loops bond graph structure and other modeling problems that may prevent the generation of close form sets of differential equations CAMP AND CAMPG The Computer Aided Modeling Program CAMP and its capabilities is the parent program of CAMPG CAMP was designed to run on a wide range of minicomputers and PCs using standard displays that do not have graphics capabilities Using CAMP it is possible to generate models for simulation languages even if no color graphics capability were available in your PC or in a terminal attached to a minicomputer The CAMP program can be used for this purpose The bond graph model is entered by a description from the keyboard The program is self explanatory as it displays interactive instructions on the screen Using CAMP in the non graphics mode will produce the same models generated using CAMPG The output files used as input models for simulation languages in CAMP and CAMPG are completely compatible The difference between these two software packages is that instead of entering the bond graph graphically using the mouse as in CAMPG it is entered as a text description in CAMP The graphical environment in CAMPG helps explore the model and its causality as it is being drawn on the screen CAMP will do this with messages displayed on the screen The individual equations and modeling problems can be examined directly In CAMP these are presented to the user in the form 18 of error or
35. command ACSLCLG MODEL right before the system displays the ACSL prompt the computer generated a file called MODEL EXE Therefore in order to run it without compiling it again just enter the name of the file as MODEL and the computer will display the ACSL prompt At this point any ACSL run time command could be used SAVING THE MODEL FILES Once a simulation has been done new modifications to the input file may be necessary and then the translation and compilation process will have to take place again When running ACSL with a model file CAMPSL CSL that was originally generated by CAMPG and then modified it is suggested that the user changes the name of this file so that if he runs CAMPG again the new model won t override the old modified and edited CAMPSL CSL file CAMPG has a safeguard against this problem It will save the last CAMPSL CSL file on the file CAMPSL OLD Useful Run Time Commands used with CAMPG ACSL The user may run a simulation problem once an ACSL input file has been generated and parameters values have been specified When the ACSL gt prompt appears the user is in the ACSL program There are several things to consider prior to the start of the simulation First a decision needs to be made by the user as to which variables are to be observed or plotted as the simulation takes place Establishing a variable list is accomplished with the PREPAR command For example ACSL gt PREPAR T Q2 F3 E3 165 This com
36. e10 Q10 C10 f9 f8 f11 P11 I11 ellzelO dP11 e11 1 2 e4 e5 f7 f8 e9 e10 f10 2f9 f11 d9Q10 f10 e3 e4 T3x4 f6 f7 T6x7 e8ze7 e9 dP8 e8 e2 el e3 f5 f4 f6 dP2 e2 do5 f5 Sadditional state variables dQ2 f2 dQ8 f8 dQ1l1 f11 Build vector of derivatives p qdot n p_qdot1 dP11 p_qdot2 dQ10 p_qdot3 dP8 p_qdot4 dP2 p_qdot5 d Q5 Derivatives vector p_qdot dP11 dQ10 dP8 dP2 dQ5 dQ2 dQ8 dQ11 Define output vectors efforts flows sthis is to make plotting easy vect out e5 2 8 11 e2 e8 ell e10 Q5 6 RUN MATLAB Using the CAMPG MATLAB model perform a computer simulation to obtain the values of variables that will help make design decisions These include the torques forces and displacements of the gears the flywheel and the shaft These variables are 131 F Q5 W1 W2 W3 Thetal Theta2 Theta3 Twist Wdl Wd2 Wd3 SEI E2 E10 Force between teeth Relative displacement between teeth Angular velocity of gear 1 Angular velocity of gear 2 Angular velocity of flywheel Angle of rotation of gear 1 Angle of rotation of gear 2 Angle of rotation of flywheel Shaft angle of twist Angular acceleration of gear 1 Angular acceleration of gear 2 Angular acceleration of flywheel Input torque Torque on gear 1 Torque on shaft The commands that create these new outputs are in the CAMPGEQU M file shown above and t
37. e103 dP102 e102 Build vector of derivatives p_qdot n p_qdot1 dQ11 p_qdot2 dQ14 p_qdot3 dQ109 p_qdot4 dQ107 p_qdot5 dP9 p_qdot6 dP12 p_qdot7 dP104 p_qdot8 dP102 Derivatives vector p_qdot dQ11 dQ14 dQ109 dQ107 dP9 dP12 dP104 dP102 vect_out e9 e12 e104 Results What follows are the graphs that are output from the two previous files As will be seen the graphs that are seen below match the graphs fro 239 these systems when they are modeled separately as in the examples in chapters two and three Fig 5 12 Simulation Results of Simultaneous Simulation Fig 5 13 Simulation Results of Simultaneous Simulation 60 40 20 80 60 40 20 CERE Height in shorter Surge Tank 0 20 40 60 80 100 120 140 160 180 200 Height in taller Surge Tank 0 20 40 60 80 100 120 140 160 180 200 Pressure in upper segment of standpipe IHRE Pressure in upper segment of standpipe 240 200 Fig 5 14 Crash test model simultaneously computed Fig 5 14 Crash test model simultaneously computed Force N Distance the Dummy s head travels 0 4 0 2 0 2 0 4 Distance meters 0 6 0 8 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 Time seconds
38. f5 f6 f13 f12 14 7 8 dOoli f11 dQ14 f14 fA f9 f2 f9 f3 f12 e5 ell e7 el4 e10 f 10 R10 el3 f13 R13 fl f4 e9 e2 e4 e5 e10 e12 e3 e6 e7 el3 dP9 e9 dP12 e12 Build vector of derivatives p qdot n p_qdot1 dQ11 p_qdot2 d9Q14 p adot3 dP9 p_qdot4 dP12 Derivatives vector p adot dQ11 dQ14 dP9 dP12 Define output vectors efforts flows Sample structure for simulation outputs effort vector el e8 e12 e4 flow vector f1 f2 3 f4 output vector effort vector flow vector 153 Example for graphical output Plot e12 vs time The third column of effort vector subplot 211 plot t effort_vector 3 y Plot f10 vs time The fourth column of flow vector subplot 211 plot t flow vector 4 m end vect out e9 e12 AP de oe dP oe oe 154 Chapter 4 CAMPG and ACSL 4 1 Introduction Using the CAMPG ACSL system algebraic and differential equations can be solved CAMPG generates the system equations in source code form places them in an ACSL input file This file is then completed using an editor to complete the system parameter specifications nonlinear functions and ACSL library calls The input file is passed to ACSL for dynamic analysis This chapter begins with a summary of some of ACSL s capabilities and the procedures required to successfully utilizing them It then provides some examples of the CAMPG ACSL system
39. from the 1 element and the I element 1 screen CUR R screen CUR This should create a bond between the 1 element and the R element SEQUENTIAL METHOD OF BOND GRAPH CONSTRUCTION The SEQUENTIAL method builds the bond graph by joining the elements with bonds immediately after being placed on the screen Power flow is assigned from the element chosen by clicking the mouse to the element selected next Causality assignment is automatic as each bond is drawn The program properly colors the incomplete bond junctions algebraic loops and derivative causality giving the user immediate feedback on how the construction of the bond graph model is going If the generation of the bond graph is completed and still there are colored bonds it means that CAMPG detects modeling problems such as algebraic loops incomplete or incompatible bond graphs and derivative causality Lets use the same example of the previous section to illustrate this technique CAMPG CR Start CAMPG and brings up the logo containing the user name and the license 35 space bar CR EDIT CUR DELETE CUR ALL CUR YES CUR 1 CUR Middle of screen CUR C CUR CUR number Please refer to this number for maintenance and updates This clears the screen preparing it for a drawing Any other character or movement of the mouse will do the same The next three steps clear the session file If you have no previous SESSION BG
40. if chest or internal injury occurs if 1 he wears a seat belt only 2 he wears a seat belt and a shoulder strap 3 What is the critical maximum velocity when he is safe at which impact occurs Hitting the windshield chest injury internal injury seat belt failure strap failure should not occur 4 If he travels without a seat belt How long does it take for him to hit the windshield at 25 mph 40 mph 55 mph What is the force acting on him on impact at 25 mph 40 mph 55 mph RESULTS The results obtained from the simulation can be obtained in the form of numerical values or in the form of plots of variables as a function of time Several designs with different kinds of bumpers and shock absorbers were tried One of those is shown in Fig 4 14 and Fig 4 15 These simulations allow the user to make an optimum decision to satisfy the design requirements The user is able at this point to decide which is the best design and why He can perform as many simulations as he thinks are necessary In this case it was found from Fig 4 14 and Fig 4 15 that at 196 25 mph the dummy did not hit his head on the windshield Its maximum displacement was 0 81m Less than the 1 00 m allowed The force acting on his body was 9 310 newtons However this is enough to produce chest injury The maximum limit allowed is 6 688 newtons No failure of the seat belts occurs since they can resist a load of 13 340 newtons The table shown below illustra
41. is shown in Fig 4 2 and is seen below In the previous section the linear model was constructed using the SYSTEMATIC method In the case of the gear teeth the SEQUENTIAL method is used to generate the bond graph and demonstrate how to construct bond graph models using this method and CAMPG Just as a brief reminder the SEQUENTIAL method consists of assembling of all bonds immediately following the placement of the elements and 0 or 1 junction This method helps to illustrate other editing features of CAMPG such as the moving of whole bond graphs or parts of them to other parts of the screen 202 Bond Graph Model GEAR 1 GEAR 2 I Pi 7r 2 8 i 3 T 11 E p ps o N1 1pt o cag d T Ri s 2 ms 4 FLYWHEEL c c Fig 4 20 Gear Train Bond Graph Model Bond Graph Model in CAMPG CAMP G c campgurk gear Ee T M MTF single C 10 marked done single C 5 marked done single 0 9 10 11 marked done BOND FROM single C 10 marked done Fig 4 21 Gear Train Model in CAMPG 203 steps The bond graph of Fig 4 2 was constructed using the following CAMPG CR Start CAMPG and brings up the logo containing the user name and the license number Please refer to this number for maintenance and updates space bar CR This clears the screen preparing it for a drawing EDIT DELETE ALL YES SE Left of screen Any other character or movement of the mouse will do the sam
42. lmomentum lang Moment IFlux linkage Ipressure moment 1 SE source effort SF source flow TF m transformer modulus GY r gyrator modulus TEKK K K K K K Kk Kk k k k bebe KKK K K K K K KK KK K KK Kk KK Daret BOND GRAPH ANALYSIS x SYSTEM DESCRIPTION POWER FLOW BOND FROM TO 1 SEI 1122 21123 I2 ow dl 2 39 TE 34 4 TF 3 4 0_4_5_6 50456 C 5 60456 TE 6 7 7 TE67 1789 81789 IS 91789 0 9 10 11 10 09 1011 C 10 11 09 10 11 L11 CAUSALITY FLOW NOTE FROM TO BOND FROM TO 1 SEI 1123 21123 I2 3 TE34 1123 40456 TE 34 55 04596 60456 TE 6 7 7 TE67 1789 81789 IS 9 091011 1_7_8_9 10 C 10 0 9 10 11 211 11 09 10 11 Ill END OF PROGRAM The model causality and power flow tables are generated in the ACSL input file in order to assist the user to verify the input model structure and power flow The instructions at the beginning as well as the explanation of the variables in different energy domains or the verification of causality and power flow can be included in the ACSL input file as CAMPG generates this in the form so that ACSL considers that as no executable statements The user can erase on or both of these information sections 5 RUN ACSL Using the CAMP ACSL model perform a computer simulation to obtain the values of variables that will help make design decisions These include the torques forces and displaceme
43. lt External Input ss SYSTEM EQUATIONS g XDD B XD K X FM lt Second order derivative acceleration XD INTEG XDD XDIN lt first order derivative velocity 159 X INTEG XD XIN lt displacement TERMT T GE TSTP lt end condition END OF DERIVATIVE END OF PROGRAM To run the program after the model is stored on file enter ACSL OSCILLATOR VAX VMS systems ACSLCLG OSCILLATOR IBM PC The CSL file type identifying a file as an ACSL input file is not entered the computer assumes the file name is Oscillator csl The computer will respond START TRANSLATION lt will appear on screen START COMPILATION gam do MO ie START LOAD lt m ACSL lt ACSL run time prompt Ready now for run time instructions ACSL gt PREPAR T XDD XD X lt prepare T XDD XD X for plotting ACSL gt OUTPUT T XDD XD X lt prepare T XDD XD X for display ACSL gt START lt start simulation lt output written to screen d N ono Sas lt es ACSL gt PLOT XDD XD X lt If using a Tektronics graphics terminal A plot of XDD XD X vs T will be drawn on the screen ACSL gt STOP lt stop ACSL execution 160 4 3 Running ACSL Using Bond Graph Modeling Computer generated model Shown below is the bond graph that represents the same simple oscillator discussed in the previous section Using causality and power flow assignments it is possible to generate the equati
44. model from disk These files have the BG extension by default The file is loaded and integrated to the current session existing on the screen This will add the contents of a file to the current session without replacing the existing one This is used to save the current bond graph in a file under any given name To do this click the mouse on the 26 LIST RECORDS EQUATIONS OPTIONS STICKY STORE button and type the new file name The current bond graph model will be saved to that file Internal file of CAMPG Internal file of CAMPG This file will contain the differential equations generated by CAMPG in the format that any FORTRAN or C program source code It is intended for the user who is not using an existing simulation language but rather his own program The contents of this file could be integrated in a Sub program that the user could modify and use as part of his own program The following options are available under this pull down menu If sticky is selected and set to ON you are able to select an element from the left hand menu and until a different selection is made each consecutive click will place that element on the screen This is helpful when constructing large bond graphs It is also helpful if the user wants to place all the 1 and O junctions first Al junctions and elements of a 27 GRID VISIBLE HIDE OFF COLOR chosen type could be placed and long as this opti
45. motion of gear 1 and the backlash between gear teeth The influence of the compliant shaft is seen in the plot of the angular velocity of the flywheel top plot Changes are smoother in the shaft velocity since this is a capacitive element and therefore stores energy Mathematically this element performs integration of W3 and therefore eliminates the noise seen in that function This change is obvious between WD3 in Fig 4 22 and W3 in Fig 4 23 221 Figure 4 24 This figure compares the position angle of rotation of the Fig 4 25 Angle flywheel Angle of Twist Fig 4 25 gears and the angle of twist of the shaft It shows the geometrical configuration of the gear train It can be seen from this figure how the gear train starts to move in one direction while the angle of twist in the shaft changes to 2 to 2 degrees S TORQUE ON GEARL AND ON SHAFT N 0 00 E2 103 LB FT 5 00 0 00 0 25 4 30 0 75 1 00 Shows the torque at the input gear This plot is similar to the one of the acceleration The relationship can be explained by Newton s Law in rotation since the rotational moment of inertia is the relational constant Therefore the torque is proportional to the angular acceleration of gear 1 Fig 4 24 gives a good understanding of the stress level changes within the shaft and therefore can be used to design the shaft 222 Chapter 5 Advanced Features 5 1 Advanced Menu Features EXPLAIN Explain is the firs
46. next steps are done to clear the session file and allow the user to start fresh with a new model If there is no previous SESSION BG file this step is snot necessary 33 DELETE CUR ALL CUR YES CUR 1 CUR There is a button on the left icon menu which has a 1 in it This is the ONE junction in the bond graph Click the mouse on these buttons and the computer will store the element to a buffer Then to place it on the screen it is necessary to click the mouse in any desired screen location Middle of screen CUR Place the 1 on the screen by moving the C CUR I CUR R CUR cursor to the desired location and clicking Now select a C element by clicking the mouse while the cursor is on the C button on the elements menu Place this to the left of the 1 by moving the cursor and clicking the mouse The distance is arbitrary Select an I and place it to the right of the 1 Select an R and place it above the 1 BOND SYMBOL CUR Go to the top box on the left menu This 1 screen CUR is the bond symbol Click here Notice that the PROMPT BOX reads BOND FROM It is asking where you would like to start your first bond Click on the 1 element on the screen 34 C screen CUR Click on the C element on the screen A bond should appear between these two elements Notice that both power and causality are assigned 1 screen CUR I screen CUR This should create a bond
47. procedure What this will do is create one set of simulation files but with two different dynamic systems represented in the one set of simulation files To make the distinction between the two separate systems some of the techniques that are described above will be implemented in this example For example the user controlled numbering will be used to create a gap in the numbering of the bond graphs and therefore distinction between the two systems EXAMPLE In this example it is going to be demonstrated how the user can run one simulation that represents two different dynamic system Both of the systems that are demonstrated in this example are discussed in detail in chapters two and three For more in depth detail on either of these two systems see either chapter two or three The two dynamic systems that are going to be used again are the example of the Crash Test and the Hydroelectric Power Plant Pictures of both the physical systems are seen in Fig 5 9 and Fig 5 10 Fig 5 9 Physical System of Dummy in Car 234 n to Turblne Fig 5 10 Physical System of Hydroelectric Power Plant Seen below in Fig 5 11 are the bond graphs of the two systems in the same CAMPG session window This window is interfaced with Matlab and the three files CAMPGMOD CAMPGEQU and CAMPGSYM are created In this example only the first two of the three files are going to be used Bond Graphs of Both Systems 235 CAMP G untit
48. system is ready to be integrated This file will send the calculated derivatives of the states to the integrating engine which in turn will then send the newly determined states back to the first file campgmod m This example listing is the listing for the linear example that is seen in section 3 7 The only difference between this listing and the one seen in section 3 7 is that this one has not yet been edited by the user This 56 oe oe de oe oe dP de dP oP de dP oe oe oe oe oe is exactly the way the this file would look just after the interfacing with Matlab has been done As seen here the sections of the file are very clear and straight forward Listing of campgequ m function p qdot campgequ t p q PS Ces des campgequ m CAMPG MATLAB function System differential equations state Vectors global C3 R4 I6 C9 R10 I11 global SF1 global TIME STEP EFFORTS FLOWS System Differential Equations First Order Form LTD Define State Variables Q9 p q 1 Q3 p q 2 Pll p q 3 P6 p q 4 State variables vector p_q 09 03 P11 P6 ET Define derivatives dp dq and output variables e f f1 SF1 e3 293 C3 f6 P6 I6 f7 f6 e9 99 C9 f11 P11 I11 f5 f6 f8 f7 f11 f9 f8 f10 f8 do9 f9 f2 fl f5 f3 f2 f4 f2 elO flO R10 do3 f3 e4 f4 R4 e8 e9 e10 ell e8 dP11 e11 e2 e3 e4 e5 e2 e7 e8 el e2 e6 e5 e7 dP6 e6 Build vector of derivatives p qd
49. system messages The CAMP program prompts the user for the necessary information and then builds the CAMPSL CSL model file used as input to ACSL and other languages CAMPG does this through a menu selection using the mouse and computer graphics capabilities that allow the user to enter the actual bond graph model on the screen CAMP can run on any monitor and attached to a minicomputer or mainframe requires an alphanumeric keyboard or any text ASCII terminal CAMPG runs on computers and terminals of high resolution It requires a PC XT or AT type with a 640k of memory It will run on 8088 based computers to the 80286 80386 or 80486 computers It requires an EGA or VGA monitor a hard disk is recommended a mouse and driver CAMP and CAMPG are fully supported programs with their respective documentation and installation instructions tailored to each individual type of computer 2 2 How to Use CAMPG STARTING CAMPG Start CAMPG by clicking on the CAMPG icon in the CAMPG desktop folder of the Programs START menu Pressing any key or moving the mouse clears the initial logo and prepares the graphics screen for input CAMPG automatically brings up the last SESSION BG file if one exists This way the user has the last model he worked on ready to go again or the screen can be cleared and start a new one CREATING A BOND GRAPH The screen that appears as CAMPG starts is shown in Fig 2 1 There is a menu on the left that contains icons for the ki
50. the previous section Note the non linear constitutive relation of the C5 element is entered as a modification of the linear version of E5 1 C5 Q5 Here the non linear equation is E5 KG DEAD 0 1 0 1 Q5 This model description in the form of source code is shown is shown below 208 THIS IS A CAMP GENERATED MODEL DESCRIPTION 1 EDIT THIS FILE ENTER VALUES OF PHYSICAL PARAMETERS INITIAL CONDITIONS INPUTS AND TIME CONTROLS IN PLACES WHERE THE QUESTION MARKS APPEAR 2 FOR NON LINEAR SYSTEMS REPLACE THE LINEAR RELATIONS BY NON LINEAR FUNCTIONS FOLLOWING THE PROPER CAUSAL RELATIONS 3 THE TABLE BELOW PROVIDES A GUIDELINE FOR PHYSICAL MEANING OF GENERALIZED VARIABLES USED IN BOND GRAPH NOTATION PROGRAM CAMPACSL ACSL INPUT FILE Gear train with backlash Non linear model INITIAL INITIAL CONDITIONS CONSTANT PIIIN 0 P2IN 0 P8IN 0 QSIN 0 CONSTANT QIOIN 0 TIME CONTROL T TIME CINTERVAL CINT 0 0008 CONSTANT FINTIM 1 0 SYSTEM PHYSICAL PARAMETERS i CONSTANT D 0 4 T3x4 5 T6x7 1 0 18 0 01 I11 2 0 8 KG 200000 C10 1 4000 PII 4A ATAN 1 DEFINE PI RADEG 360 PII END OF INITIAL DYNAMIC DERIVATIVE EXTERNAL INPUTS SE F T SF F T SEI 100 Sin 20 T lcm SYSTEM EQUATIONS He el SEI fl f2 e2 el e3 f2 P2 D e3 e4 T3x4 f3 f2
51. the bonds elements and junctions in a different color than normal This color is set to Red as the default color but the user can define what they want this color to be by changing the color settings as described in COLOUR from above See Fig 5 6 for an example of this When the system has determined a causality problem the user can use the Explain option as 230 described in EXPLAIN from above to help determine the cause of the problem CAMP G c campg bgmodels valvespr Frise f eoe rncervoce satura options more TT uU T paste completed delete single BOND 48 done t gdeliete single BOND 49 done BOND FROM dideiete single I done ant Fig 5 6 Large Bond Graph Model PSEUDO BOND GRAPHS Pseudo bond graphs can be created simply to help the user understand the system better and to get a better understanding of everything that will be involved in modeling the system An example of this can be seen in Fig 5 7 231 CAMP G c campg bgmodels weompres NETTES e een Dese options rens Do T mE 4 IG ee AX oO ee tne a w e ON Ly b delete single BOND 49 done delete single I done 1 Eloading from c campg bgmodels weoompres bg done picked readyt cffpaste completed i Fig 5 7 Use of Pseudo bond graphs COPY AND FLIP BOND GRAPH STRUCTURES In many cases in a real system there are several parts which are identical to each other
52. the dialogue box will indicate the status or error message GENERATE THE MATLAB FILES Continuing from the previous step once the bond graph has been completed pick the INTERFACE button and within it the MATLAB option seen Fig 3 27 CAMPG will generate the CAMPGMOD M CAMPGEQU M and CAMPGSYM M files used to perform system simulation In this example the CAMPGMOD M and CAMPGEQU M files are going to be used 125 s H dP dP dP oe oe oe 5 ENTER PARAMETER VALUES Edit the CAMPG model to enter the linear and non linear constitutive relations of physical elements into the CAMPGEQU M file This file completed was shown in the previous section Note the non linear constitutive relation of the C5 element is entered as a modification of the linear version of E5 Q5 C5 One method that will represent this nonlinearity is shown here if Q5 1 e5 KG Q5 elseif Q5 1 e5 KG Q5 else e5z0 end This is input into the CAMPGEQU M file in place of the line that originally defined e5 Below is a listing of the CAMPGMOD M and CAMPGEQU M files The model causality and power flow tables are generated in the CAMPGMOD M file in order to assist the user to verify the input model structure and power flow The instructions at the beginning as well as the explanation of the variables in different energy domains or the verification of causality and power flow can be included in the CAMPGMOD M file as CAMPG generates this in the form
53. the vector t p q where t time and p q vector of state variables 81 t p_q is a column vector with rows t p_q 1 p_q 2 P q 3 t p dq ode23 campgequ tspan initial Q9 p_q 1 Q3 p q 2 P11 p q 3 P6 p q 4 State variables vector p_q Q9 Q3 P11 P6 Sample Matlab structure for plotting simulation results state variables figure 1 plot t p q 1 r grid title Distance the Dummy s head travels ylabel Distance meters xlabel Time seconds subplot 212 plot t p q 2 m grid title variable p q 2 stored in column 2 color magenta ylabel p q 2 units xlabel Time seconds Sample structure for plotting Output Variables as defined in campgequ m Example If the efforts and flows were defined as EFFORTS STEP e5 ell e4 FLOWS STEP f2 9 8 figure 2 Plot ell vs TIME Second column of EFFORTS vector plot TIME EFFORTS r grid title Force Acting on the Dummy ylabel Force N xlabel Time seconds Plot 8 vs time Third column of FLOWS vector t subplot 212 plot TIME FLOWS 3 m grid title Flow variable of vector FLOWS 3 stored in column 3 MECHANICAL ELECTRICAL HYDRAULIC TRANSLATION ROTATION l 522 2 2 z 529 4 2 E Effort For
54. this even before any derivation of the equations have been attempted 105 Armature Armature Load Resistance Damping Inertia M R I b T F wwe SELES GYSI TF AM ELECTRICAL MECHANICAL 8 COMPONENTS COMPONENTS Load Damping Fig 3 17 Bond Graph Model CAMPG is interfaced with Matlab as seen below in Fig 3 7 For detailed step by step instructions on creating the bond graph in CAMPG see the preceding examples se ES A ES Le EN amis ee ACSL DsL CssL CAMP G untitled a iS MATLAB ipee SSEEyouwww SSS bond from 1 4 5 6 to TF bond 7 bona from TF 7 to 1 bond 8 t s fgbond from 1 8 to I bond 9 BOND FROM cffeond from 1_8_9 to R bona 10 TE Fig 3 17 CAMPG Display with Bond Graph Model 106 After interfacing CAMPG with Matlab CAMPG has generated the M input files which describes the equations of motion in first order form with the momentum as the state variable Speed control can be easily analyzed by tracking the velocity output signal in any of the bonds 8 9 or 10 The position however needs another integration of the velocity This can be accomplished in three ways One way is to create a dummy C element to produce the integration The second way is to increase the number of states in the MATLAB system equations and include the angular velocity as one of the states so that the position angle is calculated as a result of the integration of all state derivatives The third wa
55. turning on strip plot S can be substituted for SET T for TRUE and F for FALSE SET GRDSPL FALSE Turns off grid for strip plots PLOT Q2F3 Generates two strip plots one of Q2 one of F3 S DAMPED OSCILLATOR F3 0 00 e ao v o e Q e No Qa g 7 8 57 9 86 13 1 16 4 19 7 23 0 c sss 1 Seconns Fig 4 8 Plot Grid control and number of strip plots 172 4 6 Setup Files It is possible to speed up the simulation and the graphical result using setup files These files store a set of ACSL runtime commands in a file A setup file is a working file during the simulation and the ACSL system knows to execute the commands from this file The SET CMD command is used to control and set the ACSL input commands to this file or to the computer terminal The setup file stores the ACSL commands in groups starting with a label and the PROCEED keyword A set of command or a set of commands can be executed if the user enters the label that heads up the list of commands and ends with an END Using the SETUP files saves a great deal of time not only by saving the time to enter the commands but the execution of groups of commands Commands that are on the SETUP file don t need to be typed again at the ACSL prompt These files are known also as SETUP files or COMMAND files These files provide an easy way to do several simulations study different cases and enter several options of the ACSL commands that otherwise will be too long to d
56. 04890670 W1 0 09512880 W2 12 9536000 W3 0 17995200 THETAI 3 70499000 THETA2 21 3271000 THETA3 21 8639000 TWIST 0 53677700 WD1 29 1373000 WD2 3747 41000 WD3 46 8426000 SEI 11 6549000 E2 11 6549000 E10 37 4741000 T 0 40000000 F 0 Q5 0 07155820 W1 1 10078000 W2 12 7074000 W3 1 38311000 THETAI 6 00811000 THETA2 25 9406000 THETA3 24 1799000 TWIST 1 76062000 WD1 247 340000 WD2 12291 4000 WD3 153 643000 SEI 98 9358000 E2 98 9358000 214 E10 122 914000 T 0 48000000 W1 0 63115600 F 0 Q5 0 02229690 W2 14 8046000 W3 2 23269000 THETAI 6 67062000 THETA2 34 6306000 THETA3 33 9018000 TWIST 0 72881400 WD3 63 6010000 E10 50 8808000 T 0 56000000 W1 1 85102000 WD1 43 5816000 SE1 17 4327000 WD2 5088 08000 E2 17 4327000 FO Q5 0 06954550 W2 7 48477000 W3 1 27490000 THETAI 7 80752000 THETA2 43 0223000 THETA3 42 2949000 TWIST 0 72735000 WD3 63 4732000 E10 50 7786000 T 0 64000000 W1 1 29959000 WD1 244 794000 SE1 97 9178000 WD2 5077 86000 E2 97 9178000 FO Q5 0 00757349 W2 4 93688000 W3 0 22562900 THETAI 8 84244000 THETA2 43 7783000 THETA3 43 5761000 TWIST 0 20214300 WD3 17 6403000 E10 14 1122000 T 0 72000000 W1 2 36478000 WDI 57 8774000 SEI 23 1510000 WD2 1411 22000 E2 23 1510000 F 0 Q5 0 06375560 W2 5 46525000 W3 1 74294000 THETAI 9 99345000 THETA2 46 3143000 THETA3 46 5299000 TWIST 0 21561100 WD3 18 8156000 E10 15 0525000 T 0 80000000 W1 0 01586070 WD1241 414000 WD2 1505 25000 SE
57. 1 CUR Pick the 1 junction from the menu on the left and place it two grids to the right of the SE element Both elements are red now CUR You will see on the Status Box the message Bond from and the cursor turned to a small circle and an arrow pointing left Click on the SE element The cursor will change direction as a circle and an arrow pointing right The Status Box reads Bond to Click the cursor on the 1 junction or as close to it as you can The bond that joins the SE element and the 1 junction will be displayed along with a bond number and the causality assignment Note that the 1 is red this indicates the bond graph is not complete Any bond or element in red indicates some difficulty with the graph The user can get an explanation in any case To do this click the mouse on the ANALYZE button choose explain the cursor will change and then click on 1 element The message displayed on the dialogue box is explain 1 1 too few bonds CUR Now select an I element by clicking the mouse while the cursor is on the I button on the elements menu Place these two grids above the junction by moving the cursor and clicking the mouse The distance is arbitrary CUR Draw the bond between the 1 and the I element click the mouse on the 1 and then on the I The cursor will change direction on each click and the bond 2 will appear on the screen 122 TF CUR Select the TF element from the menu and place it to the r
58. 1 8 9 10 84 9 1 89 10 1 8 9 11 078 PRR HOO CAUSALITY FLOW oe NOTE FROM TO BOND FROM o m en e o AN PRA on OW 00N pa d de dP dP oe oe dP oe oe oe oe oe oe o PR FOWURIDUAWNE pM zl 9 00 JU Pi UNHP m End of model H o rj H pP Wn ERE Bu 0 0o JU10U01 S 9 S cal oy PRPRPA HRPRPORPHRRHON H H 5 Run the files in Matlab This is done by issuing the following command at the Matlab command prompt CAMPGMOD 6 The following lines were used to generate the output in the form of plots Sample output plots can be seen at the end of this section with the results figure 1 plot t p q 1 r grid title Distance the Dummy s head travels ylabel Distance meters xlabel Time seconds DESIGN CRITERIA 85 The simulation must produce a design of the seat belts and the bumper so that it satisfies the following conditions 1 He doesn t hit the windshield if he travels at 25 and at 55 mph 2 What is the force acting on his chest and waist at 25 mph and at 55 mph Compare the data on injuries and determine if chest or internal injury occurs if 1 he wears a seat belt only 2 he wears a seat belt and a shoulder strap 3 What is the critical maximum velocity when he is safe at which impact occurs Hitting the windshield chest injury internal injury seat belt failure strap failure a
59. 1 k R b C 1 k R b Bumper Seat Belts Fig 3 7 Crash test bond graph model 75 x zx eo fam 2 a Bond Graph as Created in CAMPG E ete cate rneervoce ture options move Po PT a move single C_3 marked done move single C_3 marked done Mnove single R 4 marked done BOND FROM cZBmove single I_6 marked done D Fig 3 8 Bond Graph completed in CAMPG The SYSTEMATIC method was used to enter the bond graph model shown in Fig 3 8 Below is a detailed description how this was done The symbol CUR means to select with the cursor The symbol CR means to enter from the keyboard kk eoe sese K K K K K K K K seo K K K K K K K K K oer K eoe K KK K K K K KK K KK KK K K K K CAMPG lt CR gt This brings up the CAMPG screen with a logo Any movement of the mouse or typing any character will clear the logo and show a 76 EDIT CUR DELETE CUR ALL CUR YES CUR OPTIONS CUR STICKY CUR ON CUR 1 CUR CUR CUR CUR blank screen or will bring up the latest model generated and stored in the SESSION BG file These next three steps clear the screen if there is an existing session file If there is no previous SESSION BG file these steps are not necessary This pull down menu selection will be used to turn on the STICKY function so that all the similar elements can be placed all at once This step allows the SYSTEMATIC METHOD of building the bond graph model
60. 10 D 0 e1 03 C3 SF1 R4 P6 16 R4 C 0 1 C3 0 1 16 R4 D 1 R4 e6 03 C3 SF1 R4 P6 16 R4 09 C9 P6 1I6 R10 P11 111 R10 C 1 C9 1 C3 1 I11 R10 1 I6 R4 1 I6 R10 D 1 R4 oQuUu EESE Setting initial conditions Q9IN 0 Q3IN 0 P61N 16763 96 P11IN 1117 6 Creating Initial Conditions vector to be used for simulation IC Q9IN Q3IN P11IN P6IN Setting the variables to be used for simulation C3 1 300000 R4 80000 16 1500 C9 1 10000 R10 500 I11 100 SF1 0 Creating the vectors to be passed to the S function for simulation AA double subs A BB double subs B CCzdouble subs C DD double subs D DD D 97 Generate vector of transfer functions Example e3 s SE1 s 4 s SF10 s q4 s SE1 s Define SI matrix syms s Find the size of A and then figure out I I eye 4 Use Matlab Symbolic Tool Box to do symbolic matrix erations leading to the calculation of symbolic transfer functions Transfer Functions Matrix H Oo H C inv s I A B D pretty collect H Frequency Response Sample structures num den H bode num den Frequency Response Bode Plots num den 2ss2tf A B C D 1 bode num den ode de de de oe oe oe oe oe oe oe oe oe oe oe TD oe oe oe oe oe oe oe oe 5 Run the file in Matlab This is done by issuing the following command at the Matlab command prompt CAMPGSYM 5 Create a Simulink m
61. 219 Chapter5 Advanced Features 223 5 1 Advanced Menu Features up o OPERE PR REAN S NEU 223 EXPLAIN oera oe pang eR Pesto a Ud atn br dE aR 223 BELEK qe 224 B K DIAG M 225 25 2 User Preference SEUNG S sos ty beeen ERE EXER RAS DOE ERE SER Mad 226 STICKY us obtu cte ciat Qs 226 GRID i oue A OR REA ERU EE E REOR OE E OR RUE 226 FUNCTIONS idisse POEM s Deas ees 226 DISPLAY MODE 555 dec te exe o E et dT ene deus 226 COLOUR e wastes eh is e Ne LI Mp A NS d 226 5 3 Advanced Bond Graph Features eese 227 Large Bond Graphs ii sec I EX HERR ERN e E ERR RSS 227 Multipart Elements 21252 2350 yon eae sees TEE REDDERE Pate 228 User Controlled Numbering 2 eee ten oe Deer e ens 220 Automatic Causality Detection cc ce cee ence ence eee eens 230 Pseudo Bond Graphs see des eat cede ei eines cea yea eens toned 231 Copy And Flip Bond Graph Structures ccs cece eee 232 SUDSY SEMIS 22s ciis t eresas pee bee TERR LEER REL ey 233 Simultaneous Simulations esee 233 Example etc RUE RE ME 234 Physical System of Dummy in Car eee eee ee ees 234 Physical System of Hydroelectric Power Plant 235 Bond Graphs of Both Systems sees 236 CAMPGHMNIOD M 2c 54 vd repa MEER VO Ud REA ET LH ROSE 236 CAMPOFQU M dices eds UR ND TO DVD 238 Technical References 242 vii Chapter 1 CAMPG QUICK
62. 24 BLK DIAG Blk Diag is the third item located under the Analyze menu The purpose of this option is to view the block diagram that corresponds to the individual elements and junctions When this option is invoked the icon turns to the same eye as it does when Peek is used Once again the user simply needs click on the element or the junction to see a block diagram representation of that element or junction For an example of this see the following picture Fig 5 3 MTF BLK DIAG Fig 5 3 Simulink equivalent blocks for the Bond Graph Elements 225 5 2 User Preference Settings STICKY Sticky is located first under the Options menu Sticky is used to keep an option on When Sticky is set to On any menu item or bond graph element that is used will continue to be available until the user changes to another menu item or bond graph element GRID Grid is located second under the Options menu With this option the user can turn the grid on and off as well as hide the grid FUNCTIONS Functions is located third under the Options menu This indicates that Sources are not constants DISPLAY MODE Display Mode is located fourth under the Options menu This option is used to switch the display from color to black and white This allows the user to print the screen with older printers and have the print come out with much greater quality COLOUR Colour is located fifth under the Options men
63. 3 0 4 0 5 0 6 0 7 0 8 0 9 1 Time seconds Fig 3 10 Force acting on the dummy 87 The table shown below Table 1 illustrates the results of the different simulations considering different velocities and physical parameters INITIAL NOF BUMPER SEAT BELTS DUMMY VELOCITY BELTS K2 B2 K1 B1 E11 Q9 N m N s m N m N s m IN m 25 1 300 000 80 000 10 000 500 9 310 0 8167 25 2 300 000 80 000 20 000 1 000 13 147 0 5144 55 1 300 000 80 000 10 000 500 20 483 1 7968 55 2 300 000 80 000 20 000 1 000 29 035 1 1300 55 1 300 000 80 000 10 000 1 000 25 547 1 3780 55 1 300 000 80 000 10 000 1 500 26 714 1 1100 55 1 300 000 80 000 8 000 1 500 25 990 1 1670 55 1 300 000 80 000 5 000 3 000 36 639 0 7500 55 2 300 000 50 000 5 000 3 000 31 184 0 7810 55 2 300 000 10 000 5 000 3 000 25 426 1 0360 55 2 100 000 10 000 5 000 3 000 15 986 0 8580 55 2 50 000 10 000 5 000 3 000 13 129 0 7440 Table 3 1 Simulation Results The impact at 55 mph is shown in the table above The displacement of the dummy is 1 79m so he hits the windshield in 0 065 sec Chest injury also occurs at 20 483 newtons The values of the shock absorbers can be changed in the bumper and in the seat belts The dummy hits the windshield in about 1 sec at 25 mph but in just 0 05 sec at 55 mph without a seat belt This example illustrates the whole process of modeling and simulation using CAMPG Matlab for linear systems The next section will explore the same example bu
64. 5 Fig 4 14 Force Displacement at 25 MPH FORCE ACTING ON THE PASSENGER ELL AND 8 DISPLACEMENT 09 AT SPEED SS MILE H 0 40 T SEC Fig 4 15 Force Displacement at 55 MPH 198 8 8 DISPLACEMENT AND FORCE GN DRIUER AT 25 O BELTS Fig 4 16 Crash Test Simulation with no seat belts at 25 MPH B g DISPLACEMENT ANO FORCE ON DRIVER AT SS 0 SETS Fig 4 17 Crash Test Simulation with no seat belts at 55 MPH 199 4 10 Nonlinear System Example Gear Train with Backlash PROBLEM Design of precision gear trains requires analysis of forces velocities torques and realistic models considering the tolerances and slack between gear teeth This analysis is important in order to prevent fatigue failure on gear teeth and the transmitting shafts This will contribute to determine the materials size of parts and tolerance adjustments that are related to the generation of contact forces This involves making a dynamic model and performing the analysis of the gear train considering the backlash between the gear teeth The system shown in Fig 4 8 seen below consists of a gear set and a flywheel Gear 1 is driven by a cyclic torque described by a harmonic function The system drives the flywheel through a set of gears having excessive backlash The shaft connecting gear 2 and the flywheel is not rigid it has a torsional spring constant of K 4000 in Ib radian I1 0 4 1b sec 2 in R1 radius 5 0 in THETA 1
65. 9 Click the mouse on any element junction or bond The equations for that junction bond or the constitutive relations of the physical elements will be displayed Once the bond graph is completed CAMPG is ready to process the model to generate the Matlab files discussed earlier in section 3 3 This example showed how to use the STICKY feature and the SYSTEMATIC METHOD The bond graph could also have been created by the SEQUENTIAL METHOD This means connecting the elements immediately after they were placed on the screen instead of at the end The elements and bond are laid out sequentially Both of these methods create the same end product and the relative efficiency of each depends on the type of bond graph being constructed and the ability of the user to use the most familiar method for that person INTERFACE CUR From this menu the user can select the simulation language go back to DOS or Windows and saves the current model on the screen in a file named SESSION BG MATLAB CUR Select to generate the Matlab model and simulation files 4 CAMPG generates a computer model description and writes the files CAMPGMOD M CAMPGEQU M and CAMPGSYM M Only CAMPGMOD M and CAMPGEQU M files are shown below Section 3 8 uses the CAMPGSYM M file see that section for a complete example of using that file These files have been edited to include the values of the physical parameters initial conditions and external inputs To see the files as Matlab c
66. C Fig 4 9 Procedureal Example 0 00 3 75 179 Shown below is a portion of a new CAMPG ACSL input file that defines the procedural for a different input function in this case a harmonic with time controls at the onset and at the end PROGRAM CAMPACSL Demonstration of Procedural DYNAMIC DERIVATIVE Use of Procedural allows a set of FORTRAN statements to define the input SF1 The roadway input changes from level to harmonic and back to level PROCEDURAL SF1 T SF1 0 IF T GT 5 SF1 6 283 COS 6 283 T IF T GE 10 SF1 0 0 END Me cot SYSTEM EQUATIONS Hn el e3 f1 SF1 END OF DERIVATIVE END OF DYNAMIC END OF PROGRAM 180 8 PROCEDURAL EXAMPLE SUSPENSION SYSTEM N 0 00 Q4 DELTA X 10 0 2 00 J 0 00 SF1 ROAD INPUT 10 0 n3 c e 8 00 11 0 14 0 n RT il Fig 4 10 Procedural Generated Display EIGENVALUE ANALYSIS ANALYZ command FORM ANALYZ SUBCOMMAND TRIM EIGEN EIGVEC JACOB 181 The ANALYZ command invokes the linear analysis capability of ACSL This is used to evaluate the Jacobian trim the state variables to null the rates and calculate eigenvalues and their associated eigenvectors The TRIM sub command transfers the initial conditions to the state variables computes the JACOBIAN and then using Newton iteration and the steepest descent step adjusts the state variables until the derivatives go to zero The sub com
67. D MODEL DESCRIPTION 1 EDIT THIS FILE INITIAL PLACES ENTER VALUES OF PHYSICAL CONDITIONS WHERE PARAMETERS INPUTS AND TIME CONTROLS IN THE QUESTION MARKS APPEAR FOR NON LINEAR SYSTEMS REPLACE THE LINEAR RELAT IS BY NON LINEAR FUNCTIONS FOLLOWING THE PROPER CAUSAL RELATIONS 3 THE TABLE BELOW PROVIDES A GUIDELINE FOR PHYSICAL MEANING OF GENERALIZED VARIABLES USED IN BOND GRAPH NOTATION PROGRAM CAMPACSL 1 ACSL INPUT FILE INITIAL INITIAL CONDITIONS Q19IN P30IN Q1OIN QI6IN Q24IN Q47IN P32IN 77 SOIN PS2IN TIME CONTROL Q21N 2 Q8IN P29IN Q13IN CONSTANT CONSTANT CONSTANT CONSTANT CONSTANT CONSTANT CONSTANT STANT STANT 7 7 T TIME THIS IS A CAMP GENERATED MODEL DESCRIPTION 1 EDIT THIS FILE ENTER VALUES OF PHYSICAL PARAMETERS INITIAL CONDITIONS INPUTS AND TIME CONTROLS IN PLACES WHERE THE QUESTION MARKS APPEAR 2 FOR NON LINEAR SYSTEMS REPLACE THE LINEAR RELATIONS BY NON LINEAR FUNCTIONS FOLLOWING THE PROPER CAUSAL RELATIONS 3 THE TABLE BELOW PROVIDES A GUIDELINE FOR PHYSICAL MEANING OF GENERALIZED VARIABLES USED IN BOND GRAPH NOTATION fm 3 Wind Cj CAMPG loading from session bg done revions session loaded from session and placed 7 p gt Search Folders EJ C Documents and Settings All Users Desktop CAMPG t m w File and Folder Tasks Y el a Bond Graph CAMP G Other Plac
68. E OF TWIST SHAFT SETPRNPLT F CALPLT F STRPLT T GRDSPL T YINSPL 2 0 Y ASSP L 25 PLOT XAXIS T XTAG SEC TWIST THETA3 TAG DEG END PROCED EE SET CALPLT F STRPLT T GRDSPL T TTLSPL T INSETS 1 0 SET TITLE FORCE BETWEEN GEAR TEETH PLOT XAXIS Q5 XTAG in F TAG Ib END PROCED FF SET CALPLT F STRPLT T GRDSPL T TTLSPL T YINSPL 1 0 SET TITLE DISPLACEMENT BETWEEN GEAR TEETH w PLOT XAXIS T XTAG SEC Q5 TAG IN END PROCED GG SET CALPLT F STRPLT T GRDSPL T EE T YINSPL 1 0 SET TITLE INPUT TORQUE PLOT XAXIS T XTAG SEC SE1 TAG LB FT END PROCED HH 217 SETCALPLT F STRPLT T GRDSPL T TTLSPL T YINSPL 2 0 Y ASSP L 25 SET TITLE TORQUE ON GEARI AND ON SHAFT li PLOT XAXIS T XTAG SEC E2 TAG LB FT E10 TAG LB FT END SET CMD DIS STOP The plots are generated by entering the AA BB CC DD EE FF GG HH labels at the ACSL gt prompt The prompt will appear as soon as each plot is completed DESIGN CRITERIA The contact force between teeth depends upon the relative position of the gears due to the slack between them The contact force is zero in position where the teeth are not in contact but increases proportionally to the displacement after contact has been made Using this nonlinear relation and a cyclic input torque it is important to find the torques generated internally on the gears and the shaft due to the dynamics of the system I
69. Eg Pa c T o n J e pe 1 1 pt J A o n loading from session bg done v Bprevions session loaded from session and placed BOND FROM Fig 1 3 CAMPG black and white display Use the OPTIONS menu to change to black and white display T za o lt 74 apg 2 ol The user at this point is free to enter a new Bond Graph Model in CAMPG and have CAMPG generated the code that goes into the different simulation environments This menu is reached by clicking on the INTERFACE menu CAMP G session options memes o m MATLAB SIMULINK o D le 2 xl 5 2 111 A A D el Q Sm o a L3 n T4 o oa loading from session bg done t Bprevions session loaded from session and placed BOND FROM Fig 1 4 CAMPG INTERFACE menu 1 8 CAMPG ACSL INTERFACE Once the Bond Graph model has been entered into CAMPG it will generate the appropriate files for the interface input files to ACSL Choose the ACSL option interface from the menu CAMPG will interface with the user with a window that looks like the following figure The CAMPG ACSL model files have been succesfully generated and written in the working directory Edit file campsl csl to complete the input model to fiCSL Use Windows Notepad or other editor campsl csl is the model input to ACSL ress any key to continue Fig 1 5 CAMPG ACSL console w
70. G DQ9 Q9IN P11 INTEG DP11 P11IN TEMINATE CONDITIONS TERMT T GE FINTIM END OF DERIVATIVE END OF DYNAMIC END OF PROGRAM The causality and power flow can be verified since CAMPG will generate the bond graph causality and power flow tables shown below These can stay in the file since they do not interfere with the ACSL input format and it will consider this tables as non executable statements Token K k k Kk Kk Kk k kk kkk KEK K K K K K KK K KK KKK KK kK ues BOND GRAPH ANALYSIS 7 POWER FLOW BOND FROM TO 1 SEI 0125 20125 1234 31234 c3 41234 RA4 193 50125 1567 61567 I 6 71567 07 118 807118 189 0 9189 10 C 9 1018910 R 10 1107118 Lil CAUSALITY FLOW NOTE FROM TO BOND FROM TO 10125 SE 1 2 1223 4 0125 Ts S 1234 4 RA 1234 50125 1567 61567 I6 707118 1252087 818910 07 118 9C9 1 89 10 JO R 10 189 I0 1107118 Lil END OF PROGRAM 5 Execute ACSL with the model shown in the previous section This is done by issuing the commands ACSLCLG CAMPSL PC ACSL CAMPSL The ACSL commands necessary for calculation of variables or plots are entered at this stage The next step shows a summary of the commands used in this simulation 194 6 The simulation was speed up using the SETUP file shown below The Setup file was used to generate sets of graphical output with options and commands stored in sections with labels A B C
71. Generated Block Diagrams from Bond Graph Models CAMPG as a Tool Box for SIMULINK Proceedings of the International Conference on Bond Graph Modeling and Simulation ICBGM 2001 Phoenix Arizona January 2001 Piguet I Granda J Mocellin G CAMPG SYSQUAKE an integrated Environment to Understand DynamicSystems and Design Controllers Proceedings of the International Conference on Bond Graph Modeling and Simulation ICBGM 2001 Phoenix Arizona January 2001 Borutsky W Granda J Determining Sensitivities from and Incremental True Bond Graph Proceedings of the International Conference on Bond Graph Modeling and Simulation ICBGM 2001 Phoenix Arizona January 2001 246 30 31 du 33 34 35 Morris M Granda J Four Way Hydraulic Control Valve Design using Bond Graph Models Computer Generated Block Diagrams and SIMULINK S Functions Proceedings of the International Conference on Bond Graph Modeling and Simulation ICBGM 2001 Phoenix Arizona January 2001 Granda J Methodes De Modelisation De Discontinuites De Systemes Nonlineaires Utilisant Des Modeles Generes Par Ordinateur Des M Functions Matlab Et Des S Functions Simulink In French July 2000 The English version is entitled Modeling Methods For Nonlinear Discontinuities Using Computer Generated Models Matlab M Functions And Simulink S Funtions Presented at Conference International Francophone d Automatique Ecole Centrale de Lille France 5 8 Jul
72. Granda J Channell G V 8 Internal Combustion Engine Bond Graph Model a Detailed Modeling Procedure Proceedings of the International Conference on Bond Graph Modeling and Simulation ICBGM 97 Phoenix Arizona January 1997 Pg 233 H A Mergen Granda J Bond Graph Models and Finite Element Models for Engine Valve Spring Transient Response Proceedings of the International Conference on Bond Graph Modeling and Simulation ICBGM 97 Phoenix Arizona January 1997 Pg 129 Granda J J Advances in Modeling and Simulation of Dynamic Multiphysics Systems New Challenges Proceedings of the International Conference on Bond Graph Modeling and Simulation ICBGM 97 Phoenix Arizona January 1997 Pg 9 Granda J J Reus J Three dimensional Bond Graph Models Using CAMPG Proceedings of the International Conference on Bond Graph Modeling and Simulation ICBGM 95 Las Vegas NV January 1995 Granda J J The future and Role of Bond Graphs in Industry Proceedings of the International Conference on Bond Graph Modeling and Simulation ICBGM 95 Las Vegas Nv January 1995 Granda J J Dauphin Tanguy G Rombaut C Power Electronics Converter Electrical Machine Assembly Bond Graph Models simulated 248 44 45 46 4T 48 49 50 51 with CAMP ACSL IEEE International Conference Letouquet France October 1993 Granda J J Computer Aided Modeling of Multiport Element and Large Bond Graph Models with CA
73. I 96 5658000 E2 96 5658000 F 0 Q5 0 04296190 W2 13 1844000 W3 2 28386000 THETAI 10 7690000 THETA2 56 3064000 THETA3 56 5460000 TWIST 0 23965500 WD3 20 9138000 E10 16 7311000 T 0 88000000 W1 1 52376000 WD1 71 9759000 SE1 28 7904000 WD 1673 11000 E2 28 7904000 FO Q5 0 07345380 W2 5 60466000 W3 0 93763800 THETAI 12 0746000 THETA2 64 5815000 THETA3 64 4084000 TWIST 0 17305700 WD3 15 1021000 E10 12 0817000 WD1 237 211000 SE1 94 8845000 WD2 1208 17000 E2 94 8845000 215 T 0 96000000 F 0 Q5 0 08378780 W1 1 28332000 W2 5 18064000 W3 0 13954800 THETAI 14 0324000 THETA2 65 3612000 THETA3 65 3053000 TWIST 0 05589940 WD1 85 8286000 WD2 390 252000 WD3 4 87814000 SEI 34 3315000 E2 34 3315000 E10 3 90252000 T 1 00000000 F 0 Q5 0 05285740 W1 0 48549300 W2 470774000 W3 0 63250100 THETAI 13 9239000 THETA2 66 5909000 THETA3 66 1257000 TWIST 0 46518100 WD1 228 236000 WD2 3247 57000 WD3 40 5947000 SEI 91 2945000 E2 91 2945000 E10 32 4757000 ACSL gt STOP USE OF SETUP FILES IN SIMULATION Using ACSL interactively is very useful and the designer gains an insight of the system and its performance as well as modeling errors The numerical and graphical results can be obtained very quickly and without much typing of commands and specification for plots if a set of this specification is stored in a SETUP file The SETUP file shown below was used to study the dynamic performance of the gear train Using a SETUP file the
74. I9 R10 R2 2 G3x4 2 R6 2 T7x8 100 1000 I9 700 5 100 1000 2 R10 800 E NOR E External inputs se t sf t global SE1 SE1 1 DEREN Simulation Time Control t02 0 Initial Time tf 3 Final Time tspan tO tf MTS Computer Simulation t p dq ode23 campgequ tspan initial plots of the velocity and the position of the armature and the load figure 1 subplot 212 plot t p_q 1 19 b grid title Simulation Velocity of armature and load subplot 211 plot t p_q 2 m grid title Simulation Position angle end Campgequ m function p qdot campgequ t p q E acxstamer4 es campgequ m CAMPG MATLAB function System differential equations state Vectors 108 global R2 G3x4 R6 T7x8 I9 R10 global SE1 System Differential Equations First Order Form pq Define State Variables P9 p q 1 theta p q 2 variables vector P9 Define derivatives dp dq and output variables e f el SE1 f9 P9 IO9 f10 f9 f8 f9 el0 f10 R10 7 8 T7x8 f6 f7 f4 f7 e6 f6 R6 e3 4 G3x4 e2 el e3 2 e2 R2 f3 f2 e4 3 G3x4 e7 e4 e6 e8 e7 T7x8 e9 e8 e10 dP9ze9 fl f2 dtheta f9 Derivatives vector p adot dP9 dtheta Campgsym m clear CAMPG MATLAB Symbolic State Space Model Convert system physical parameters to symbols syms R2 G3x4 R6 T7x8 I9 R10 Generate A B matr
75. IN SIMULATION ASIM Vienna Austria Chapter of this book to be published by the Technical University of Vienna The chapter is entitled Granda J Advances in Software for Automation of The Modeling and Simulation Process Of Non Linear Multienergy Systems Using MATLAB SIMULINK ACSL And CAMPG February 2000 J J Granda and F E Cellier eds Proceedings of ICBGM 99 4th International Conference on Bond Graph Modeling and Simulation Simulation Series Vol 31 Nr 1 SCS Publishing ISBN 1 56555 155 9 Jan 1999 J J Granda and G Dauphin Tanguy eds Proceedings of ICBGM 97 3th International Conferen on Bond Graph Modeling and Simulation Simulation Series Vol 29 Nr 1 SCS Publishing ISBN 1 56555 103 6 Jan 1997 F E Cellier and J J Granda eds Proceedings of ICBGM 95 2th International Conference on Bond Graph Modeling and Simulation Simulation Series Vol 27 Nr 1 SCS Publishing ISBN 1 56555 037 4 Jan 1995 J J Granda and F E Cellier eds Proceedings of ICBGM 93 Ist International Conference on Bond Graph Modeling and Simulation Simulation Series Vol 25 Nr 1 SCS Publishing ISBN 1 56555 Jan 1993 Granda J J Computer Aided Modeling Program CAMP a Bond Graph Preprocessor for Computer Aided Design and Simulation of Physical Systems Using Digital Simulation Languages Thesis University of California Davis December 1982 RESEARCH PAPERS 15 Granda J J S Domain Bond Graph Models Computer Ge
76. MPG International Conference on Bond Graph Modeling and Simulation ICBGM 93 San Diego Ca January 1993 Granda J J Kong N Time Dependent Computational Relations between Finite Elements and Bond Graph Modeling International Conference on Bond Graph Modeling and Simulation ICBGM 93 San Diego Ca January 1993 Granda J J Kong N Pseudo Bond Graph Models and Finite Element Models of Transient Heat Transfer Problems International Conference on Bond Graph Modeling and Simulation ICBGM 93 San Diego Ca January 1993 Granda J J Methodology of Bond Graph Modeling and Simulation with Computer Graphics for Undergraduate and Graduate Students Multiconference on Engineering Education San Diego January 1990 Granda J J Barlow M Three Dimensional Transient Heat Transfer Analysis Using Finite Elements and Computer Graphics CADDAM Conference October 1989 Granda J J Tang S Computer Simulation of Heat Transfer Models using a Pseudo Bond Graph Network TRANSACTIONS Journal of the Society for Computer Simulation September 1989 Granda J J Lee K Computer Simulation of Mechanical Manipulators with model reference adaptive controllers Proceedings of the Southeastern Simulation Conference Hunstville Alabama October 1987 Granda J J Sime K Computer Aided Modeling of the Four Stroke Internal Combustion Engine Proceedings of the 30th Heat Transfer and 249 52 53 54 55 56 57 58
77. MPG will place the user inaposition to edit the CAMPSL CSL file that it generates Now the user needs to enter the values of the initial conditions time control physical parameters nonlinear equations nonlinear functions activated bond specifications signals and any other description necessary to complete the model The INITIAL section contains definitions of the initial conditions time control and physical parameters The DERIVATIVE section needs specifications of the input functions CAMPG generated the ACSL input file with marks in the places where numerical values or functions definitions need to be specified to complete the model 5 RUN ACSL The user runs ACSL using the CAMPSL CSL as its input file This file was completed in the previous step The inputfile can have any other name that the user wants to use Now the user is in a position to enter and take advantage of all the ACSL run time commands and simulation capabilities The user can issue commands to simulate display and plot the calculated values The PREPAR OUTPUT START and PLOT commands are used for this purpose Section 5 5 offers more information on this step 6 OPTIMIZE SIMULATION Once familiar with the previous steps and confident to obtain results from ACSL the user can proceed to optimize and speed up the simulation as well as run several different simulations on the model under study This can be achieved by entering a series of runtime commands but it
78. Model of Drive Train Nonlinear Dead Space Contact ce eeeceeee cence eee ees tvi dE Procedure For Solution 4 ieeidec eese r rone e eorr De Ras pte did Generating an engineering model sesesssss Generating the corresponding bond graph MATLAB TIS oue iere escat be eet Eo dL absent acu vacua Desie Gritetid io oer EE ST PASTE ERM WEE SUN RE Results 90 100 101 103 103 103 108 108 109 113 113 115 115 116 116 117 118 118 3 10 Hydroelectric Power Plant with Surge Tanks 141 OBIBUUVESE resnie o oere Sesvorod ep eile seeded ME NALE NND ELS 141 D sign criteria 1 25 rr Sead ra bade de edad CRX RE pans eh ENTRY NER 142 Bat GHs 20 a op a DA GI END Uaod Ma dus iens 144 CAMPG MATLAB Solution 0 cece cece eee eneeeeeeeenees 145 Chapter 4 CAMPG and ACSL 155 4T Introduction Nr 155 Explicit Structure of a Simulation Model 156 Model Description Procedure 1 5 eerte 157 4 2 Running ACSL Using Differential Equations and Functional Blocks 158 Running a Basic ACSL Model sssssumRRee 158 4 3 Running ACSL Using Bond Graph Modeling n 161 Computer generated model oe ree ere e toe ees 161 4 4 Different Ways to Execute the CAMPG ACSL System 163 Generate model for first time seeeseeseessese 163 Model file exists o
79. OCITY BELTS K2 B2 K1 B1 E11 Q9 N m N s m N m N s m IN m 25 1 300 000 80 000 10 000 500 9 310 0 8167 25 2 300 000 80 000 20 000 1 000 13 147 0 5144 55 1 300 000 80 000 10 000 500 20 483 1 7968 55 2 300 000 80 000 20 000 1 000 29 035 1 1300 55 1 300 000 80 000 10 000 1 000 25 547 1 3780 55 1 300 000 80 000 10 000 1 500 26 714 1 1100 55 1 300 000 80 000 8 000 1 500 25 990 1 1670 55 1 300 000 80 000 5 000 3 000 36 639 0 7500 55 2 300 000 50 000 5 000 3 000 31 184 0 7810 55 2 300 000 10 000 5 000 3 000 25 426 1 0360 55 2 100 000 10 000 5 000 3 000 15 986 0 8580 55 2 50 000 10 000 5 000 3 000 13 129 0 7440 Table 3 2 Simulation results The impact at 55 mph is also seen in the table above The displacement of the dummy is 1 79m so he hits the windshield in 0 065 sec Chest injury also occurs at 20 483 newtons The values of the shock absorbers can be changed in the bumper and in the seat belts The dummy hits the windshield in about 1 sec at 25 mph but in just 0 05 sec at 55 mph without a seat belt This example illustrates one use of the CAMPGSYM M file The next section will demonstrate how to obtain transfer functions with the CAMPGSYM M file 102 3 8 Obtaining Transfer Functions Example Multienergy System Example Bond Graph modeling is the appropriate method when systems have components in different energy domains but they act as a complete dynamic system One of the most classic ones is the model of
80. RIPTION POWER FLOW BOND FROM TO L SE_1 1 1 2 3 2 1 1 2 3 I2 3 1 12 3 TE 3 4 4 TE 3 4 0456 5 0456 c 5 6 0456 TF 6 7 7 TE 6 7 1789 8 1 789 I_8 9 1 7 8 9 0 79 10 11 10 0 9 10 11 C 10 dl 0 9 10 11 I 11 CAUSALITY FLOW 129 BOND FROM TO d 1 SE_1 112 3 2 1132 3 1 2 3 TF 34 1 23 4 0456 TF 34 5 C5 0456 6 0456 TF 6 7 7 TF 6 7 1 7 8 9 8 17 89 I8 9 0 9 10 11 1 7 8 9 10 C 10 0 9 10 11 11 0 9 310 11 IL End of model CAMPGEQU M Listing function p qdot campgequ t p q Rond Rap campgequ m CAMPG MATLAB function System differential equations state Vectors global I2 T3x4 C5 T6x7 I8 C10 I11 vect_out global SE1 System Differential Equations First Order Form State pq Define State Variables Pll p q 1 Q10 p q 2 P8 p q 3 P2 p q 4 Q5 p q 5 Q2 p q 6 Q8 p q 7 Q11 p q 8 SE1 100 sin 20 t KG 200000 variables vector P11 910 P8 P2 Q5 Define derivatives dp dq and output variables e f el SE1 f2 P2 I2 f3 f2 e5 is non linear and it is a function of Q5 Making e5 a function of Q5 and accounting for the 2in backlash spacing if Q5 1 130 e5 KG Q5 elseif Q5 gt 1 e5 KG Q5 else e5 0 end Scontinuing with linear constitutive relations 4 3 T3x4 e6 e5 e7 e6 T6x7 f8 P8 I8
81. RIVATIVE END OF PROGRAM Here the CONSTANT statement is used to define all the parameters The three periods are used to express continuation of the definition in this case CONSTANT defined in the previous line GENERATION OF ACSL PLOTS The ACSL prompt appears again after the start command is done executing the simulation The user may now tell ACSL to create some plots of the variables listed in the PREPAR command ACSL is capable of plotting line plots printer plots and strip plots Plots are generated using the PLOT command The PLOT command is entered followed by the variable or variables you want to plot ACSL assumes that the first variable listed in the PREPAR statement is the independent variable usually time which is placed on the X axis The variables that follow are interpreted to be the dependent variables to be plotted as a function of the independent variable time For example if the user wants to plot Q2 as a function of time then enter the command ACSL PLOT Q2 This command will generate a plot of Q2 versus time with automatic scaling assuming time was the first variable in the PREPAR list 168 Labels colors scaling and much more can be added to these plots with the appropriate syntax of the options of the PLOT command Several of these options are explored in the following section and others are listed in the ACSL manual PLOT CONTROL OPTIONS The plot command has many options that allow t
82. SEGMENT SEGMENT CUR The cursor will change shape to a cross Click the mouse on the SE element it can be any other 207 element or junction The bond graph segment will turn blue CUR Move the cursor to the desired new location for the element picked The bond graph will be redrawn in the new location All junction and elements have their corresponding bonds numbers and causality marks If there is any one bond or element on the screen that it is red use the ANALYZE button and pick EXPLAIN then click on the red bond or element A message on the dialogue box will indicate the status or error message GENERATE AN ACSL INPUT FILE Continuing from the previous step once the bond graph has been completed pick the EXIT button and within it the ACSL option CAMPG will generate the CAMPSL CSL file used as ACSL input The model description here will help illustrate some features of this file not yet discussed CAMPG will generate a set of instructions at the beginning of the file as shown below These are helpful instructions to structure the input file correctly It also includes an explanation of the variable equivalences in different energy domains This gives the physical interpretation to the variables in the equations and expressions ENTER PARAMETER VALUES Edit the CAMPG model to enter the linear and non linear constitutive relations of physical elements into the ACSL input file The completed model input file was shown in
83. Select the 1 from the menu on the left to place the ONE JUNCTIONS Move the cursor and click in the middle of the screen Move the cursor 4 grids to the right and 4 grids down and click again to place the second 1 Move the cursor 8 grids to the left and click to put the third 1 on the screen TI SF CUR CUR CUR CUR CUR CUR CUR CUR CUR CUR Select the 0 from the left hand menu to place the ZERO JUNCTIONS on the screen Click the cursor at 4 grids to the left of the 1 middle of screen and at 4 grids to the right of it Select C from the menu in order to place the capacitive elements C on the Bond graph Place one of the C elements 2 grids below and 2 grids to the left of the 1 element on the left then move 8 grids to the right and place the other Select the resistive elements R from the left hand menu Place these R elements 4 grids to the right of each C element Select the T element from the left menu Place the two inertia elements I 4 grids above the central 1 and 4 grids to the right of the right most 0 Select the FLOW SOURCE from the menu on the left Place this SF 4 grids to the left of the left most 0 78 bond symbol CUR Select the BOND SYMBOL top box in the left hand menu to join all of the elements with bonds SF screen CUR Click on the SF on the screen O screen CUR Click on the closest 0 on t
84. TART RANGE ALL T 0 1 00000000 F 799 510000 876 132000 Q5 0 10399800 0 10438100 W1 3 05866000 3 62343000 W2 20 7567000 21 5832000 W3 0 20755400 2 64094000 THETAI 0 14 3570000 THETA2 0 24510000 66 8484000 THETA3 0 66 1257000 TWIST 2 08848000 2 03426000 WD1 10772 2000 9755 07000 WD2 73588 0000 85657 6000 WD3 182 254000 77 523000 SE1 99 9999000 99 9998000 E2 4308 87000 3902 03000 E10 145 803000 142 018000 ACSL gt OUTPUT T F Q5 W1 W2 W3 THETA1 THETA2 THETA3 TWIST WD1 WD2 WD3 SE1 E2 E10 NCIOUT 100 ACSL gt SET TCWPRN 72 FORCE 3 COLUMN OUTPUT WIDTH 213 ACSL START TO FO Q5 0 WI 0 W2 0 W3 0 THETAI 0 THETA2 0 THETA3 0 TWIST 0 WDI 0 WD2 0 WD3 0 SEI 0 E2 0 E100 T 0 08000000 FO Q5 0 08635910 W1 0 02511270 W2 10 9065000 W3 1 42032000 THETAI 1 42483000 THETA2 2 17613000 THETA3 1 98043000 TWIST 0 19569700 WD1 249 893000 WD2 1366 22000 WD3 17 0778000 SEI 99 9574000 E2 99 9574000 E10 13 6622000 T 0 16000000 F 0 Q5 0 07939610 W1 0 74132100 W2 1 68343000 W3 2 59304000 THETAI 3 03126000 THETA2 10 6072000 THETA3 11 2325000 TWIST 0 62526200 WD1 14 5935000 WD2 4365 15000 WD3 54 5644000 SE1 5 83741000 E2 5 83741000 E10 43 65 15000 T 0 24000000 FO Q5 0 05020320 W1 2 02947000 W2 3 56703000 W3 0 89309100 THETAI 3 50849000 THETA2 20 4189000 THETA3 20 1499000 TWIST 0 26899500 WD1 249 041000 WD2 1877 94000 WD3 23 4742000 SE1 99 6165000 E2 99 6165000 E10 18 7794000 T 0 32000000 FO Q5 0
85. a DC motor This is an electromechanical system It was deliberately chosen because keeping continuity with the theory expressed above it is important to link the approach to multi energy systems and demonstrate the automated computer formulation approach considering the electrical components and the mechanical ones as a single system Nowadays the trend is to prepare mechanical engineers in electronics The new area of Mechatronics is a perfect place for application of the techniques outlined here Nise 2 analyzes the process for a d c motor A comparison of the approach is useful to illustrate the differences in the conventional approach outlined in Nise 2 and the one proposed here The figure shown below is that of a D C motor Physical Model of D C Motor e 4 700 kg m H Ja7 5 kg m D 800 N m s rad D 2N m s rad Fig 3 14 Electromechanical System Model 103 The process of making the model starts with the identification of the components The resistors in the circuit the armature inertia the gyrator the gear set damping components and the load are represented by R C GY LTF elements The 1 junction provide the summation points for the voltages in the electrical side and for the torques on the mechanical side Armature Armature Load Resistance Damping Inertia Nc R eo T T wes SE iles GY lise EH ELECTRICAL MECHANICAL S COMPONENTS COMPONENTS Load Damping Fig 3 15 Electromechanical System Bond Graph Mod
86. acitive elements C on the Bond graph Place one of the C elements 2 grids below and 2 grids to the left of the 1 element on the left then move 8 grids to the right and place the other Select the resistive elements R from the left hand menu Place these R elements 4 grids to the right of each C element Select the I element from the left menu Place the two inertia elements I 4 grids above the central 1 and 4 grids to the right of the right most 0 Select the FLOW SOURCE from the menu on the left Place this SF 4 grids to the left of the left most 0 Select the BOND SYMBOL top box in the left hand menu to join all of the elements with bonds SF screen CUR Click on the SF on the screen O screen CUR Click on the closest 0 on the screen 190 O screen CUR Click on the same 0 screen CUR Click on the lower left 1 on the screen There should be now have 2 bonds on the screen Continue this process until the rest of the bonds have been created Notice that some of the bonds are red just after they are placed This means that the system detects an error in the bond graph construction These errors while the bond graph is being assembled are simply warnings to the user that the bond graph is not a close form system but rather some bonds are not complete yet They also tell the user that the causality cannot be completed up to that point If these errors continue after comp
87. align the bond graph in the vertical and horizontal directions Setting for the ambiguous causality and other problems with the bond graph structure Color of the derivative causality indicator Option for messages and other bond graph problems ANALYZE contains the features that makes CAMPG a design tool CAMPG is able to detect errors in bond graphs When an error is detected the element or bond is given a red color In order to understand in detail what those changes in color as the graph is being 29 EXPLAIN PEEK MEMORY drawn the following option provide an inside view of the bond graph This feature gives explanations of the bonds and elements Once EXPLAIN is selected a stethoscope shape will be the cursor on the screen This indicates that the user will listen to what is wrong with the bond graph by clicking in the red bonds or elements and seeing a message displayed on the bottom window DIALOGUE BOX This is useful when there is an error red element or bond in the bond graph The user could click in any other part of the bond graph that does not have the warning color A massage indicating the status of that element or bond will be displayed This feature allows you to examine the equations throughout the bond graph structure These equations can be examined at each bond element or junction After selecting PEEK move the cursor which is now an eye to any element and click The describing equatio
88. ariables to be plotted to the following EFFORTS or FLOWS vectors Activate in campgmod m suggested structure of graphical output TIME STEP 1 t Define time vector EFFORTS STEP e5 e11 e4 Define efforts vector FLOWS STEP f2 f9 f8 Define flows vector STEP STEP 1 In campgmod m the following structure is included Sample structure for plotting Output Variables as defined in campgequ m Example If the efforts and flows were defined as EFFORTS STEP e5 ell e4 59 5 FLOWS STEP f2 9 8 figure 2 Plot ell vs TIME Second column of EFFORTS vector amp subplot 211 plot TIME EFFORTS 2 b grid title Effort variable of vector EFFORTS 2 stored in column Plot 8 vs time Third column of FLOWS vector iJ subplot 212 plot TIME FLOWS 3 m grid E title Flow variable of vector FLOWS 3 stored in column 3 This is where the desired outputs are all collected into vectors The vectors are created here and they are called set as global variables in Matlab This enables them to be building in this file and then plotted in the CAMPGMOD M file The user can enable and the edit these vectors to contain any outputs that they are interested in monitoring or they can leave this alone if they do not need to monitor any outputs CAMPGSYM M This file is used by itself It does not require the use of any other file that CAMPG crea
89. art the simulation and graphical output of results This is achieved by entering ACSL run time commands A comprehensive explanation of these commands is presented in the ACSL reference manual 163 MODEL FILE EXISTS ON DISK If a file describing a simulation model has been created and is stored in a disk file you may execute ACSL using that file by entering ACSLCLG filename The system will respond with several messages indicating that the model is being processed in the following stages A TRANSLATION A translator converts the ACSL input file into code B COMPILATION The FORTRAN compiler uses this code to generate an object code C LINKING The system LINKER joins the system libraries and produces an executable file D EXECUTION The executable file runs the simulation If the user wants to run ACSL with and existing CAMPSL CSL input file simply enter the command ACSLCLG CAMPSL EXECUTABLE FILE OF MODEL EXISTS ON DISK A model that has been simulated with parameter values can be studied further without having to recompile or link The reason for this is that during the TRANSLATION COMPILATION and LINKING stages an EXECUTABLE file with the same name and EXE file type is generated and written to the default disk drive This file is an executable version of the user s model For this reason it can be called and executed as any other executable file 164 4 5 For example if the ACSL system was called with the
90. atements are organized in SECTIONS that start with a keyword and end with an END statement These sections are INITIAL DYNAMIC DERIVATIVE and TERMINAL These sections follow the explicit structure of ACSL input files They are summarized below A more extensive explanation can be found in the ACSL documentation PROGRAM INITIAL Statements performed before the run begins State variables do not have the initial condition values at this point Statements calculated only once prior to the start of a simulation END DYNAMIC DERIVATIVE Statements needed to calculate the derivatives of each INTEG statement The dynamic model Differential equations END Statements executed every communication interval END TERMINAL Statements executed when the termination condition TERMT becomes true END END 156 Statements describing the problem do not need to be sequentially ordered since the ACSL translator will perform a logical sort and generate code that will be compiled and executed sequentially ACSL processes the model input file in three stages A Translation a Compilation and a Run Time stage The translation processes the model file for the Fortran compiler Once the model is compiled the linker produces an executable file that links the model and the ACSL libraries This executable file runs and allows the user to enter the commands to calculate display values and plot graphics output that is used in designing complete systems The expl
91. bal C3 R4 I6 C9 R10 I11 global SF1 global TIME STEP EFFORTS FLOWS This section is needed so this file will recognize the parameters that the user defined in this first file called campgmod m Defining the State Variables System Differential Equations First Order Form S Define State Variables Q9 p q 1 03 p q 2 P11 p q 3 P6 p q 4 This section is need for the next section This section sets the values for the state variables that are used in the equations in the following section 58 Derivative and Output Variable Equations ad ae Define derivatives dp dq and output variables e f fl SF1 e3 03 C3 f6 P6 I6 f7 f6 e9 99 C9 f11 P11 I11 f5 f6 f8 f7 f11 f9 f8 f10 f8 do9 f9 f2 fl f5 f3 f2 f4 f2 e10 f10 R10 dOo3 f3 e4 f4 R4 e8 e9 e10 ell e8 dP11 e11 e2 e3 e4 e5 e2 e7 e8 el e2 e6 e5 e7 dP6 e6 This section contains the equations that define the dynamics of the entire system This section contains the states in derivative form and also contains a single equation for each of the possible outputs Derivative Vector Derivatives vector p qdot dQ9 dQ3 dP11 dP6 This is where the derivative form of the states are all collected into one vector and then sent to the integrating engine Sample for Building Desired Output Vectors Define output vectors efforts flows Sample Structure Add any effort flow or other v
92. campgequ tspan initial status Q11 p q 1 914 p q 2 P9 p q 3 P12 p q 4 State variables vector pq Q11 O14 P9 P12 Sample Matlab structure for plotting simulation results figure 1 subplot 211 plot t p q 1 A b grid axis O 200 0 601 title Height in shorter Surge Tank subplot 212 plot t p q 2 A m grid axis O 200 0 901 title Height in taller Surge Tank figure 2 subplot 211 plot t Efforts 1 1 b grid title Pressure in upper segment of standpipe subplot 212 plot t Efforts 2 1 m grid zoom title Pressure in upper segment of standpipe Note Some of this file was cut out to save space Listing of Campgequ function p qdot campgequ t p q E edu ses campgequ m CAMPG MATLAB function System differential equations state Vectors global I9 R10 C11 I12 R13 C14 vect out global SE1 SE2 SE3 SF8 if t 100 SF8 1 152 oe oe oe de oe oe oe elseif t 100 amp t 100 1 SF8 10 t 1000 else SF8 0 end System Differential Equations First Order Form uie bees Define State Variables O11 p q 1 Q14 p q 2 P9 p q 3 P12 p q 4 State variables vector pq Q11 Q14 P9 P12 T Define derivatives dp dq and output variables e f el SE1 e2 SE2 f9 P9 IO9 e3 SE3 12 P12 112 e4 el e11 011 C11 5 f 9 e6 ell f6 f12 el4 014 C14 f7 f12 e8zel4 f8 SF8 f10 f9 fll
93. can move elements and their attached bonds For example if a 1 or a O junction is moved to different location on the screen its attached bonds will still be connected but their distance to the corresponding elements will be different thus changing the appearance of the bond graph It can be used to make room for new elements of to change the aesthetic appearance of the bond graph model Either a SINGLE section element and its bonds or an entire SEGMENT can be moved to a new location This pull down menu contains a number of files which CAMPG will create upon request When a selection is made you are prompted to input a filename Input any file name and press return The files include LIST EQUATIONS RECORDS AND CONFIG 25 A detailed explanation of each file structure is contained in section 4 0 CAMPG FILES The FILES menu also contains functions which allow you to manipulate existing files CONFIG SESSION LOAD STORE This file stores the SET UP options for the entire CAMPG system It contains settings for selected options There is no need to edit this file unless there is problem with the system Please consult your system manager CAMPG saves the current model under a SESSION BG file so that it automatically loads the last bond graph model that was worked on This selection allows for changing the name of the session file from its default SESSION BG This selection is used to load any existing bond graph
94. can be done quickly and avoiding mistakes by placing these commands in a SETUP file This file can be linked to the ACSL simulation at runtime and ACSL will read and execute the commands in it Several simulations can be done 184 with different parameter values and conditions for executions as well as the great variety of plots that ACSL is capable of generating The user may find more information about this on Section 5 6 and the ACSL reference manual 4 9 Linear System Example Vehicle Crash Test PROBLEM The dummy in the figure shown below is driving his new VW Rabbit into a wall Will his shock absorbing bumper k2 b2 and his seat belts k1 b1 prevent him from hitting the windshield without breaking his collarbone DATA ON INJURIES SAE Handbook Seat belts must be tested to 3000 Ibs 1 334 x 104 N Chest can sustain a force of 1500 Ibs distributed over 30 in Seat belt effective area 30 in Shoulder strap seat belt combination 60 in PHYSICAL PARAMETERS M 1500 Kg ki 1 x 10 N m b 500 N s m m 100kg k 23x10 N m b 8 x 10 N s m 185 Physical System of Dummy in Car Fig 4 11 Seat Belts Design OBJECTIVES 1 Generate an engineering model of a physical system 2 Transform the engineering model of reality into a computer model for simulation using the Computer Aided Modeling Program CAMPO 3 Perform interactive simulation and generate numerical and graphical output using the Advanced
95. ce Torque Voltage Pressure SEF Flow Velocity Ang Vel Current Volume Flow Rate Q Gen Disp Displacement Angle Charge Volume P Gen Momentum Momentum Ang Moment Flux Linkage Pressure Moment TF M Transformer Modulus SE Source Effort GY R Gyrator Modulus SF Source Flow 82 Listing of CAMPGEQU M function p qdot campgequ t p q T quensebuiosqqubes campgequ m CAMPG MATLAB function System differential equations state Vectors global C3 R4 I6 C9 R10 I11 global SF1 global TIME STEP EFFORTS FLOWS System Differential Equations First Order Form Slrckds Define State Variables Q9 p q 1 Q3 p q 2 Pll p q 3 P6 p q 4 State variables vector pq 09 Q3 P11 P6 Suas Define derivatives dp dq and output variables e f 1 SF1 e3 03 C3 f6 P6 I6 f7 f6 e9 09 C9 f11 P11 I11 f5 f6 f8 f7 f11 f9 f8 f10 f8 do9 f9 f2 fl f5 f3 f2 fA f2 e10 10 R10 dQ3 2f3 e4 f4 R4 e8 e9 el0 ell e8 dP11 e11 e2 e3 e4 e5 e2 e7 e8 el e2 e6 e5 e7 dP6z ze6 Build vector of derivatives p qdot n p_qdot1 dQ9 p_qdot2 dQ3 p_qdot3 dP11 p_qdot4 dP6 Derivatives vector p_qdot dQ9 dQ3 dP11 dP6 Define output vectors efforts flows Sample Structure Add any effort flow or other variables to be plotted to the following EFFORTS or FLOWS vectors 83 Activate
96. cking on the two elements This method joins the 0 or 1 junctions with elements as the bond graph is being constructed Causality and power flow are assigned at the same time 21 2 3 CAMPG FEATURES AND MENUS The screen is divided into four sections The top section contains the main menu key words The left vertical icon set section is used to select the different elements The bottom section has a dialogue window and a status window that tells the user what CAMPG is to do next The rest and biggest section of the screen is the area used for the bond graph model display DIALOGUE BOX STATUS BOX QUICK DELETE PULL DOWN MENUS Comments about the current operation are written in the large box in the lower left corner This box located in the lower right corner prompts the user for the next action For example when the user selects the BOND box the STATUS BOX asks him to select the first element to be bonded This allows you to delete elements bonds and their numbers one at a time Just select the DEL box in the lower left hand corner and then click on the items to be deleted The last item can be undeleted by selecting the UND Undo which is also located in the lower left corner CAMPG uses pull down menus located at the top of the screen Fig 2 1 to facilitate bond graph construction and Digital Simulation Language interface A detailed explanation of each menu is shown below in the order in which they appear o
97. components of the gear train 140 3 10 CAMPG MATLAB Hydroelectric Power Plant with Surge Tanks This section will show the user another type of nonlinearity and how to deal with it This will show the user how to deal with a source of flow that is nonlinear POWER PLANT A hydroelectric power plant has a turbine that delivers power when the flow Qo is 1 cubic meter per second When the generator trips off the line Qo is reduced to zero in 0 1 seconds to prevent over speeding There are two surge tanks to prevent excessive pressures in the standpipe OBJECTIVES 1 Design the tanks so that the areas will be such that no overflowing will occur when Qo is shut down 2 If the slope of the standpipe changes how does the surge levels in the tanks change if everything else is held constant To change the slope keep the lengths of the of the standpipe segments the same That means that the change in heights of the standpipe segments will have to change to change the slope of them 3 Generate graphical displays using the computer and show the levels of water in the tanks and the corresponding pressures in the standpipe segments 4 Also use tabular displays to show the peak pressure in the standpipes and the peak height is the tanks 141 Model of Physical System o to Turbine Fig 3 34 Hydraulic Power Plant System DESIGN CRITERIA Careful consideration must go into the modeling of this system when the wate
98. cons and the SYSQUAKE model generated by CAMPG CAMPG WINDOW a Du Template for linear models from CAMP G Bo Camog CAMPG New amples TUTORIA Manual Project Di n bene NM Mew wet variable par standard bond graph parameters ir im variable paro initial values PUE 5 D CH ait F 5 variable A B C D state space linear time invariant model CAMPG Examples Examples MATLAB variable in out index of input and output for transfer WINDOW ACSL MATLAR 7 0 1 r2 i de transfer function model w lower and higher initial values of the g Working Diracton Y My Computer COL I al o Fig 1 14 CAMPG SYSQUAKE interface This is an interesting interface because once SYSQUAKE receives the model from CAMPG the user is presented with a screen for time and frequency 14 response that automatically can be display as the physical parameters change SYSQUAKE allows the user to change the physical parameters by the use of sliders and see immediately the response in the time and frequency domain Chapter 2 CAMPG Basics 2 1 Introduction PURPOSE OF THIS MANUAL The first part of this manual provides an introduction to the many features of CAMPG It begins with a general description of the purpose and capabilities of the package then it provides a detailed description of how to use the software Once completing the example problems outlined in Section 3 and the tutorials of Section 6 the user should
99. converted into a format that can be read and understood by the user If the user desires he she can obtain the transfer functions in numeric format along with the symbolic format that is inherent to this file To do so some modifications to the file must be made If the user does not wish to see the transfer functions in symbolic format they can remove the SYMS command in the beginning of the file and define the variables in terms of their actual values If the user wishes to see the symbolic and the numeric format of the transfer functions this can be done also To do this the user needs to redefine the parameters as their actual numeric value and create another set of A B C and D matrices names something else say AA 66 BB CC DD Then the transfer functions need to be generated But this time they need to be generated twice once for the symbolic matrices and once for the numeric matrices An example of this is seen below Bosius Setting initial conditions Q9IN 0 Q3IN 0 P61N 16763 96 P111N 1117 6 sCreating Initial Conditions vector to be used for simulation IC Q9IN Q3IN P11IN P6IN sSetting the variables to be used for simulation C3 1 300000 R4 80000 16 1500 cC9 1 10000 R10 500 I11 100 SF1 0 sCreating the vectors to be passed to the S function for simulation AA double subs A BB double subs B CC double subs C DD double subs D Generate vector of transfer functi
100. d power flow of the bond graph This file can be submitted for simulation using ACSL following the procedure outline in the previous section 162 4 4 Different Ways to Execute the CAMPG ACSL System The menu explained in section 4 3 offers the user selections to translate compile and run an ACSL model under CAMPG There are three ways to start the CAMPG ACSL model generation and execution files GENERATE A MODEL FOR FIRST TIME A bond graph model is to be described to the computer and an ACSL input file is to be generated from scratch Enter the command CAMPG This invokes the CAMPG software package and allows the user to enter the descriptions of the simulation model using CAMPG graphic capabilities menus and instructions Once the bond graph is complete CAMPG will prompt the user with a menu to select the appropriate actions It will automatically link with an editor for the ACSL input file Complete the model description by inserting the physical parameter values non linearities function calls etc into the CAMPSL CSL model file generated by CAMPG As soon as editing of the input file is complete CAMPG will display a menu that allows the user to continue with compilation and execution Select the option to run ACSL with the input file Automatically the ACSL translation compilation and execution will take place ACSL will then place the user at the ACSL prompt Once at the ACSL prompt the user can enter ACSL commands and st
101. decisions 1 GENERATE THE BOND GRAPH The bond graph model can be created right on the screen or transferred from a model drawn on paper The technical references offer detailed explanation of the method and the methods for generating the bond graph models from real dynamic systems 2 CAMPG The bond graph model is entered using the menu and the mouse Section 3 describes this in detail CAMPG is called by entering the command CAMPG and the user proceeds to draw the bond graph model CAMPG will point out modeling problems using different colors and allowing the user to examine the system equations as the model is entered There are clear indicators on the screen as to the status of the cursor and the actions that the program will take 3 GENERATE AN ACSL INPUT FILE Once the model is completed on the screen and no modeling problems that will prevent the generation of a close form set of equations have been detected the user will select the EXIT button CAMPG will offer the choices to return to DOS or continue and interface CAMPG with a simulation language If ACSL is the language of choice then that button is 183 selected and CAMPG will generate the input file CAMPSL CSL containing all the necessary initial conditions variables parameters time controls and the system differential equations in first order form This form is completely compatible with a state variable form of the system equations 4 ENTER PARAMETER VALUES CA
102. define the nonlinear behavior or parameter values of C I R TF and GY elements Control signals and activated bonds can be also defined this way It is this capability that links the technology of bond graph modeling with a general purpose open ended simulation systems such as ACSL and other simulation languages This provides the system analyst with a tool for simulation of a wide range of multi energy non linear systems PROGRAM CAMPACSL Demonstration of Procedural INITIAL s INITIAL CONDITIONS CONSTANT P2IN 0 0 Q4IN 0 0 TIME CONTROL T TIME CINTERVAL CINT 0 1 CONSTANT FINTIM 15 SYSTEM PHYSICAL PARAMETERS CONSTANT I2 1 5 C4 1 39 478 CONSTANT R5 7 5 END OF INITIAL DYNAMIC DERIVATIVE Use of Procedural allows a set of FORTRAN statements to define the input SF1 The roadway input changes as if the driver hit some big speed bumps PROCEDURAL SF1 T SF1 0 IF T EQ 5 SF1 0 2 IF T GT T SF1 0 IF T EQ 7 SF1 0 5 IF T GT 7 SF1 0 178 END Jor SYSTEM EQUATIONS el e3 f1 SF1 e2 e3 f2 P2 12 e3 e4 e5 f3 f1 f2 e4 Q4 C4 f4 e5 f5 R5 f5 f3 dP2 e2 dQ4 f4 ee STATE VARIABLES P2 INTEG dP2 P2IN Q4 INTEG dQ4 Q4IN TEMINATE CONDITIONS TERMT T GE FINTIM END OF DERIVATIVE END OF DYNAMIC END OF PROGRAM 8 PROCEDURAL EXAMPLE SUSPENSION SYSTEM 0 00 Q4 x1073 0 25 0 50 1 00 SF1 0 00 7 50 11 2 15 0 T SE
103. ds on the type of bond graph being constructed and the ability of the user to use the most familiar method for that person EXIT CUR This menu allows the user to select the simulation language go back to DOS and saves the current model on the screen in a file named SESSION BG TO ACSL CUR Select to generate a file with a model for ACSL 4 CAMPG generates a computer model description and writes a file CAMPSL CSL shown below This file has been edited to include the values of the physical parameters initial conditions and external inputs This input file follows the required ACSL syntax for simulation PROGRAM CAMPACSL s ACSL INPUT FILE TITLE CRASH TEST MODEL INITIAL s INITIAL CONDITIONS CONSTANT Q3IN 0 P6IN 16763 96 CONSTANT Q9IN 0 P11IN 1117 6 TIME CONTROL T TIME CINTERVAL CINT 005 CONSTANT FINTIM 1 0 s SYSTEM PHYSICAL PARAMETERS K CONSTANT C3 000003333 R4 80000 CONSTANT I6 1500 C9 0001 CONSTANT R10 500 I11 100 END OF INITIAL DYNAMIC DERIVATIVE EXTERNAL INPUTS SE F T SF F T SF1 0 192 F2 F1 F5 F1 SF1 E1 E2 ES E2 E2 E3 E4 F3 F2 F4 F2 DQ3 F3 E3 Q3 C3 E4 F4 R4 E6 E5 E7 F5 F6 F7 F6 DP6 E6 F6 P6 16 F8 F7 F11 E7 E8 E11 E8 E8 E9 E10 F9 F8 F10 F8 DQ9 F9 E9 Q9 C9 E10 F10 R10 DP11 EF11 F11 P11 111 Mos STATE VARIABLES Y Q3 INTEG DQ3 Q3IN P6 INTEG DP6 P6IN Q9 INTE
104. e CUR The next three steps clear the session file If you have no previous SESSION BG file These steps are not necessary CUR CUR CUR CUR There is a box on the left icon menu which has the SE symbol in it This is the SOURCE EFFORT element in the bond graph Pick the SE with the mouse CUR Place the SE on the screen by moving the cursor to the middle of the vertical left edge of the drawing screen and a couple of grids to the right and clicking the left button of the mouse The model can start in any location of the screen CUR Pick the 1 junction from the menu on the left and place it two grids to the right of the SE element Both elements are red now 204 CUR You will see on the Status Box the message Bond from and the cursor turned to a small circle and an arrow pointing left Click on the SE element The cursor will change direction as a circle and an arrow pointing right The Status Box reads Bond to Click the cursor on the 1 junction or as close to it as you can The bond that joins the SE element and the 1 junction will be displayed along with a bond number and the causality assignment Note that the 1 is red this indicates the bond graph is not complete Any bond or element in red indicates some difficulty with the graph The user can get an explanation in any case To do this click the mouse on the ANALYZE button choose explain the cursor will change and then click on 1 element The
105. e Entering parameter values oti eti eraot o nuu Running MATLAB redeas pee roce eua dU eren vadeaupel eee Optimizing the Simulation esee iii Step by Step Explanation usce ecco etr ER ERE ERR ARASR 3 6 Linear Example Vehicle Crash Test CAMPGMOD and CAMPGEQU ssssseeII OBICCH VES 1 ids eue Annus citade ERU E NUR beet e made Procedure for solution uie E ER Pees eee CAMP SMOG M Tr D signeritetid si EE R es lls oS EO IE TE POR aes PLUR E De ERE 3 7 Linear Example Vehicle Crash Test CAMPGSYM files and SIMULINK eene Suv RP Procedure for solution caved ave sue te ta PEE OR E UE CAMPG SIMULINK State Space Model Design Criteria i eese rez e xS RENE E RE OE ea bd EE EA YE S RESUS tcs edleste optat uuene e rones D E Ere pn Iced as ae Seas 3 8 Obtaining Transfer Functions eene eus Example Multienergy System Example Physical Model of D C Motor Campgmod m Campgequ m Campesyim an o udis ey e POS Eee e pu TS ETHER MATLAB Simulation and solution of differential equations Transfer Function Step Response eesesss Bode Plot Motor Shaft Velocity Bode Plot Motor Shaft Torque ssesesss Bode Plot Position Angle at Load 3 9 Nonlinear Example Gear Train with Backlash Physical System
106. e Control Beas Simulation Time Control t0 Initial Time tf Final Time tspan tO tf Defining Outputs Ens Define Outputs global TIME STEP EFFORTS FLOWS STEP 1 55 Call to Integration Function and campgequ m t p d ode23 campgequ tspan initial Sample Plotting Commands Sample Matlab structure for plotting simulation results state variables figure 1 subplot 211 plot t p_q 1 b grid title Variable p_q 1 stored in column 1 color blue ylabel p_q 1 units xlabel Time seconds subplot 212 plot t p_q 2 m grid title variable p_q 2 stored in column 2 color magenta ylabel p_q 2 units xlabel Time seconds dP oe dP oe P dP oe oe oe Sample structure for plotting Output Variables as defined in campgequ m 2 Example If the efforts and flows were defined as EFFORTS STEP e5 ell e4 FLOWS STEP f2 9 8 figure 2 Plot ell vs TIME Second column of EFFORTS vector subplot 211 plot TIME EFFORTS 2 b grid title Effort variable of vector EFFORTS 2 stored in column Plot 8 vs time Third column of FLOWS vector subplot 212 plot TIME FLOWS 3 m grid title Flow variable of vector FLOWS 3 stored in column 3 oe CAMPGEQU M This is the file that contains the entire dynamic system This file is called by the first file campgmod m when the
107. e system equations as the model is entered There are clear indicators on the screen as to the status of the cursor and the actions that the program will take References outline in detail the fundamental principles behind the method 3 GENERATE A SET OF USABLE M FILES Once the model is completed on the screen and no modeling problems that will prevent the generation of a close form set of equations have been detected the user will select the Interface menu and then choose Matlab from the drop down menu that appears Once this has been done CAMPG will generate the M files campgmod m campgequ m and campsym m containing all the necessary initial conditions variables parameters time controls and the system differential equations in first order form This form is completely compatible with a state variable form of the system equations 71 4 ENTER PARAMETER VALUES CAMPG will place the user in a position to edit the three files that it generated Now the user needs to enter the values of the initial conditions time control physical parameters nonlinear equations nonlinear functions activated bond specifications signals and any other description necessary to complete the model The formatting and sections of these files along with the purposes and uses have been described in detail in the section called section 3 3 5 RUN Matlab The user runs Matlab using the three files created by CAMPG in the manner that is described in
108. e4 e5 f4 f3 T3x4 e5 KG DEAD 0 1 0 1 Q5 f5 f4 f6 e6 e5 f6 f T6x7 209 e7 e6 T6x7 f7 f8 e8 e7 e9 f 8 P8 18 e9 e10 f9 f8 e10 Q10 C10 f10 f9 f11 ell el0 fl1 P11 111 dPl1l ell dP2 e2 dP8 e8 dQ5 f5 dQ10 f10 Tet STATE VARIABLES Calculate Angles P11 INTEG dP11 P11IN Q2 INTEG F2 0 0 P2 INTEG dP2 P2IN Q8 INTEG F8 0 0 P8 INTEG dP8 P8IN Q11 INTEG F11 0 0 Q5 INTEG dQ5 Q5IN Q10 INTEG dQ10 Q10IN TEMINATE CONDITIONS TERMT T GE FINTIM J CHANGE VARIABLE NAMES F E5 FORCE BETWEEN TEETH W1 F2 ANGULAR VELOCITY OF GEAR 1 W2 F8 ANGULAR VELOCITY OF GEAR 2 W3 F11 ANGULAR VELOCITY OF FLYWHEEL THETA1 Q2 RADEG ANGLE OF ROTATION OF GEAR 1 THETA2 Q8 RADEG ANGLE OF ROTATION OF GEAR 2 THETA3 Q11 RADEG ANGLEOF ROTATION OF FLYWHEEL TWIST QIO RADEG SHAFT ANGLE OF TWIST WD1 DP2 D ANGULAR ACCELERATION OF GEAR 1 WD2 DPS I8 ANGULAR ACCELERATION OF GEAR 2 WD3 DP11 111 ANGULAR ACCELERAITON OF FLYWHEEL END OF DERIVATIVE END OF DYNAMIC TERMINAL END OF TERMINAL TKKK KE K K K K KK Kk Kk k kk kkk KEK K K K eee K KK oi oo P MECHANICAL ELECTRICAL HYDRAULIC x TRANSLATION IROTATIONI M ET mie re A oe reas pe DRIED Se ee eC rR a a e effort force Itorque lvoltage Ipressure 210 Ivolume flow rate f flow Ivelocity lang vel Current q gen disp Idisplacement langle Icharge lvolume p gen mom
109. ecision gear trains requires analysis of forces velocities torques and realistic models considering the tolerances and slack between gear teeth This analysis is important in order to prevent fatigue failure on gear teeth and the transmitting shafts This will contribute to 116 determine the materials size of parts and tolerance adjustments that are related to the generation of contact forces This involves making a dynamic model and performing the analysis of the gear train considering the backlash between the gear teeth The system shown in Fig 3 24 consists of a gear set and a flywheel Gear 1 is driven by a cyclic torque described by a harmonic function The system drives the flywheel through a set of gears having excessive backlash The shaft connecting gear 2 and the flywheel is not rigid it has a tensional spring constant of K 4000 in lb radian Physical System Model of Drive Train I1 0 4 Ib sec g in R1 radius 5 0 in THETA 1 13 0 8 1b sec 2 in SINUSOIDAL DRIVING TORQUE T 100 SIN 20 THETA 2 I2 0 01 Ib sec in R2 10in K TORSIONAL SPRING STIFFNESS OF SHAFT 4000 in Ib rad SCHEMATIC OF GEAR TRAIN SYSTEM THETA 3 Fig 3 24 Gear Train System The contact force between the gear teeth is defined by a dead space non linear function The force increases linearly when the gears are in contact but is zero when they are not Since the input torque is a harmonic function the tee
110. ed in the mdl files that open as the CAMPG SIMULINK interface executes DOSBox 0 72 Cpu Cycles 3000 Frameskip 0 Progra x 3 Editor C Campg working campgnum m File Edit Text Cell Tools Debug Desktop Window Help Pa HN m8oo 8 A7 8 BOM BS se o CAMP G MATLAB Numeric State Space Model campgnum m CAMP G MATLAB functio X Ax Bu gt y CxDu State Space CAMPG SIMULINK File Edit View Simulation Format Tools Help DS U8 B 2C gt fo HesBeshEmTO num den Transfer Fen CAMPG SIMULINK Time offset 0 r 100 start 45 Window Y 5 MATLAB CAMPG WIN Fig 1 13 CAMPG SIMULINK interface with Bond Graph State Space and Transfer Function 13 1 7 The CAMPG SYSQUAKE interface The CAMPG SYSQUAKE follows the same structure of others The user enters the Bond Graph model in graphical form and then chooses the SYSQUAKE interface CAMPG will automatically link to SYSQUAKE as the two programs also share the same working space The SYSQUAKE model keeps the same notation and names of the variables from the original bond graph Shown below is the display of the CAMPG message window and the SYSQUAKE graphics window that is generated as CAMPG directs the SYSQUAKE display There are four windows shown the CAMPG message window the SYSQUAKE graphics window the CAMPG i
111. een Move the cursor to the desired box and click Then move the cursor to the appropriate screen location and click again The element will appear on the screen just beneath the cursor The elements are placed following a grid that allows the bond graphs to be straight and with no distortion The grid can be turned off by the user BONDING Elements are connected with BONDS Move the cursor to the BOND box click and then click consecutively on the two elements to be bonded Power will flow from the first element selected to the second selected element or junction The order in which the mouse is clicked determines the TO and FROM direction The power flow half arrows are displayed with the respective bonds Causality is assigned automatically and both power flow and causality displayed on the screen A complete Bond Graph can be created by placing all of the elements on the screen by selecting them from the vertical menu and moving them to the desired location Next select the BOND box and connect the elements with bonds This method will be known as the SYSTEMATIC METHOD Using this technique it is possible to create any desired bond graph Another technique is the SEQUENTIAL METHOD This means that the bonds are drawn immediately after a junction or an element has been placed To do this place the first two elements Then bond these two by clicking on the first then on the second Now place the third element and bond it to the second by cli
112. el It is obvious in this example that there are two masses involved in the rotational motion the armature and the load seen in Fig 3 14 physical model Since they are coupled together they are not independent motions If we disregard this at first and start to model it as two separate inertia elements the bond graph model will detect derivative causality This bond graph model is seen in Fig 3 5 In this bond graph model inertial elements are represented causing the derivative causality that is depicted by the red I element and the causal mark on that I element Fig 3 6 seen below shows how the derivative causality is represented in CAMPG 104 CAMP G untitled rie ait rnterroce anazuze options meos TT mmm ae na bond from 1 4 5 6 to TF bond 7 bona from TF 7 to 1 bond 8 j ggbond from 1 8 to I bona 9 BOND FROM cffoond from 1 8 9 to R bona 10 Fig 3 16 CAMPG Bond Graph Model The solution is to join both inertial effects Fig 3 17 shows the bond graph model after the fix has been made Most of the literature about motors reveals the calculation of the equivalent inertia but in most cases there is no explanation as to why this is necessary The bond graph model makes this obvious What is significant here is that if one translates the schematic directly a modeling problem is detected Such detection is a property of bond graph modeling methods which predict
113. ere are two methods of building the bond graph in CAMPG 31 One method is called the SEQUENTIAL METHOD and the second one is a SYSTEMATIC METHOD Both of these are discussed in detail below SYSTEMATIC METHOD OF BOND GRAPH CONSTRUCTION The approach is to build the bond graph models by entering all the 1 junctions all O junctions first and then building the bond graph in a structured and methodical manner Power flow and causality assignments are done as the bonds join the junctions 0 and 1 and the physical elements An example of a single degree of freedom system will illustrate this method The following figures show the physical system and the bond graph for the damped oscillator CAMPG will be used to construct the bond graph systematically and create the required ACSL input file Single degree of freedom oscillator Fig 2 2 Physical System 32 C R 3 I 2 e A AIL SE Fig 2 3 Simple Bond Graph This graph was generated using the sequence of actions and commands shown below CAMPG CR space bar CR EDIT CUR Command that starts CAMPG and brings up the logo containing the user name and the license number Please refer to this number for updates This clears the screen preparing it for a drawing Pressing any other character or movement of the mouse will do the same The last SESSION BG file will be automatically displayed if no session file the screen will be blank These
114. es Examples TUTORIAL B Desktop My Documents a e CAMPG Examples Shared Documents WINDOW ACSL CAMPG New Project Di m A p Campg Manual Examples MATLAB MATLAB 7 0 1 MATLAB ufo c 2Wind DOSBox BOND FROM M Be L CAMPG SCREEN al Technical References WOM U Qv 5 42PM CAMPG ACSL working display including the Bond Graph model Window The user can utilize several display options to work with CAMPG ACSL It is suggested the user work with a set of windows that contain the CAMPG console window and the ACSL input files Such displays can look like the figures above 1 9 CAMPG MATLAB Interface The CAMPG MATLAB interface works with a graphics window and a console window When CAMPG is started with the CAMPG Screen icon then the console and the Graphics window are superimposed on one another and only appear in sequence The console window is used to give messages to the user after CAMPG has started the prepossessing of input files to MATLAB The console for CAMPG MATLAB will look like the following figure i CAMPG WINDOW n x al The CAMP G MATLAB model files have been succesfully generated and written to files in the working directory Modify the files named below to complete model Use the MATLAB Editor Windows Notepad or other editor campgmod m Model Parameter Initialization Plot control canpgequ m Model Differential Equations Non linear simulation
115. feel confident about generating a Bond Graph model using CAMPG and performing a simulation using a Digital Simulation Language ACSL for example The manual outlines in Section 5 a detailed description of simulation using the CAMPG ACSL system A detailed explanation of the simulation procedure and runtime commands is given in the tutorials of Section 6 Linear and non linear examples show how ACSL and CAMPG can be used together to solve dynamic systems problems DESCRIPTION OF CAMPG CAMPG Computer Aided Modeling Program with Graphical Input is a graphical preprocessor for Digital Simulation Languages It provides the user with tools to construct a graphic display of a bond graph on the screen CAMPG derives all the necessary equations from this bond graph and writes them to a convenient input file for the requested Digital Simulation Language Generating a bond graph model is relatively simple on CAMPG The user can use the program to build the bond graph from the physical system CAMPG will assign causality and provide descriptions of any 17 errors that might exist in the bond graph In this respect CAMPG acts as a bond graph design tool as well as a Digital Simulation Language preprocessor The modeling and design process is enhanced by the constant monitoring of the model CAMPG features allow the designer to get instantaneous information of the precision of the model because it can detect modeling problems such as derivative
116. file These steps are not necessary There is a box on the left icon menu which has a 1 in it This is the ONE junction in the bond graph Pick the 1 with the mouse Place the 1 on the screen by moving the cursor to the middle and clicking the left button of the mouse The model can start in any location of the screen Now select a C element by clicking the mouse while the cursor is on the C button on the elements menu Place this to the left of the 1 by moving the cursor and clicking the mouse The distance is arbitrary At this point you will see on the Status Box the message Bond from and the cursor turned to a small circle and an arrow pointing left Click on the 1 junction The cursor will change direction as a circle and an arrow pointing right The Status Box reads Bond 36 I CUR CUR 1 screen CUR I screen CUR R CUR CUR 1 screen CUR R screen CUR to Click the cursor on the C element or as close to it as you can The bond that joins the junction and the element will be displayed along with a bond number and the causality assignment Select an I and place it to the right of the 1 Status Box reads Bond from and the cursor turned to a small circle and an arrow pointing left Click on the 1 junction The cursor again changes direction as a circle and an arrow pointing right The Status Box reads Bond to Click the cursor on the I element or as close to i
117. g data that was created during another run of the simulation or during another run of another completely different simulation Used to determine the size of a vector or a matrix Allows the user to specify the format of the numbers that are to be displayed on the screen They can be displayed in scientific format with 4 decimal places with 8 decimal places etc Used to start a while loop Used to start a for loop Used for conditional features or parameters Used for optional conditions Used to end while for if and else statements 70 3 5 CAMPG Matlab Tutorial The following is a summary of the steps that are to be taken to generate a bond graph model from scratch and end up with the final analysis results in the form of calculated values and plots that will allow the engineer to make design decisions 1 GENERATE THE BOND GRAPH The bond graph model can be created right on the screen or transferred from a model drawn on paper The Technical References offer detailed explanation of the methods for generating the bond graph models from real dynamic systems 2 CAMPG The bond graph model is entered using the menu and the mouse This is described in detail later in this document CAMPG is called by double clicking on the icon as described earlier in section 3 2 and then the user can proceed to draw the bond graph model CAMPG will point out modeling problems using different colors and allowing the user to examine th
118. g the method that was described in 2 above pg94 the following flow source input function was created This is an example to verify that the function created does what it is supposed to do It is supposed to be constant at one cubic meter per second for a given time enough time for the system to come to equilibrium Then the function is supposed to go from one to zero cubic meters per second in 1 seconds Finally the flow is supposed to remain constant at zero cubic meters per second indefinitely Seen below in Fig 3 37 is the verification that the input function does what it is supposed to do The listing for the M file that creates this is also shown below Listing of test m counter 1 for t 0 01 200 if t 100 SF8 1 elseif t gt 100 amp t lt 100 1 SF8 10 t 1000 else SF8 0 end SF counter SF8 counter counter t1 end 145 t 0 01 200 plot t SF r ylim 5 1 5 hold on xlabel Time seconds ylabel Volume Flow Rate cfm 1 5 Volume Flow Rate cfm eo eo oa 0 5 50 100 150 Time seconds Fig 3 37 Nonlinear Function 200 After running the Simulink simulation with a few different values for the radius of the tanks the following information in Table 3 and Table 4 was determined Max pressure in Max pressure in Max relative Max relative Radius upper standpipe lower standpipe surge level in surge level in segment segment s
119. ge window 3 3 Files Created During Interfacing and Descriptions When interfacing CAMPG with Matlab CAMPG creates three files that the user uses to run the computer simulation The three files are 1 campgmod m 2 campgequ m and 3 campgsym m These files are very useful as will be seen below This is a description of the structure of each of the files along with a description of how to implement and how to modify these files to model the system correctly The first two files mentioned are used in conjunction with each other while the third file is used by itself The first file is the main 50 simulation file while the second file is a simple function file that contains the entire dynamic system for the bond graph model The first file is run from the Matlab command prompt When it runs it sets all the initial conditions bond graph elements inputs and the time interval Then it calls the second file during the integration process and calculates the integrals over the set time span Then it outputs the desired data in a graphical format i e a graph The third file is usually used by itself This file specializes in determining the transfer functions This file uses the state space form seen below y Ax Bu y Cx Du All the user needs to do is to un remark the appropriate lines and then input the desired number for the row that it will create in the state space matrix NOTE There is one other file that CAMPG creates T
120. gnals internal to the model not just a single output Bode Plot Load Angular Velocity Bode Plot Load Angular Velocity 70 80 90 20 Phase deg Magnitude dB 40 60 80 A 0 1 10 10 10 10 Frequency rad sec 114 Fig 3 21 Frequency Response Bode Plot Motor Shaft Velocity Fig 3 22 Bode Plot Motor Shaft Torque Phase deg Magnitude dB Phase deg Magnitude dB 20 40 60 80 40 50 60 70 o 10 10 10 Bode Plot Motor Shaft Velocity Bode Plot Motor Shaft Velocity 1 Frequency rad sec Bode Plot Motor Shaft Torque Bode Plot Motor Shaft Torque 12 12 5 13 13 5 14 o 10 10 10 1 Frequency rad sec 115 Bode Plot Position Angle at Load Bode Plot Position angle at load 40 60 Fig 3 23 Bode Plot Motor Shaft Torque 80 100 120 100 120 Phase deg Magnitude dB 140 160 180 Baname 1 0 1 10 10 10 10 Frequency rad sec This example illustrates how to obtain transfer functions with the CAMPGSYM M file It also is a very good example of how to deal with multienergy systems The next section will explore other possibilities with nonlinearities and Matlab 3 9 Nonlinear Example Gear Train with Backlash PROBLEM Design of pr
121. gtfn mdl CAMPG SIMULINK transfer function campgsst m CAMPG SIMULINK State Space Form These will open automatically when SIMULINK starts You can also open them indepedently by entering campgsimulink cag2sim at the MATLAB prompt key to continue Fig 1 12 CAMPG SIMULINK Console and messages display These files describe the model for SIMULINK Since SIMULINK and MATLAB share the same working space the initialization parameters in the CAMPGINI M file initialize not only the physical parameters for simulation but also CAMPG has set up the initialization of the system A B C D matrices Keep in mind that these are generated in symbolic form and can be used that way to program hardware in the loop These are initialized in the work space and their values are transferred to the SIMULINK state space blocks The CAMPGNUM M generated the transfer functions which are also initialized on the SIMULINK transfer function block The model transferred from CAMPG to SIMULINK in the state space form follows the same order of the state space vector as the state variable vector generated in CAMPG and displayed in the CAMPGINI M file and in the CAMPGNUM m file The rows of those matrices correspond to the rows of the state variable vector generated in those two files The State Space Model in SIMULINK requires two additional blocks Multiplexer for the input vector and a Demultiplexer for the vector of outputs Both of these are already includ
122. he flywheel top plot Changes are smoother in the shaft velocity since this is a capacitive element and therefore stores energy Mathematically this element performs integration of W3 and therefore eliminates the noise seen in that function This change is obvious between WD3 in Fig 3 28 and W3 in Fig 3 29 Theta 3 80 60 40 n M11 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 Theta 2 100 50 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 Theta 1 15 10 5 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 Fig 3 30 Position Angles Figure 3 30 This figure compares the position angle of rotation of the gears and the angle of twist of the shaft It shows the geometrical configuration of the gear train It can be seen from this figure how the gear 137 train starts to move in one direction while the angle of twist in the shaft changes to 2 to 2 degrees x 10 2 1 0 Ll T 2 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 E10 200 100 0 100 200 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 x 10 4 2 co 9 0 o Wwe 2 4 0 2 0 15 0 1 0 05 0 0 05 0 1 0 15 Q5 Figure 3 3 Torque Display Figure 3 31 Shows the torque at the input gear This plot is similar to the one of the acceleration The relationship can be explained by Newton s Law in
123. he input is a torque a causal effect is the acceleration and velocity of the gears These variables are affected by the discontinuity of the contact made among the gear teeth The plot at the bottom is the plot shows that gear 1 is accelerating under a basic harmonic function but the positive and negative peaks are accelerations and decelerations due to the dynamics of the geartrain The figure in the middle is the plot of the acceleration of Gear 2 It is an order of magnitude bigger and contains higher peeks of acceleration and deceleration This can be explained due to several factors The most influential ones are the gear ratio and the separations and sudden contact that the gears experience at a high frequency The acceleration at the flywheel is affected by the stiffness of the shaft it is lower in this case because the shaft is flexible zo Fig 3 29 Angular Velocities Figure 3 29 This figure shows the angular velocity of the gears and also of the flywheel The bottom figure shows a nonlinear function while the 136 flywheel velocity appears as a periodic function The changes in velocity of gear 2 occur at a high frequency This is due to the vibration of the gear train on both sides of gear 2 and rapid changes in the motion of gear 1 and the backlash between gear teeth The influence of the compliant shaft is seen in the plot of the angular velocity of t
124. he screen O screen CUR Click on the same 0 1 screen CUR Click on the lower left 1 on the screen There should be now have 2 bonds on the screen Continue this process until the rest of the bonds have been created Notice that some of the bonds are red just after they are placed This means that the system detects an error in the bond graph construction These errors while the bond graph is being assembled are simply warnings to the user that the bond graph is not a close form system but rather some bonds are not complete yet They also tell the user that the causality can not be completed up to that point If these errors continue after completion of the bond graph it means that there are loops derivative causality or incomplete bonds that will prevent the generation of a close form system of equations The user needs to investigate and correct it The errors can be determined by inspection of the bond graph or with assistance from CAMPG Click on ANALYZE then EXPLAIN and then once again on the red bond or element The DIALOGUE BOX will provide an explanation of the error Most likely the error will disappear after the bond graph has been completed This feature is excellent to assist in defining correct bond graph models The user has now completed the bond graph model You can look at the equations using ANALYZE and PEEK This can be done by selecting PEEK under the ANALYZE button the cursor will change to the eye 7
125. he user to compare variables in the bond graph plot them separately change the scale color type of lines etc A summary of these options include XHI TSTP Specifies the time limit for the values to be plotted The time in turn specifies the length on the X axis XTAG SEC Prints the tag SEC on the X axis LO Lower limit for the Y axis HI Higher limit for the Y axis TYPE n Specifies color for line plots STRPLT Requests strip plots GRDSPL Draws lines from each tick mark on the axes YASSPL Separation between strip plots XTICPL X axis tick increment in inches for line plots XTISPL Also X axis tick increment but for strip plots XINCPL X axis length in inches for line plots XINSPL Same but for strip plots The values of the last five parameters may be different for each type of terminal and the printer attached to them reference the ACSL manual for more details and more options The following examples illustrate some of the plotting capabilities available to the user on ACSL Some of the commands are applicable to all subsequent plots and the user should note this with some practice Each plot shows the command that was used to generate it 169 e PLOT Q2 Generates a line plot of Q2 versus time with automatic scaling and no axis label T is the independent variable because it was the first variable in the PREPAR command 0 06 0 00 6 90 16 0 I 24 0 32 0 40 0 Fig 4 3 Shows
126. hey are shown by them selves below F Q5 W1 W2 W3 Thetal Theta2 Theta3 Twist Wdl Wd2 Wd3 Obtained by plotting the Force on the teeth vs the distance between the teeth Q5 Obtained by plotting Q5 vs Time Obtained by plotting F2 vs Time Obtained by plotting F8 vs Time Obtained by plotting F11 vs Time Obtained by plotting Q2 360 2 pi vs Time Obtained by plotting Q8 360 2 pi vs Time Obtained by plotting Q11 360 2 pi vs Time Obtained by plotting Q10 360 2 pi vs Time Obtained by plotting E2 360 2 pi I2 vs Time Obtained by plotting E8 360 2 pi I8 vs Time Obtained by plotting E11 360 2 pi I11 vs Time 132 SEI Obtained by plotting 100 sin 20 Time vs Time E2 Obtained by plotting E2 vs Time E10 Obtained by plotting E10 vs Time 7 MODIFICATION OF CAMPGMOD M IN SIMULATUON Using Matlab interactively is very useful and the designer gains an insight of the system and its performance as well as modeling errors The numerical and graphical results can be obtained very quickly and without much typing of commands and specification for plots if these specification are typed into the CAMPGMOD M file The commands added to the CAMPGMOD M file shown below were used to study the dynamic performance of the gear train Once these commands are added to the file plots are automatically generated each time the user runs the simulation The plotting output commands are shown below Figu
127. his file is called esandfs m This file is not created every time CAMPG is interfaced with Matlab it is created once during installation of CAMPG The location of this file is seen below lt source drive gt matlab toolbox matlab general esandfs m The purpose of this file will be described later in this section CAMPGMOD M This file is used in conjunction with the file called campgequ m After CAMPG has been interfaced with Matlab this file is created 51 The user only needs to make a few minor changes to this file to make it usable The user must do the following 1 Enter the values for the bond graph elements 2 Enter the values for the inputs 3 Enter the simulation time interval 4 Create the plotting commands to plot what is required to be monitored Once these 4 things have been done the simulation can take place This example listing is the listing for the linear example that is seen in section 3 7 The only difference between this listing and the one seen in section 3 7 is that this one has not yet been edited by the user This is exactly the way this file would look just after the interfacing with Matlab has been done As seen here the sections of the file are very clear and straight forward Listing of campgmod m CAMPG MATLAB GENERATED MODEL DESCRIPTION The following files have been generated campgmod m gt m file containing model parameters intial conditions sources and simulation controls ca
128. hort surge tank long surge tank 0 2 meters 154 770 Pa 103 600 Pa 58 25 meters 89 04 meters 0 3 meters 92 735 Pa 64 498 Pa 52 15 meters 83 00 meters 0 4 meters 63 208 Pa 46 689 Pa 50 26 meters 80 29 meters 0 5 meters 45 928 Pa 35 305 Pa 50 00 meters 80 29 meters Table 3 3 146 Change in Max pressure in Max pressure in Max relative Max relative height upper standpipe lower standpipe surge level in surge level in segment segment short surge tank long surge tank 15 meters 53 160 Pa 64 500 Pa 37 15 meters 53 00 meters 30 meters 53 160 Pa 64 500 Pa 52 15 meters 83 00 meters 45 meters 53 160 Pa 64 500 Pa Overflow Overflow Table 3 4 Height in Surge Tanks with Radius of 4 meters 60 Height in shorter Surge Tank 40 20 0 20 40 60 80 100 120 140 Height in taller Surge Tank 200 40 60 80 100 120 140 160 Fig 3 38 Height display 180 200 147 Pressure in Stand Pipes with Surge Tank Radius of 4 meters x 10 Pressure in upper segment of standpipe 2 Fig 3 39 0 Pressure Plots 2 4 6 0 20 40 60 80 100 120 140 160 180 200 x 10 Pressure in upper segment of standpipe 1 0 ii m CN 1 2 3 0 20 40 60 80 100 120 140 160 180 200 Water Height in Surge Tanks with Radius of 3 meters Height in shorter Surge Tank 60 Fig
129. ices corresponding to states p sand q s s dP9 SE 1 R2 G3x4 T7x8 P9 19 T7x8 G3xA4 R2 G3x4 T7x8 P9 19 T7x8 R6 T7x8 P9 I9 R10 A 1 1 I9 R10 B 1 A 2 B 2 D 3 1 19 T7x8 G3xA4 R2 G3x4 T7x8 1 19 T7x8 R6 T7x8 0 Ae 1 R2 G3x4 T7x8 0 1 19 0 0 0 1 R2 G3x4 0 Generate C and D matrices correspoding to outputs e s and f s 9 P9 19 109 C 1 1 I9 0 D 1 0 0 7 P9 19 T7x8 C 2 1 19 T7x8 0 D 2 0 0 e7 SEl1 R2 G3x4 P9 1I9 T7x8 G3xA4 R2 G3x4 P9 19 T7x8 R6 C 3 1 19 T7x8 G3x4 R2 G3x4 1 19 T7x8 R6 0 D 3 1 R2 G3x4 0 stheta as an output C 4 0 1 D 4 0 0 A B C D Define SI matrix syms s Find the size of A and then figure out I I eye 1 Transfer Functions Matrix H H C inv s I A B D pretty collect H N1 100 N2 1000 R2 2 G3x4 2 R6 2 T7x8 N1 N2 I92700 45 N1 N2 2 R10 800 AA double subs A BB double subs B CC double subs C DDzdouble subs D oe Frequency Response Bode Plots iu 1 num den ss2tf AA BB CC DD iu printsys num den s bode num den time 0 01 3 110 w 1 1 100 figure 2 subplot 211 step num 1 den time grid title TF Step response Angular velocity of armature and load subplot 212 step num 4 den time grid title TF Step Response Pos
130. icit structure shown above is used to organize complex model descriptions CAMPG generated models follow this structure Model Description Procedure Each expression that describes a block diagram differential equations or each algebraic expression representing the equations throughout the entire bond graph are placed in the ACSL input file in a form that follows FORTRAN assignment syntax The lines of code can contain 80 characters The first 72 columns are for program instructions and the rest for identification purposes The expressions however follow free format description Statements can be written anywhere on the line from column 1 to 72 in free format form but it is a good practice to arrive at some standard to preserve the order and appearance of the text More than one statement can be entered in one line Statements can be continued on the next line by adding three consecutive periods at the end of the current line The following are helpful considerations 157 Comments can be made by enclosing them in double quotes More than one statement can be placed on one line by separating them by a dollar sign Blank lines can be inserted as desired Text editor line numbers must not appear in the model definition program 4 2 Running ACSL Using Differential Equations and Functional Blocks Running a Basic ACSL Model Let the mass of 0 02 kg be initially displaced 0 04m at time zero held and then
131. ick the mouse on any element junction or bond The equations for that junction bond or the constitutive relations of the physical elements will be displayed Once the bond graph is completed CAMPG is ready to process the model to generate the Matlab files discussed earlier in section 3 3 93 This example showed how to use the STICKY feature and the SYSTEMATIC METHOD The bond graph could also have been created by the SEQUENTIAL METHOD This means connecting the elements immediately after they were placed on the screen instead of at the end The elements and bond are laid out sequentially Both of these methods create the same end product and the relative efficiency of each depends on the type of bond graph being constructed and the ability of the user to use the most familiar method for that person INTERFACE CUR From this menu the user can select the simulation language go back to DOS or Windows and saves the current model on the screen in a file named SESSION BG MATLAB CUR Select to generate the Matlab model and simulation files 4 CAMPG generates a computer model description and writes the files CAMPGMOD M CAMPGEQU M and CAMPGSYM M Only the CAMPGSYM M file is shown below Section 3 7 uses the CAMPGMOD M and CAMPGEQU M files see that section for a complete example of using those files This file has been edited to include the values of the physical parameters initial conditions and external inputs Since in this example the
132. ight of the 1 junction CUR Status Box reads Bond from and the cursor turned to a small circle and an arrow pointing left Click on the 1 junction The cursor again changes direction as a circle and an arrow pointing right The Status Box reads Bond to Click the cursor on the 1 junction or as close to it The bond that joins the junction and the element will be displayed with its corresponding bond number one higher than the previous one and causality assignment 0 CUR Pick a 0 junction place it to the right of the TF TF screen CUR O screen CUR This should create a bond from the TF element to the 0 junction C CUR Select an C and place it below the 0 O screen CUR Click on the 0 element on the screen C screen CUR Click on the C element on the screen A bond should appear between these two elements TF CUR Select TF and place it to the right of the 0 junction 0 screen CUR TF screen CUR This should create a bond from the 0 junction and the TF element The number of the bond 123 will appear in the middle of the bond as it has for all the other bonds 1 CUR Pick a 1 junction from the menu and place it to the right of the TF6x7 TF screen CUR Click the mouse on the TF for FROM status 1 screen CUR Click on the 1 junction Note again that the numbers of the bonds appear automatically in the middle of the bonds In this case 7 I CUR Click on the I icon
133. in campgmod m suggested structure of graphical output TIME STEP 1 t Define time vector EFFORTS STEP e11 Define efforts vector FLOWS STEP f2 9 8 Define flows vector STEP STEP 1 In campgmod m the following structure is included Sample structure for plotting Output Variables as defined in campgequ m Example If the efforts and flows were defined as EFFORTS STEP e5 ell e4 FLOWS STEP f2 f9 f8 figure 2 Plot ell vs TIME Second column of EFFORTS vector subplot 211 plot TIME EFFORTS 2 b grid title Effort variable of vector EFFORTS 2 stored in column 2 Plot 8 vs time Third column of FLOWS vector E subplot 212 plot TIME FLOWS 3 m grid title Flow variable of vector FLOWS 3 stored in column 3 The causality and power flow can be verified since CAMPG will generate the bond graph causality and power flow tables shown below in the CAMPGMOD M file These can stay in the file since they do not interfere with the function of the file since they are remarked out S He e ke ke e e e e ke kk ke e e e ke KKK KEK Beebe eee BOND GRAPH ANALYSIS ck He ce ke ck ke ke se ke ke ke ck ke ke k k k SSYSTEM DESCRIPTION POWER FLOW BOND oe l l l l dP oe dP dP dP oe oe oe 0 OU i WNE FROM TO SF 1 Q 1 2 5 01 2 5 1234 12 34 c3 12 34 RA 0125 1516 7 15 67 TG 1 5 6 7 0 7 8 11 0 7 8 1
134. in more detail below QUICK DELETE Use of this button will delete an element a bond a loose element of or bond junction The user clicks the mouse on this button the cursor will change for this mode and then the user picks the element or junction to be deleted by clicking the mouse on that location 38 EDIT DELETE The DELETE button under the EDIT menu allows for several selections DELETE SINGLE for just one element GROUP to delete an element I C R TF GY 0 1 and all its attached bonds at the same time SEGMENT will delete the whole structure attached to the selected element or junction Finally ALL will delete every bond graph existing on the screen at the time Clears the whole screen 2 5 Interfacing with a Digital Simulation Language ACSL INPUT FILE PREPARATION CAMPG can be used as a preprocessor for Digital Simulation Languages or the user s own program As such it creates the necessary input files for these languages Selection of the EXIT menu of CAMPG upper left hand side will display the different languages for which CAMPG will create an input file in source code form Select the appropriate digital simulation language by clicking the mouse on the appropriate box The required input file will be created and placed in your directory The menu with the selection of the Simulation Language 39 CAMPG simulation language interface menu CAMP G session options eoe TI vU MATLAB SIMULINK 29
135. in position where the teeth are not in contact but increases proportionally to the displacement after contact has been made Using this nonlinear relation and a cyclic input torque it is important to find the torques generated internally on the gears and the shaft due to the dynamics of the system It is necessary to find values and graphical plots for the design variables such as angles angular velocities accelerations and the dynamic forces acting on the different components These will assist the designer to prevent fatigue failure because now the stress levels can be calculated The position of the gears is important to calculate as knowledge of the angular displacements can assist in satisfying geometric constraints and determining the acceptable backlash 134 RESULTS The results of the calculations are shown in the following figures They show plots of the angular velocities angular accelerations and torques and all other design variables of interest established in the design criteria Other variables can be calculated or plotted besides the ones explained in the design criteria and plotted below because CAMPG has generated all internal variables and all were calculated as a result x 10 WD3 o I iM ANN LU TT NAM M Muti WIRE il Wi Ty APUD PUELLA Fig 3 28 Angular Acceleration 135 Figure 3 28 Since t
136. in the menu Place the I above the last 1 junction 1 screen CUR I screen CUR Generates a bond between the 1 and the I element 0 CUR Pick the 0 from the menu place it the right of the last 1 junction 1 screen CUR 0 screen CUR Draws a bond between 1 and the 0 junction C CUR Pick C from the menu and place it below the last 0 junction 0 screen CUR C screen CUR Generates bond between 0 and C I CUR Pick I and place it to the right of the 0 junction 0 screen CUR 124 I screen CUR This step completes the bond graph by drawing a bond from the last 0 junction to the I element Now the whole bond graph can be moved to the right to have it on the center of the screen This is done with the following steps EDIT CUR Pick the EDIT button and select the MOVE button There will be two choices SINGLE and SEGMENT Pick SEGMENT SEGMENT CUR The cursor will change shape to a cross Click the mouse on the SE element it can be any other element or junction The bond graph segment will turn blue CUR Move the cursor to the desired new location for the element picked The bond graph will be redrawn in the new location All junction and elements have their corresponding bonds numbers and causality marks If there is any one bond or element on the screen that it is red use the ANALYZE button and pick EXPLAIN then click on the red bond or element A message on
137. indow EP CAMPSL CSL Notepad File Edit Format View Help THIS IS A CAMP GENERATED MODEL DESCRIPTION 1 EDIT THIS FILE ENTER VALUES OF PHYSICAL PARAMETERS INITIAL CONDITIONS INPUTS AND TIME CONTROLS IN PLACES WHERE THE QUESTION MARKS APPEAR 2 FOR NON LINEAR SYSTEMS REPLACE THE LINEAR RELATIONS BY NON LINEAR FUNCTIONS FOLLOWING THE PROPER CAUSAL RELATIONS 3 THE TABLE BELOW PROVIDES A GUIDELINE FOR PHYSICAL MEANING OF GENERALIZED VARIABLES USED IN BOND GRAPH NOTATION INPUT FILE INITIAL INITIAL CONDITIONS CONSTANT Q19IN CONSTANT P3OIN CONSTANT Q10IN CONSTANT Q16IN CONSTANT Q24IN CONSTANT Q27IN Q47IN P32IN CONSTANT P31IN CONSTANT PAIN P5O0IN CONSTANT PSIIN 77 PS2IN 77 TIME CONTROL T TIME Fig 1 6 CAMPSL CSL input files The CAMPG ACSL model f and written in the les have been succesfull Edit Fil Use Window amps 1 cs 1 Notepad or te the input canpsl csl is the model input to ACSI y hey to continue prs ME114 F Granda s m voyager e K gVim Easy ETT EIE 1277 3 RCSL model fil e been succesfully generated and written in the working directory Edit file to complete the input model to ACSL Use Windows Notepad or other editor campsl csl is the model input to ACSL any key to continue P CAMPSL CSL Notepad File Edt Format View Help THIS ISA CAMP GENERATE
138. ique to windows XP as it checks the communication ports Click on ignore and the program will execute normally CAMPG by default uses a working directory with name c Campg Working when the program is started with any of the icons above You can use this Icon to create a different working directory for a new project When you use this a New Project Working directory is created under c Campg Working directory and also in the Desktop This gives you the opportunity to work either on the new working directory on the desktop of the c Camg Working New project directory or in the desktop You can change the name of this directory or move it to a new location you want To activate CAMPG with this New Working Directory click on the session file or other bg file in this directory and enter your new Bond Graph Model in CAMPG This icon is used to look at the CAMPG documentation This manual in PDF format is available to the user Double click on this and if you have the Adobe Acrobat reader installed on your computer you will be able to see this entire manual electronically id CAMP G TUTORIAL qm Ll Examples ACSL Examples MATLAB Technical References CAMPG has a tutorial on line also The tutorial will appear in form of a local Web page with links to follow and point out to the different instructional presentations This icon points to the Bond Graph Examples directory with contain a set of bg files with are bond graph exa
139. ition Angle at load xlabel time sec figure 3 bode num 1 den w title Bode Plot Load Angular Velocity figure 4 bode num 2 den w title Bode Plot Motor Shaft Velocity figure 5 bode num 3 den w title Bode Plot Motor Shaft Torque figure 6 bode num 4 den w title Bode Plot Position angle at load Send The transfer functions in the s domain that were obtained from the CAMPGSYM M file are as follows num 1 den 0 0035712 s S 2 1 4463 s num 2 den 0 035712 s s42 1 4463 s 111 num 3 den 0 25 s 2 0 28569 s s 2 1 4463 s num 4 den 0 0035712 S 2 1 4463 s Shown in Fig 3 18 and Fig 3 19 are two different computations of the system The top of Fig 3 8 is the direct time simulation results obtained by the integration of the differential equations generated in logical sequence and integrated within MATLAB The bottom of Fig 3 19 is generated by the use of the step input on the transfer function generated from the symbolic A B C D matrices generated from the bond graph The figure on the bottom of Fig 3 19 is exactly that of the top of Fig 3 18 for the position angle The other one corresponds to the angular velocity of the armature and load f9 shown at the bottom of Fig 3 183 and corresponding to the top figure of Fig 3 19 This verifies the results not only of the simulation but also of the computer genera
140. lar bone DATA ON INJURIES SAE Handbook Seat belts must be tested to 3000 Ibs 1 334 x 10 N Chest can sustain a force of 1500 lbs distributed over 30 in Seat belt effective area 30 in Shoulder strap seat belt combination 60 in PHYSICAL PARAMETERS M 1500 Kg k 1 x 10 N m b 500 N s m m 100kg k 23x10 N m b 8 x 10 N s m 73 Physical System of Dummy in Car k1 m a mE ww C Fig 3 6 Seat belt design dynamic model OBJECTIVES 1 Generate an engineering model of a physical system 2 Transform the engineering model of reality into a computer model for simulation using the Computer Aided Modeling Program CAMPO 2 Perform interactive simulation and generate numerical and graphical output using Matlab 4 Interpret the results make design decisions and perform simulation of several models in an interactive way PROCEDURE FOR SOLUTION Construct an engineering model of the crash test and consider only the time when the bumper is in contact with the wall Fig 3 6 shows the engineering model of the crash test 74 2 Generate a bond graph model A bond graph model for this system is seen in Fig 3 7 3 Enter the Bond Graph description into the CAMPG program Fig 3 8 shows the CAMPG screen that was generated after entering the bond graph model Bond Graph Model I M Ey 6 Car 7 Wal sp 15 9 3 1L 5 0 H41 m Dummy p 8 j 1 1 PA x pA io C
141. le has been broken down into easier to see sections Some of the file was excluded from this second listing This was done because the only parts that are going to be shown here are the parts that the user may have to change Converting Physical Parameters to Symbols Convert system physical parameters and system matrices to symbols syms C3 R4 I6 C9 R10 I11 This section is needed to convert the physical parameters to symbols This is done so the transfer functions will all be symbolic The matrices that are created will also be symbolic Creating A and B Matrices in Terms of the States Generate A B matrices corresponding to states p sand q s Dan dQ9 P6 16 P11 111 A 1 0 0 1 111 1 16 B 1 0 dQ3 SF1 P6 I6 A 2 0 0 0 1 16 B 2 1 dP11209 C9 P6 16 R10 P11 I11 R10 A 3 1 C9 0 1 I11 R10 41 I6 R10 B 3 0 dP6 03 C34SF1 RA4 P6 16 R4 09 C9 P6 16 R104 P11 I11 R10 A 4 1 C9 1 C3 1 111 R10 1 16 R4 1 16 R10 B 4 1 R4 64 This section is the section were the A and B matrices are actually created The A and B matrices are used in the format y Ax Bu Where x is the state vector and u is the input vector The states are the P s and Q s and the inputs are the sources Creating C and D Matrices in Terms of the States Generate C and D matrices correspoding to outputs e s and f s 1 SF1 C 0 0 0 0 D 1 e3203 C3
142. led Lie f eare rncereoce anauze options meros CTI 4 e HTF move segment SF 19 marked done SF_100 marked done 0 18_19_25 marked done BOND FROM storing to multisust bg done Fig 5 11 Simultaneous Simulation of two unrelated systems In the file called CAMPGEQU notice the differential equations that describe the two systems Notice the two systems are both described in the set of equations and also notice that since we used the user definable numbering in CAMPG that indeed the set of equations represents both dynamic systems Listing of CAMPGMOD M pee ane CAMPGMOD M MATLAB MODEL INPUT FILE 236 P9IN 0 P12IN 0 Q11IN 0 Q14IN O P102IN 16763 96 P1041N 1117 6 Q107IN 0 Q109IN O initial Q11IN Q14IN Q109IN Q107IN P9IN P12IN P104IN P102IN Beg op Gia System Physical Parameters global I9 R10 C11 112 R13 C14 1102 1104 C107 R108 C109 R110 global Efforts counter I9 1000 50 1 R10 100000 C11 A 1000 9 8 I12 1000 50 1 R13 100000 C14 A 1000 9 8 I102 1500 1104 100 C107 1 300000 R108 80000 C109 1 10000 R110 500 Bi ode serus External inputs se t sf t global SE1 SE2 SE3 SF8 SF100 SE1 1000 9 8 20 SE2 1000 9 8 20 SE3 1000 9 8 20 SSF8 Will be defined in CAMPGEQU file SF100 0 7 TERET Simulation Time Control t0 0 Initial Time tf 200 Fi
143. letion of the bond graph it means that there are loops derivative causality or incomplete bonds that will prevent the generation of a close form system of equations The user needs to investigate and correct it The errors can be determined by inspection of the bond graph or with assistance from CAMPG Click on ANALYZE then EXPLAIN and then once again on the red bond or element The DIALOGUE BOX will provide an explanation of the error Most likely the error will disappear after the bond graph has been completed This feature is excellent to assist in defining correct bond graph models The user has now completed the bond graph model You can look at the equations using ANALYZE and PEEK This can be done by selecting PEEK under the ANALYZE button the cursor will change to the eye Click the mouse on any element junction or bond The equations for that junction bond or the constitutive relations of the physical elements will be displayed Once the bond graph is completed CAMPG is ready to process the model to generate an input file for ACSL This example showed how to use the STICKY feature and the SYSTEMATIC METHOD The bond graph could also have been created by the SEQUENTIAL METHOD This means connecting the elements 191 immediately after they were placed on the screen instead of at the end The elements and bond are laid out sequentially Both of these methods create the same end product and the relative efficiency of each depen
144. ll should not occur 4 Ifhe travels without a seat belt How long does it take for him to hit the windshield at 25 mph 40 mph and 55 mph What is the force acting on him on impact at 25 mph 40 mph and 55 mph RESULTS The results obtained from the simulation can be obtained in the form of numerical values or in the form of plots of variables as a function of time Several designs with different kind of bumpers and shock absorbers were tried These simulations allow the user to make an optimum decision to satisfy the design requirements The user is able at this point to decide which is the best design and why One can perform as many simulations as the user thinks are necessary In this case it was found from Fig 3 9 that at 25 mph the dummy did not hit his head on the windshield Its maximum displacement was 0 81m Less than the 1 00 m allowed It was found from Fig 3 10 that the force acting on his body was 9 310 newtons However this is enough to produce chest injury The maximum limit allowed is 6 688 newtons No failure of the seat belts occurs since they can resist a load of 13 340 newtons 86 Force N Distance the Dummy s head travels 0 4 0 2 0 ra o s 02 E co e S 0 4 E a 0 6 0 8 1 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 Time seconds Fig 3 9 Head Displacement Force Acting on the Dummy 5000 0 5000 10000 0 0 1 0 2 0
145. mand EIGEN calculates the Jacobian and then evaluates and lists the complex eigenvalues and optionally the eigenvectors If used the EIGVEC sub command should precede EIGEN as it determines whether eigenvectors are to be calculated Once set EIGVEC stays defined until explicitly changed The sub command JACOB calculates the Jacobian about the current point in state space by numerical perturbation The result is then printed out as a large matrix The ACSL Ref 4 manual contains a complete listing of ACSL operators and other run time commands FORTRAN SUBROUTINES Any user defined FORTRAN function or subroutine may be used in the simulation input file by including it following the END statement that matches the PROGRAM statement The translator looks for the following REAL FUNCTION INTEGER FUNCTION LOGICAL FUNCTION SUBROUTINE FUNCTION PROGRAM 182 4 8 Once one of these key words is found it assumes all the rest of the lines in the model definition section are to be passed directly to the FORTRAN compiler The format of these statements is not changed in any way so FORTRAN format must be followed exactly i e start in column seven or beyond etc CAMPG ACSL Tutorial The following is a summary of the steps that are to be taken to generate a bond graph model from scratch and end up with the final analysis results in the form of calculated values and plots that will allow the engineer to make design
146. mand will tell ACSL to save the values of time T displacement Q2 velocity F3 and force E3 These variables are calculated and could be plotted later Place the independent variable usually time T first because ACSL uses this information in the plotting routine to define the X axis If an output listing of values of any variable is to be displayed as the simulation goes on use the OUTPUT command followed by the list of variables For Example ACSL gt OUTPUT T Q2 F3 E3 This requests ACSL to display the numerical values of these variables on the screen and write them to the ACSL output data file The simulation will start with the command ACSL gt START Once the simulation and all requested calculations have been performed ACSL will come back with the prompt ACSL gt RUNTIME CHANGES TO PHYSICAL PARAMETER VALUES Changes to the physical parameter values can be made at runtime without the need to edit again the input file For example to change the value of the mass M or any constant value during simulation use the command ACSL gt SET M 0 06 166 This changes the value of the mass without having to go through the editing of the input file or he whole translation and compilation procedure again The next time the START command executes the simulation again M will be 0 06 until changed again The source file that describes the model is not modified ACSL needs to perform the simulation with the new values agai
147. marked done Fig 5 6 Complex multiports fields USER CONTROLLED NUMBERING The user has the option of specifying the number of the bond graph bonds This can be very useful when creating bond graphs for a system that has several bond graphs that are all used to create a complete simulation but are not connected to each other as far as the bond graph is concerned This way the user can create the bond graphs individually and then control the numbering so when the equations are all put together there are no elements or bonds with the same name It is recommended that the user create all the bond graphs for a single system if the system consists of more than one bond graph in the same CAMPG bond graph model This way all the equation will 229 automatically be incorporated into the files that are created when an interface is chosen See Fig 5 7 for an example of this CAMP G c XcampgXbgmodelsXmultsus P rne f eoe fincerrace anaisze options meros TT E Ea Ea ES can t load from c campg bgmodels mulsys bg can t locate element or bond att goading from c campg bgmodels multsys bg done picked ready t BOND FROM L Npaste completed aie Fig 5 7 Bond Graph renumbering option AUTOMATIC CAUSALITY DETECTION CAMPG automatically detects if there are any causality problems in a bond graph If there are problems the bond graph in the CAMPG display will show where the problems exist by displaying
148. matching END statement The PROCEDURAL key word defines the beginning of a block of PROCEDURAL code to be executed in the sequence given i e the code within the PROCEDURAL block is not sorted by the ACSL translator The following two examples use the simple suspension system to illustrate the use of the procedural Here the objective is to define a set of FORTRAN statements to be executed in sequence and define the input road conditions SF1 The plots that follow the input files show the input function and the displacement of the vehicle DELTA X Q4 Note that each procedural needs an END statement The first example Fig 3 9 shows a file of a simple suspension system It defines the input function SF1 at time 5 sec as zero if time is greater than 5 sec and again with a value of 5 at time equal 7 sec Fig 4 10 shows a plot of the input function SF1 and the resulting motion of the 177 mass m plotted as Q4 vs time It clearly demonstrates the discontinuities defined in this function The second example Fig 4 11 uses the same system by defines SF1 as a function of time T to be 0 to be a harmonic function after 5 sec and zero again after 10 sec This illustrates that nonlinear discontinuous functions can be defined with a procedural and work with the bond graph structure and equations generated by CAMPG The dynamic graphical display of SF1 and the response Q4 are shown in Fig 3 12 The same methods can be applied to
149. message displayed on the dialogue box is explain 1 1 too few bonds CUR Now select an I element by clicking the mouse while the cursor is on the I button on the elements menu Place these two grids above the 1 junction by moving the cursor and clicking the mouse The distance is arbitrary CUR Draw the bond between the 1 and the I element click the mouse on the 1 and then on the I The cursor will change direction on each click and the bond 2 will appear on the screen CUR Select the TF element from the menu and place it to the right of the 1 junction CUR Status Box reads Bond from and the cursor turned to a small circle and an arrow pointing left 205 junction Click on the 1 junction The cursor again changes direction as a circle and an arrow pointing right The Status Box reads Bond to Click the cursor on the 1 junction or as close to it The bond that joins the junction and the element will be displayed with its corresponding bond number one higher than the previous one and causality assignment 0 CUR Pick a 0 junction place it to the right of the TF TF screen CUR O screen CUR This should create a bond from the TF element to the 0 junction C CUR Select an C and place it below the 0 CUR O screen CUR Click on the 0 element on the screen C screen CUR Click on the C element on the screen A bond should appear between these two elements TF CUR Select TF a
150. mpgequ m gt m function containing the system first order differential equations campgsym m m file containing system matrices in symbolic form For simulation and control edit these files Enter values for physical parameters initial conditions inputs and time controls in places where the marks appear Standard generalized variables in Bond Graph notation used d CAMPGMOD M MATLAB MODEL INPUT FILE EFE rere Initial conditions Q9IN Q3IN P11IN P6IN initial Q9IN Q3IN P11IN P6IN 52 oe oP de oe oe oe oe oe oP de oe oe oe oe de oe de oe oP de oe de oe oe oe oP oe oe oe oe oP oe oe System Physical Parameters global C3 R4 I6 C9 R10 I11 C3 RM I6 9 C9 R10 I11l S diio External inputs se t sf t global SF1 SF1 Simulation Time Control t0 Initial Time tf Final Time tspan tO tf Define Outputs global TIME STEP EFFORTS FLOWS STEP 1 ees Computer Simulation Solution of system equations using Matlab ode23 or ode45 function The campgequ m function contains the system differential equations in state variable form It returns the vector t p q where t time and p q vector of state variables t p_q is a column vector with rows t p q 1 p q 2 p_q 3 t p_q ode23 campgequ tspan initial Q9 p q 1 Q3 p q 2 Pll p q 3 P6
151. mples that can be modeled and processed for all CAMPG interfaces This icon links MATLAB with the c CAMPG WORKING directory If you double click on this icon the MATLAB command windows and the last CAMPG files input for MATLAB will start This icon opens a directory with examples of the CAMPG ACSL generated files This icon opens the directory with examples of the CAMPG MATLAB generated files When this icon is clicked a local web page with links to the different publications will appear La When this icon is clicked the user opens the c Campg Working Working directory Directory 1 7 Bond Graph Model Entry CAMPG will start and after an initial display of the uses and license move the mouse and the following display will appear MTF DEL UNDO BOND FROM Fig 1 2 CAMPG initial session bg display The previous screen uses the default configuration setting for the screen background and colors However the user can operate CAMPG in black and white The reason is that the user can take screen shots and capture the CAMPG window display and its bond graph Back and white displays are usually preferred for documentation purposes and to enter into a word processing or presentation software like PowerPoint The following figure illustrates this kind of display CAMP G session E eie eait intertoce nature options meo PP TT uU o D i fA m D T J f pa Ti m a el E ES 2
152. n and calculate the design variables that are under study In order to do this enter the command ACSL START This process is useful when trying to alter variables to generate and optimum design It is important to notice however that it is possible to change ONLY the variables defined with the CONSTANT definition In order to change the values of these parameters the runtime SET command is used However if it is used on a variable that has not been defined as a constant the computer will recalculate values based on the original ACSL input file definition For this reasons any parameter that we want to vary at runtime needs to be defined as a CONSTANT Otherwise the system simply will ignore the change The following example shows the placement and syntax of the CONSTANT command in the ACSL input file generated by CAMPG PROGRAM CAMPACSL ACSL INPUT FILE INITIAL CINTERVAL CINT 0 05 Time Control T time CONSTANT FINTIM 5 0 1220 02 C3 510204 R4 0 05 P2IN 0 0 Q3IN 0 04 Final time Physical parameters initial periods continue definition of constants END OF INITIAL DERIVATIVE SE1 0 EXTERNAL INPUT SE F T SF F T SYSTEM EQUATIONS el SE1 fl f2 167 e2 el e3 e4 f2 P2 12 e3 Q3 C3 3 f2 e4 f4 R4 f4 f2 dP2 e2 dQ3 f3 DES STATE VARIABLES p P2 INTEG dP2 P2IN Displacement Q3 INTEG dQ3 Q3IN Momentum TERMT T GE FINTIM Terminate Condition END OF DE
153. n disk 12i err Ee 164 Qi Trans al DIE ours cov Mea oueaaed EE NM TENE 164 be Complilallon suos Rau e t EDD Live eue ts 164 Linking ege pe ie ved shawna bee AM E TERETE 164 s Bxecnob uidet eu tu aa Ata M LULA EO fO EL 164 Executable file of model exists on disk 0 2 eee cece cece ee eens 164 Saving the model files 22 ie c e Eee eis RE La d 165 4 5 Useful Run Time Commands used with CAMPG ACSL 165 Runtime Changes to Physical Parameter Values 166 Generation Of ACSL Plots Seo p eR e XXE YRNREAST AN 168 Plot Control Options 2 lt occdsesseteisw users EV E RES EEA NEM RET EEAE 169 4 6 Setup Piles ico E E ARX e ERN S taxis Y XY EEE TAN ERA Sg 173 PREPARA eise UV Uti RN Add MC NE REM 176 TCWPRN A net hae aedes aie pane ne 176 CALPE ursi ovt ees REA EEREEERA SERE RENEE UAR ES EN E VR 177 PRNPE TS PAL SE ese ve a ota nS E Pe CH EET ERU NE qian 177 DII e s weet cn eat ua hte Nr CL utn dud Vera RELY 4 7 Important ACSL Features cece cece eee e eee eee eeeeeeeneee ones PROCEDURAL iiie on ER chee ein Uo CODI a COR EIGENVALUE ANALYSIS ise ees vh RA RUE PENUSSKUNE PS ANALYZ command coe oou Eme cru ERO Lots SUBCOMMANB TRIM iusisseskoxee o Ey oe Eee x CPG Un cay BEIGEN seceeespexy YET UPESIsUA OE aE IS TRAGY BG ui sisse soe ERO DE SERE JACOB edo DPI VEO RUM FORTRAN SUBROUTINES oit kite hene ERA HORAE SERVERS REAL FUNCTION ioocetcix ep eo Ehre ien Oboe po us
154. n the CAMPG screen 22 EXIT TO ACSL TO DSL CSMP TO CSSL REDRAW EDIT This allows the user to exit the CAMPG program The different selections in this menu allow the user to either exit TO DOS without creating any input files to the digital simulation languages or to exit to a specific language Interface to the Advance Continuous Simulation Language ACSL It Creates the ACSL input file CAMPSL CSL This would also close the graphics session and start the editing phase The editing phase is necessary to place any non linearities or functions that either are user generated of they are part of a simulation language This option selects the interface to IBM s Dynamic Simulation Language or to CSMP Continuous System Modeling Program It also starts the editing phase of the DSL input file generated by CAMPG This is the CAMPG DSL file This option will produce an interface file for the CSSL IV language This selection is used to refresh and redraw the screen at any time This pull down menu contains features that perform modifications and editing of bond graphs It is used by clicking the cursor on the EDIT box a sub menu will be displayed Click again on the desired selection After the 23 DELETE SINGLE GROUP SEGMENT ALL selection is made the REQUESTED ACTION BOX will prompt you to select either the portion of the bond graph to be acted upon or other options that are displayed Four method
155. n the bumper is in contact with the wall Fig 3 6 shows the engineering model of the crash test as well as its corresponding bond graph 2 Generate a bond graph model Fig 3 7 shows step by step the process of generating the Bond Graph model of the crash test 3 Enter the Bond Graph description into the CAMPG program Fig 3 8 shows the CAMPG screen that was generated after entering the bond graph model The SYSTEMATIC method was used to enter the bond graph model shown in Fig 3 8 Below is a detailed description how this was done The symbol CUR means to select with the cursor The symbol CR means to enter from the keyboard kk eee ek K K K see K K sek K K K K K K K K K ze K K K K K K K K K K KK K KK KK K K K K CAMPG lt CR gt This brings up the CAMPG screen with a logo Any movement of the mouse or typing any character will clear the logo and show a blank screen or will bring up the latest model generated and stored in the SESSION BG file 90 EDIT CUR DELETE CUR ALL CUR YES CUR OPTIONS CUR STICKY CUR ON CUR 1 CUR CUR CUR CUR 0 CUR These next three steps clear the screen if there is an existing session file If there is no previous SESSION BG file these steps are not necessary This pull down menu selection will be used to turn on the STICKY function so that all the similar elements can be placed all at once This step allows the SYSTEMATIC METHOD of building the bond gra
156. n the screen O screen CUR Click on the same 0 1 screen CUR Click on the lower left 1 on the screen There should be now have 2 bonds on the screen Continue this process until the rest of the bonds have been created Notice that some of the bonds are red just after they are placed This means that the system detects an error in the bond graph construction These errors while the bond graph is being assembled are simply warnings to the user that the bond graph is not a close form system but rather some bonds are not complete yet They also tell the user that the causality can not be completed up to that point If these errors continue after completion of the bond graph it means that there are loops derivative causality or incomplete bonds that will prevent the generation of a close form system of equations The user needs to investigate and correct it The errors can be determined by inspection of the bond graph or with assistance from CAMPG Click on ANALYZE then EXPLAIN and then once again on the red bond or element The DIALOGUE BOX will provide an explanation of the error Most likely the error will disappear after the bond graph has been completed This feature is excellent to assist in defining correct bond graph models The user has now completed the bond graph model You can look at the equations using ANALYZE and PEEK This can be done by selecting PEEK under the ANALYZE button the cursor will change to the eye Cl
157. nal Time tspan t0 tf Be 5 5G Soke Computer Simulation Solution of system equations using Matlab ode23 function The campgequ m function contains the system differential equations in state variable form It returns the vector t p q where t time and p q vector of state variables t p dq ode23 campgequ tO tf initial counter 1 status odeset outputfcn esandfs t p_q ode23 campgequ tspan initial status Q11 p q 1 Q14 p q 2 Q109 p_q 3 Q107 p_q 4 P9 p q 5 P12 p q 6 P104 p q 7 P102 p q 8 State variables vector pq Q11 O14 Q109 0107 P9 P12 P104 P102 SPlotting stuff for the Hydroelectric Power Plant 237 figure 1 subplot 211 plot t p_q 1 A b grid axis 0 200 0 60 title Height in shorter Surge Tank subplot 212 plot t p_q 2 A m grid axis 0 200 0 90 title Height in taller Surge Tank figure 2 subplot 211 plot t Efforts 1 1 b grid title Pressure in upper segment of standpipe subplot 212 plot t Efforts 2 1 m grid zoom title Pressure in upper segment of standpipe SPlotting stuff for the Crash Test oe figure 3 plot t p q 3 r grid xlim 0 1 title Distance the Dummy s head travels ylabel Distance meters xlabel Time seconds figure 4 plot t Efforts 3 r grid xlim 0 1 title Force Acting on the Dummy ylabel Force N xlabel
158. nd place it to the right of the 0 0 screen CUR TF screen CUR This should create a bond from the 0 junction and the TF element The number of the bond will appear in the middle of the bond as it has for all the other bonds 1 CUR Pick a 1 junction from the menu and place it to the right of the TF6x7 TF screen CUR Click the mouse on the TF for FROM status 206 1 screen CUR Click on the 1 junction Note again that the numbers of the bonds appear automatically in the middle of the bonds In this case 7 I CUR Click on the I icon in the menu Place the I above the last 1 junction 1 screen CUR I screen CUR Generates a bond between the 1 and the I element 0 CUR Pick the 0 from the menu place it the right of the last 1 junction 1 screen CUR 0 screen CUR Draws a bond between 1 and the 0 junction C CUR Pick C from the menu and place it below the last 0 junction 0 screen CUR C screen CUR Generates bond between 0 and C I CUR Pick I and place it to the right of the 0 junction 0 screen CUR I screen CUR This step completes the bond graph by drawing a bond from the last 0 junction to the I element Now the whole bond graph can be moved to the right to have it on the center of the screen This is done with the following steps EDIT CUR Pick the EDIT button and select the MOVE button There will be two choices SINGLE and SEGMENT Pick
159. nds of physical elements that can be used There is a set of pull down menus at the top These start with the keywords like EXIT REDRAW EDIT FILES OPTIONS ANALYZE The message dialogue box is at the 19 bottom left and a status box on the bottom right corner There are two yellow bars one horizontal the other one vertical They are used to scroll the bond graph model in the horizontal and vertical direction This way the user can enter a bond graph that is bigger than the screen would display All of the elements required to construct a bond graph are located on the left side of the screen in the vertical menu Fig 2 1 The boxes contain the menu selections for a BOND an EFFORT SOURCE SE and then a FLOW SOURCE SF Following these are the ZERO JUNCTION 0 the ONE JUNCTION 1 the physical elements RESISTOR R INERTIA ELEMENT I the CAPACITOR ELEMENT C the CAMPG starting screen ts WINE o version 5 5 Windows XP c Copyright 1999 2007 CADSIM ENGINEERING P 0 Box 408 Davis California 95617 http www bondgraph com email campg bondgraph com A Licensee Daimler Chrysler AG Dr Dietrich Sahm Energy Management and PowerNet GR EEB HPC G 008 50 71059 Sindelfingen GERMANY Serial CW55XP 1008073136 CL1 FLE x Fig 2 1 CAMPG Initial Screen PLACING ELEMENTS The menu of elements on the left side of the screen is used to place any of the elements SE SF 0 1 R L C TR GY on the scr
160. nerated Transfer Functions for Electrical Circuits and Operational Amplifiers 244 16 17 18 19 20 21 22 Proceedings of the 2007 Internatinal Conference on Bond Graph Modeling and Simulation San Diego January 2007 Nguyen L Ramakrishnan J Granda J International Space Station Centrifuge Rotor Models A Comparison of the Euler Lagrange and the Bond Graph Modeling Approach Proceedings of the 2007 Internatinal Conference on Bond Graph Modeling and Simulation San Diego January 2007 Granda J J Ramakrishnan J Louis H Nguyen Centrifuge Rotor Models A Comparison of the Euler Lagrange and the Bond Graph Modeling Approach AIAA Houston Annual Technical Symposium 2006 Gilruth Center May 2006 Granda J J Nguyen Louis Alternative Techniques for Developing Dynamic Analysis Computer Models of the International Space Station Space Shuttle and Orbiter Repair Maneuvers 47 AIAA ASME ASCE AHS ASC Structures Structural Dynamics amp Materials Conference Newport Rhode Island April 2006 J J Granda I Sandoval L Horta Morphing Structural Concepts Evaluation Criteria Using Dimensionless Analysis and Computer Simulation 46th AIAA ASME ASCE AHS ASC Structures Structural Dynamics amp Materials Conference Austin Texas April 2005 Elramady Alyaa Granda J J Modal Analysis of the Zvesda Mission of the Space Station With Bond Graphs Proceedings of the 2005 Internatinal Conference on B
161. ng can take place a bond graph needs to be created in CAMPG that represents the system being modeled To create a bond graph follow the steps below 1 Start CAMPG by double clicking on the icon as seen in Fig 3 1 This icon is located in the CAMPG desktop folder or in the CAMPG Start Menu All programs 45 Either move the mouse or press the Enter key This will clear the screen from Fig 3 2 to Fig 3 3 Now CAMPG is ready for you to enter the bond graph or work with an existing one Create the bond graph This procedure is explained in detail in each of the examples in sections 3 7 3 8 and 3 9 Once the bond graph is created and it is free from errors CAMPG is ready to interface with Matlab Select the menu called Interface A drop down menu should appear as in Fig 3 4 Choose the menu choice called Matlab Once this has been done CAMPG will display something similar to what is seen in Fig 3 5 Press the space bar and CAMPG will continue Then CAMPG will exit and the user will be at the desktop with all three of the files it just created open and ready to have initial conditions time interval and element values input along with what ever else the system requires to be accurate CAMPG Executable Icons TIE d e CAMP G CAMPG WINDOW SCREEN Fig 3 1 CAMPG starting icon 46 CAMPG Initial Screen CAMP G version 5 5 Mindows XP c Copyright 1999 2007 CADSIM ENGINEERING P O Box 4083 Davis Calif
162. ns will appear on the screen underneath the cursor This brings up general accounting information concerning the current CAMPG session computer usage It helps evaluate the memory size and computer resources necessary to complete the current model Limitations on memory and resources will determine the size of the model that a particular computer could handle 30 SCROLL BARS There are two bars in between the main drawing area and the left side menu as well as the bottom DIALOGUE BOX These bars are displays as yellow bars They can be used for scrolling the bond graph sideways or backwards or forwards This indicates that the bond graph model is generated in a window that can be moved around in order to generate large bond graphs QUICK DELETE This feature allows the use to delete an element or bond quickly without going to the EDIT menu It will delete a single element or bond unless the STICKY option is set to on in which case it could delete more that one element or bond UNDELETE The undelete feature allows the user to recover the last deleted elements bonds groups or segments It displays quickly the bond graph the way it was before the delete action 2 4 Generating Bond Graph Models Once you have CAMPG installed on a computer the user is ready to generate a bond graph model with graphical input The symbol CUR means to select with the cursor clicking the mouse The symbol CR means press ENTER from the keyboard Th
163. nts of the gears the flywheel and the shaft These variables are F Force between teeth Q5 Relative displacement between teeth Wi Angular velocity of gear 1 W2 Angular velocity of gear 2 W3 Angular velocity of flywheel Thetal Angle of rotation of gear 1 Theta2 Angle of rotation of gear 2 Theta3 Angle of rotation of flywheel Twist Shaft angle of twist Wdl Angular acceleration of gear 1 Wd2 Angular acceleration of gear 2 Wd3 Angular acceleration of flywheel SEI Input torque E2 Torque on gear 1 E10 Torque on shaft The interactive commands used in ACSL are shown below along with some of the calculations in the form of numerical tables The PREPAR 212 command is used to prepare the variables for calculation and graphical output The OUTPUT command is used to display the calculations on the screen This can be turned off by the command OUTPUT CLEAR This allows the user to prepare different variables for calculation and then plotting The RANGE command helps to find the maximum and minimum values of the design variables The plots are generated using the options explained in Section 5 2 2 The variable NCIOUT defines the number of calculation that the computer will go through before it prints a value The following output shows the variable values every 100 steps ACSL gt SET TITLE GEAR TRAIN WITH BACKLASH ACSL gt PREPAR T F Q5 W1 W2 W3 THETA1 THETA2 THETA3 TWIST WD1 WD2 WD3 SE1 E2 E10 ACSL gt ACSL gt S
164. o at the ACSL prompt This is a practical idea a SETUP FILE is created using the editor This file defines the run time commands for a simulation The ACSL system reads this file by passing control of the ACSL input to this file In the IBM PC this is accomplished by naming the SETUP file with the same name as your input file and the extension CMD In order to transfer control of the input command to this SETUP file The SET command is used as follow ACSL gt SET CMD 10 IBM PC Unit 10 is defined as the logical unit identified with the CMD file The above command allows the commands in the setup file to be available for execution 173 Other computers have a similar way of associating the SETUP file to the simulation For a VAX computer under VMS for example the procedure is as follow At the VAX prompt and before ACSL is called enter gt ASSIGN SETUP DAT FORO10 This command identifies Unit 10 with the SETUP DAT file Start ACSL For example use file OSCILLATOR CSL gt ACSL OSCILLATOR lt translation compilation loading steps At the ACSL prompt ACSL gt enter the following commands ACSL gt SET CMD 10 lt connects unit 10 to SETUP DAT file The setup file could have been named OSCILLATOR CMD following the convention for the IBM PC ACSL gt START lt start calculation If the file contains this command it is not necessary to issue it here lt numerical output
165. odel as seen in Fig 3 11 98 Simulink Model ES crashsym28s Force Felt Separate by Dummy 1 10000 Correction to get Q9 as an Output Gain is ca Distance Dummy s Head Travels Fig 3 11 CAMPG SIMULINK state space model 7 Once the Simulink model has been created double click on the State Space block to get the input screen to open See Fig 3 2 for this screen Input the names or the matrices that are to be used Simulink In this case they are AA BB CC and DD Block Parameters State Space Input Window Fig 3 12 Matrices Initialization 99 8 Run the Simulink simulation to get the results This is done by clicking on the play button that is seen on the Simulink model See Fig 3 11 9 Double click on the scopes in the Simulink model seen in Fig 3 11 to see the results See Fig 3 13 for the resulting plots as seen on the scopes Resulting Plots Force Felt by Dummy Iof xi Distance LT s Fig 3 13 SIMULINK scopes simulation display DESIGN CRITERIA The simulation must produce a design of the seat belts and the bumper so that it satisfies the following conditions 100 He doesn t hit the windshield if he travels at 25 and at 55 mph 2 What is the force acting on his chest and waist at 25 mph and at 55 mph Compare the data on injuries and determine if chest or internal injury occurs if 1 he wears a seat belt only 2 he wears a seat belt and a shoulder strap 3 What i
166. on is on This option also applies to other functions such as delete The user can delete sequentially elements and bonds as long as this option is set to ON This option helps to shape the bond graph to self align the elements and bonds with horizontal and vertical axis There are three options within GRID A grid point mesh is displayed on the screen All elements and bonds will be automatically positioned and aligned with the visible grid points This generates a very orthogonal even drawing The grid points do not show up on the screen but GRID is still on The elements and bonds are placed exactly at the cursor location There is no grid alignment for bonds or elements The bond graph is drawn to the exact locations selected by the user Colors can be assigned to all the elements bonds grid points and colors that modify the bond graph depending on error messages or modeling problems To change the color of your selection 28 BOND ELEMENT NUMBER MARKED GRID AMBIO DERIV OTHER ANALYZE click the mouse on the COLOR option and a menu containing the following selections will be displayed Colors are changed by selecting one of this options and clicking the mouse on the color displayed on the color table Bonds that join elements and junctions Single and multiport elements Bond numbers Selected bonds and structures for moving to a different location on the screen Grid points that help
167. ond Graph Modeling and Simulation New Orleans January 2005 Granda J J The CAMPG Symbolic Solution to Algebraic Loops in Bond Graph Models Proceedings of the 2005 Internatinal Conference on Bond Graph Modeling and Simulation New Orleans January 2005 Granda J Montgomery R Automated Modeling And Simulation Using The Bond Graph Method For The Aerospace Industry Proceedings of 245 23 24 20 26 2T 28 29 the 2003 AIAA Modeling and Simulation Technologies Conference 11 14 Austin Texas August 2003 Montgomery R Granda J Using Bond Graphs for Articulated Flexible Multi bodies Sensors Actuators and Controllers with Application to the International Space Station Proceedings of the International Conference on Bond Graph Modeling and Simulation ICBGM 2003 Orlando Florida January 2003 Granda J The CAMPG MATLAB SIMULINK Computer Generated Solution of Bond Graph Derivative Causality Proceedings of the International Conference on Bond Graph Modeling and Simulation ICBGM 2003 Orlando Fla January 2003 Granda J The Role of Bond Graph Modeling and Simulation in Mechatronics Systems An Integrated Software Tool CAMPG Matlab Simulink Journal of Mechatronics Oxford England November 2002 Borutzky W Granda J Bond graph based frequency domain sensitivity analysis of multidisciplinary systems Journal of Systems and Control Engineering July 2002 Granda J Computer
168. ons Example e3 s SE1 s 4 s SF10 s q4 s SE1 s Define SI matrix syms s Find the size of A and then figure out I I eye 4 Use Matlab Symbolic Tool Box to do symbolic matrix operations leading to the calculation of symbolic transfer functions Transfer Functions Matrix H H C inv s I A B D pretty collect H HH CC inv s I AA BB DD pretty HH collect HH 67 3 4 The above information on how to create real matrices from the symbolic matrices could be used in conjunction with Simulink to model the system Using this file with Simulink could be an alternative method to modeling the system as opposed to the method discussed in section 3 7 Using the AA BB CC and DD matrices that are real matrices in Simulink would produce the same results that are produced in section 3 7 This will be discussed in Section 3 9 Useful Runtime Commands used with CAMPG MATLAB Matlab has an entire suite of commands that are built in Many of these are very useful in getting the data that is desired from the model Some of the more useful runtime commands are listed below with a short description of each For a more complete list of Matlab runtime commands and a more detailed description with examples of how to use each command type helpdesk at the Matlab command prompt in the Matlab workspace SUBPLOT Used to put multiple plots on the same graph PLOT Used to plot the values in the vector
169. ons of the system and place them in the structure of an ACSL input file Bond Graph Fig 4 2 Bond Graph of Single Degree of Freedom System CAMPG can be used to create the ACSL an input file that has the same structure as the one created by the editor in the last example To do this run CAMPG and create the bond graph shown below following the guidelines presented in the modeling generation phase explained in Section 3 of this manual Once the bond graph model has been completed on the screen select EXIT and the TO ACSL from the upper left corner of the CAMPG 161 screen The file CAMPSL CSL will be created Once parameter values have been entered it looks like this PROGRAM CAMPACSL ACSL INPUT FILE INITIAL CONSTANT P2IN 0 0 Q3IN 0 04 Initial Conditions CINTERVAL CINT 0 05 Time Control T time CONSTANT FINTIM 5 0 Final time CONSTANT 1220 02 C3 510204 RA 0 05 Physical parameters END OF INITIAL DERIVATIVE SE1 0 EXTERNAL INPUT SE F T SF F T SYSTEM EQUATIONS el SE1 fl f2 e2 el e3 e4 f2 P2 D e3 Q3 C3 3 f2 e4 f4 R4 f4 f2 dP2 e2 dQ3 f3 Ert STATE VARIABLES i P2 INTEG dP2 P2IN Displacement Q3 INTEG dQ3 Q3IN Momentum TERMT T GE FINTIM Terminate Condition END OF DERIVATIVE END OF PROGRAM The individual equations form a close form set of differential equations in state variable form and can be verified using the causality an
170. ornia 95617 http www bondgraph com email campg bondgraph com Licensee Daimler Chrysler AG Dr Dietrich Sahm Energy Management and PowerNet GR EEB HPC G 008 50 71059 sindelfingen GERMANY Serial cCwWS5xP 1008073136 CL is Fig 3 2 CAMPG Starting Screen 47 CAMPG Working Screen CAMP G untitled L rie enix terrace anaiuza options meo T loading from session bg done previons session loaded from session and placed BOND FROM Fig 3 3 CAMPG Desktop Working Screen 48 CAMPG Interface Menu CAMP G s ion ACSL MATLAB e m SIMULINK SYSQUAKE EAsys VISIM c FORTRAN UNIVERSAL o lt SE 1 R R I R I R I R I 1 140 138 1 T 1 T a 1 o 1 o 1 o 1 69 o x 4 14 I c c c c c DEL UNDO loading from session bg done previons session loaded from session and placed BOND FROM Fig 3 4 CAMPG Simulation Language Interface Menu 49 Working One Moment Please The CAMPG MATLAB model files are been generated and written to files in the working directory Edit files campgmod m campgequ m campgsym m to complete model Use Windows Notepad or MATLAB EDIT or other editor campgmod m model input to Matlab campgequ m model differential equations and state vectors campgsym m symbolic state matrices CAMPG will interface now to MATLAB Edit Files CAMPGMOD M CAMPGEQU M CAMPGSYM M Press any key to continue Fig 3 5 CAMPG messa
171. ot n p_qdot1 dQ9 p qdot2 dQ3 p_qdot3 dP11 p_qdot4 dP6 Derivatives vector p_qdot dQ9 dQ3 dP11 dP6 Define output vectors efforts flows Sample Structure Add any effort flow or other variables to be plotted to the following EFFORTS or FLOWS vectors Activate in campgmod m suggested structure of graphical output TIME STEP 1 t Define time vector EFFORTS STEP e5 e11 e4 Define efforts vector FLOWS STEP f2 9 8 Define flows vector STEP STEP 1 In campgmod m the following structure is included Sample structure for plotting Output Variables as defined in campgequ m 57 dP dP dP oe dP oe oe oe oe oe Example If the efforts and flows were defined as EFFORTS STEP e5 e11 e4 FLOWS STEP 2 9 8 figure 2 Plot e11 vs TIME Second column of EFFORTS vector subplot 211 plot TIME EFFORTS 2 b grid title Effort variable of vector EFFORTS 2 stored in column 2 Plot f8 vs time Third column of FLOWS vector subplot 212 plot TIME FLOWS 3 m grid title Flow variable of vector FLOWS 3 stored in column 3 What follows is the same file seen above but this time the file has been broken down into easier to see sections Some of the file was excluded from this second listing This was done because the only parts that are going to be show here are the parts that the user may have to change Global Declaration glo
172. p q 4 State variables vector p_q Q9 Q3 P11 P6 Sample Matlab structure for plotting simulation results state variables figure 1 subplot 211 plot t p_q 1 b grid title Variable p_q 1 stored in column 1 color blue ylabel p_q 1 units xlabel Time seconds subplot 212 plot t p_q 2 m grid title variable p_q 2 stored in column 2 color magenta ylabel p q 2 units xlabel Time seconds Sample structure for plotting Output Variables as defined in campgequ m Example If the efforts and flows were defined as EFFORTS STEP e5 ell e4 FLOWS STEP f2 f9 f8 figure 2 Plot e11 vs TIME Second column of EFFORTS vector subplot 211 plot TIME EFFORTS 2 b grid title Effort variable of vector EFFORTS 2 stored in column 2 Plot 8 vs time Third column of FLOWS vector subplot 212 plot TIME FLOWS 3 m grid title Flow variable of vector FLOWS 3 stored in column 3 MECHANICAL ELECTRICAL HYDRAULIC TRANSLATION ROTATION 53 g SE Effort Force Torque Voltage Pressure SF Flow Velocity Ang Vel Current Volume Flow Rate Q Gen Disp Displacement Angle Charge Volume P Gen Momentum Momentum Ang Moment Flux Linkage Pressure Moment TF M Transformer Modulus SE Source Effort GY R Gyrator Modulus SF Source Flow
173. ph model Select the 1 from the menu on the left to place the ONE JUNCTIONS Move the cursor and click in the middle of the screen Move the cursor 4 grids to the right and 4 grids down and click again to place the second 1 Move the cursor 8 grids to the left and click to put the third 1 on the screen Select the 0 from the left hand menu to place the ZERO JUNCTIONS on the screen 91 CUR C CUR CUR R CUR CUR I CUR CUR SF CUR CUR bond symbol CUR Click the cursor at 4 grids to the left of the 1 middle of screen and at 4 grids to the right of it Select C from the menu in order to place the capacitive elements C on the Bond graph Place one of the C elements 2 grids below and 2 grids to the left of the 1 element on the left then move 8 grids to the right and place the other Select the resistive elements R from the left hand menu Place these R elements 4 grids to the right of each C element Select the T element from the left menu Place the two inertia elements I 4 grids above the central 1 and 4 grids to the right of the right most 0 Select the FLOW SOURCE from the menu on the left Place this SF 4 grids to the left of the left most 0 Select the BOND SYMBOL top box in the left hand menu to join all of the elements with bonds SF screen CUR Click on the SF on the screen 92 O screen CUR Click on the closest 0 o
174. r grid title Twist subplot 312 plot t Efforts 1 b grid title Force subplot 313 plot t 100 sin 20 t r grid title Input Torque New figure with E10 E2 and F vs Q5 128 figure 5 subplot 311 plot t Efforts 8 r grid title E10 subplot 312 plot t Efforts 5 b grid title E2 subplot 313 plot Efforts 9 Efforts 1 r grid ylabel Force xlabel Q5 sNew figure with Q5 figure 6 plot t Efforts 9 r grid title Q5 end Nas p dues BOND GRAPH NOTATION GENERALIZED VARIABLES BOND GRAPH NOTATION Ej a Ge se ee ts a Me ee Me ee MECHANICAL ELECTRICAL HYDRAULIC TRANSLATION ROTATION E Effort Force Torque Voltage Pressure SEF Flow Velocity lAng Vel Current Volume Flow Rate Q Gen Disp Displacement Angle Charge Volume P Gen Momentum Momentum Ang Moment Flux Linkage Pressure Moment TF M Transformer Modulus SE Source Effort GY R Gyrator Modulus SF Source Flow E na a a UND UND DUO UND a aD aa UND UND GEO UND a UND aa UND CD UND UD GNO an GER GED UID CEP UD GU OUS UUD CUP UD CEP OUO UND O GNO GUD UND O UND UMP OED ena aman DD MED UD UD UMS UM UID UND MED GUD CEP CEP GER UD GE c S He He e e He e e He He ke e He He e dej dee dee FOR e e IORI e de de de ko de ko dee Bi ach Ga E BOND GRAPH ANALYSIS SSYSTEM DESC
175. r flow is cut to zero This is another type of a nonlinear system This problem can be solved one of a few different ways Two of these methods will be discussed here 1 This way is to break the problem up into three different systems Then model each of the three systems individually but in order from A to C as described below This can be done equally the same in Simulink or Matlab In Simulink three different models would be created In Matlab three different sets of files that make up the model representation would be created 142 A The first system being when all the initial conditions are zero and running until equilibrium has occurred B The second system would be done using the ending values for the states from the first system for the initial conditions of the second system This system would only cover when the flow is being cut from 1 cubic meter to zero in 1 seconds C The third system would then use the ending values from the states in the second system for the initial conditions is the third system This third and final system would then run until equilibrium has been established 2 This way is to create a function or a set of conditional statements that will fully represent the nonlinearity for the flow source Qo In Simulink this can be done by creating an input function using the built in sources and adding them together While in Matlab this can be done by using a set of conditional statements The method tha
176. re with the Theta s figure 3 subplot 313 plot t p q 6 radeg r grid title Theta 1 subplot 312 plot t p q 7 radeg b grid title Theta 2 subplot 311 plot t p q 8 radeg r grid title Theta 3 sNew figure with W s figure 2 subplot 313 plot t Efforts 2 r grid title W 1 subplot 312 plot t Efforts 3 b grid title W 2 subplot 311 plot t Efforts 4 r grid title W 3 sNew figure with accellerations figure 1 subplot 313 plot t Efforts 5 radeg I2 r grid title WD1 subplot 312 plot t Efforts 6 radeg I8 b grid title WD2 subplot 311 plot t Efforts 7 radeg I1l1 r grid title WD3 sNew figure with Twist Force and Input torque 133 figure 4 subplot 312 plot t p q 2 radeg r grid title Twist subplot 313 plot t Efforts 1 b grid title Force subplot 311 plot t 100 sin 20 t r grid title Input Torque New figure with E10 E2 and F vs Q5 figure 5 subplot 312 plot t Efforts 8 r grid title E10 subplot 311 plot t Efforts 5 b grid title E2 subplot 313 plot Efforts 9 Efforts 1 r grid ylabel Force xlabel Q5 sNew figure with Q5 figure 6 plot t Efforts 9 r grid title Q5 DESIGN CRITERIA The contact force between teeth depends upon the relative position of the gears due to the slack between them The contact force is zero
177. reates them see section 3 3 Listing of CAMPGMOD M CAMPG MATLAB GENERATED MODEL DESCRIPTION The following files have been generated 80 campgmod m gt m file containing model parameters intial conditions sources and simulation controls campgequ m gt m function containing the system first order differential equations campgsym m gt m file containing system matrices in symbolic form For simulation and control edit these files Enter values for physical parameters initial conditions inputs and time controls in places where the marks appear Standard generalized variables in Bond Graph notation used dob CAMPGMOD M MATLAB MODEL INPUT FILE clear Fossnes Initial conditions O9IN 0 Q3IN 0 P111N 1117 6 P6IN 16763 96 initial Q9IN Q3IN P11IN P6IN B c weal System Physical Parameters global C3 R4 I6 C9 R10 111 C3 1 300000 R4 80000 I6 1500 C9 1 10000 R10 500 I11 100 E i Ss eat External inputs se t sf t global SF1 SF1 0 Bing ans Simulation Time Control t02 0 Initial Time tf 1 Final Time tspan t0 tf TP Define Outputs global TIME STEP EFFORTS FLOWS STEP 1 EEE EE Computer Simulation Solution of system equations using Matlab ode23 or ode45 function The campgequ m function contains the system differential equations in state variable form It returns
178. released with an initial velocity equal to zero Let the spring constant be 1 96N m and the damper coefficient 0 05N sec m It is desired to analyze the system response to an initial displacement or an external input Single degree of freedom Oscillator Fig 4 1 Single degree of Freedom System Using the free body diagram the differential equation of motion can be found by applying Newton s Law This is done by writing expressions 158 for the sum of the external forces acting on the mass and setting it equal to the rate of change of linear momentum of the mass The equation is mx t bx kx 0 The objective is to find the solution for x t Double integration must be performed to find x t This is possible by calculating the second time derivative of x and then using the integration functions of ACSL twice to find the value of x t The input model is generated and describes the equations in the form of source code The initial parameters initial conditions and the above description of the differential equation are entered using any text editor that will generate an ASCII file The following ACSL input file was entered using the system editor PROGRAM OSCILLATOR ACSL INPUT FILE INITIAL CONSTANT M 0 02 K 1 96 B 0 05 lt Physical parameters CONSTANT XDIN 0 0 XIN 0 04 lt Initial conditions CONSTANT TSTP 5 0 lt Final time CINTERVAL CIN 0 05 lt time step interval END OF INITIAL DERIVATIVE F 0
179. rm Derivatives vector p qdot dQ9 dQ3 dP11 dP6 System Differential Equations State Space form A B C D symbolic matrices Derivatives dp dq and output variables e f t Generate A B matrices corresponding to states p sand q s dO9 P6 16 P11 I11 A 1 0 0 1 111 1 16 B 1 0 dQ3 SF1 P6 16 A 2 0 0 0 1 16 B 2 1 dP11 09 C9 P6 I6 R10 P11 111 R10 A 3 1 C9 0 1 111 R10 1 16 R10 B 3 0 dP 6 03 C3 SF1 R4 P6 16 R4 09 C9 P6 16 R10 P11 111 R10 A 4 1 C9 1 C3 1 111 R10 1 16 R4 1 16 R10 B 4 1 R4 Generate C and D matrices correspoding to outputs e s and f s 1 SF1 C D 0 0 0 0 1 61 e3 93 C3 C 0 1 C3 0 0 D 0 f6 P6 I6 C 0 0 0 1 16 D 0 7 P6 16 C 0 0 0 1 16 D 0 e9 09 C9 v Clk 2 69 0 0 0 D 0 11 P11 111 amp Ct 10 0 17111 0 D 0 f5 P6 I6 C 0 0 0 1 16 D 0 f8 P6 I6 P11 I11 C 0 0 1 111 1 16 D 0 f9 P6 I6 P11 I11 C 0 0 1 111 1 16 D 0 f10 P6 I6 P11 I11 C 0 0 1 111 1 16 D 0 2 SF1 P6 16 C 0 0 0 1 16 D 1 3 SF1 P6 16 C d 0 0 0 1 16 D 1 fA SF1 P6 I6 C 0 0 0 1 16 D 1 elO
180. rotation since the rotational moment of inertia is the relational constant Therefore the torque is proportional to the angular acceleration of gear l Fig 3 31 gives a good understanding of the stress level changes within the shaft and therefore can be used to design the shaft 138 Input Torque 100 50 0 50 100 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 Twist 4 2 0 a MNA A ta MAUL tuU AN AN ILU T CARI UBL EI NIN il WI IW IM TEN 2 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 x 10 Force 2 i LU I 4 Fig 3 32 Forces Figure 3 52 This figure shows in detail the torque input function position and relation between contact forces and displacements The top figure represents the input torque of gear 1 The bottom figure shows the relation between force and displacement This is the fundamental nonlinear constitutive relation that allows the representation of the backlash as a C element in the bond graph model 139 0 15 0 05 0 01 02 03 04 05 06 07 08 09 1 Fig 3 33 Teeth Gear Position Figure 3 33 This is a plot of the teeth gears position it clearly shows how the gears separate as Q5 changes sign It shows also that the contact is not completely uniform but it is influenced by some jitter motion due to the dynamics of the other
181. s of deletion exist One element only can be deleted CAMPG will not allow you to delete a single element if a bond is attached because it considers the bond and the element as separate items You could delete the bond and then the element separately It deletes an element and the attached bonds All items attached to the selected object will be deleted It means delete all the structure that is continuously connected to the selected element or bond Be careful if your entire bond graph is connected it is all one segment It will delete everything on the screen including segments of graphs that may not be linked together After selecting the method of deletion use the cursor to locate the portion of the bond graph to be acted upon A different cursor will appear to warn the user that delete is on PICK This selection is used for copying elements or segments to another location on the screen It allows you to mark either a SINGLE element or an entire SEGMENT Once the 24 PUT MOVE FILE user has marked an element or a SEGMENT he can copy it to another place on the screen by moving the cursor to other location and clicking one of the left button It is used to place the elements or segments that have been selected with PICK So this option is automatically on after PICK has been selected You can place last PICK item in any location Selection of MOVE allows you modify the shape of the bond graph because it
182. s the critical maximum velocity when he is safe at which impact occurs Hitting the windshield chest injury internal injury seat belt failure and strap failure should not occur 4 Ifhe travels without a seat belt How long does it take for him to hit the windshield at 25 mph 40 mph and 55 mph What is the force acting on him on impact at 25 mph 40 mph and 55 mph RESULTS The results obtained from the simulation can be obtained in the form of numerical values or in the form of plots of variables as a function of time Several designs with different kind of bumpers and shock absorbers were tried These simulations allow the user to make an optimum decision to satisfy the design requirements The user is able at this point to decide which is the best design and why He She can perform as many simulations as the user thinks are necessary In this case it was found from the table below that at 25 mph the dummy did not hit his head on the windshield Its maximum displacement was 0 81m which is less than the 1 00m allowed The force acting on his body was 9 310 newtons However this is enough to produce chest injury The maximum limit allowed is 6 688 newtons No failure of the seat belts occurs since they can resist a load of 13 340 newtons The table shown below Table 2 illustrates the results of the different simulations considering different velocities and physical parameters 101 INITIAL NOF BUMPER SEAT BELTS DUMMY VEL
183. simulation can be quick and the plots can be generated immediately on the screen or to the hard copy device available on the user s computer This is helpful for running multiple simulations as well as multiple plots The following file contains each plot specification defined by the PROCED and the END keywords If using the PC the CMD Command control is delegated to the SETUP file by the command ACSL gt SET CMD 10 Unit 10 is the default unit associated with the SETUP file GEAR CMD The default option is that the SETUP file has the same name as the model file and the CMD file type SET TITLE GEAR TRAIN WITH BACKLASH PREPAR T F Q5 W1 W2 W3 THETA1 THETA2 THETA3 TWIST WD1 WD2 WD3 SE1 E2 E10 216 OUTPUT T F Q5 W1 W2 W3 THETA1 THETA2 THETA3 TWIST WD1 WD2 WD3 SE1 E2 E10 NCIOUT 100 SET TCWPRN 72 FORCE 3 COLUMN OUTPUT WIDTH PROCED AA SET TITLE ANGULAR ACCELERATION GEARS AND FLYWHEEL SETPRNPLT F CALPLT F STRPLT T GRDSPL T YINSPL 1 0 Y ASSP L 5 PLOT XAXIS T XTAG SEC WD1 WD2 WD3 TAG RAD SxS END PROCED BB SET TITLE ANGULAR VELOCITY OF THE GEARS T SET PRNPLT F CALPLT F STRPLT T GRDSPL T YINSPL 1 0 PLOT XAXIS T XTAG SEC W1 W2 W3 TAG RAD SEC END PROCED CC SET TITLE ANGLES OF ROTATION GEAR 1 AND GEAR 2 SETPRNPLT F CALPLT F STRPLT T GRDSPL T YINSPL 2 0 Y ASSP L 25 PLOT XAXIS T XTAG SEC THETA1 THETA2 TAG DEG END PROCED DD SET TITLE ANGLE FLYWHEEL ANGL
184. so that Matlab considers that as no executable statements The user can erase one or both of these information sections CAMOGMOD M Listing CAMPG MATLAB GENERATED MODEL DESCRIPTION The following files have been generated campgmod m gt m file containing model parameters initial conditions sources and mulation controls campgequ m gt m function containing the system first order differential equations 126 symbolic form campgsym m gt m file containing system matrices in For simulation and control edit these files Enter values for physical parameters initial conditions inputs and time controls in places where the marks appear Standard generalized variables in Bond Graph notation used Disie CAMPGMOD M MATLAB MODEL INPUT FILE clear all JE m Initial conditions P11IN 0 P8IN 0 P2IN 0 Q5IN O Q10IN O Initial conditions vector initial P11IN Q10IN P8IN P2IN Q5IN 0 0 0 B orantis System Physical Parameters global I2 T3x4 C5 T6x7 I8 C10 I11 counter Efforts I2 4 T3x4 5 C5 Using non linear relationship instead T6x7 1 I8 01 c10 1 4000 I11 8 counter 1 oa toenses External inputs se t sf t global SE1 SE1 100 sin 20 t Simulation Time Control oe AP de oe oe oe oe oe oe t02 0 Initial Time tf 1 Final Time tspan tO tf 2 eee Computer Simulation
185. t The bond that joins the junction and the element will be displayed with its corresponding bond number one higher than the previous one and causality assignment This should create a bond from the 1 element and the I element Select an R and place it above the 1 Click on the 1 element on the screen Click on the R element on the screen A bond should appear between these two elements 37 1 screen CUR R screen CUR This should create a bond from the 1 element and the R element The bond graph has been created Try using some of the other features that CAMPG offers For example look at the equations by selecting ANALYZE then PEEK then selecting any of the elements Try moving the bond graph by selecting EDIT then MOVE then SEGMENT Now click on any section of the bond graph One more click somewhere else will move the whole bond graph to a new location The user will realize at this point it is simple to create a bond graph model using CAMPG It is also simple to modify the graph once it has been built The most used operations for this are the delete and placement of new elements The placement of new elements can be easily handled as explained in the example above The deletion of elements or bonds has a couple of alternatives One is the quick delete operation that deletes one element of bond The one is the delete options under the EDIT menu The user can practice these forms of deletion explained
186. t is necessary to find values and graphical plots for the design variables such as angles angular velocities accelerations and the dynamic forces acting on the different components These will assist the designer to prevent fatigue failure because now the stress levels can be calculated The position of the gears is important to calculate as knowledge of the angular displacements can assist in satisfying geometric constraints and determining the acceptable backlash 218 RESULTS The results of the calculations are shown in the following figures They show plots of the angular velocities angular accelerations and torques and all other design variables of interest established in the design criteria Show below is a set of these variables for the parameters given It is possible to study different parameter values interactively without modifying the input file and using run time commands in order to try several designs Other variables can be calculated or plotted besides the ones explained in the design criteria and plotted below because CAMPG has generated all internal variables and all were calculated as a result When changes are made interactively all interactive commands of the ACSL program can be used to analyze the system S ANGULAR ACCELERATION GEARS AND FLYWHEEL WD3 102 RAD SXS 1 00 2 00 109 104 WBZ 2 00 1 00 WD 1 2 00 5 0 50 0 75 1 00 T SEC 0 2 ee c e Fig 4 22 Angular Acceleration 219
187. t item located under the Analyze menu The purpose of this option is to explain any problems with the bond graph This is used when the bond graph has a problem and the user cannot determine the problem this can be used as a tool in helping determine the problem When this option is invoked the cursor changes to a stethoscope The user simply needs to click on the bond graph element junction or bond to see an explanation of the problem The explanation will appear in the message box For an example of this see the following picture Fig 5 1 CAMP G session rie eat rcersaca waiuee options meow m i DEL X E 3 D z I loading from session bg done Bprevions session loaded from session and placed BLK DIAG Fig 5 1 Non linear hydraulic mechanical system 223 PEEK Peek is the second item located under the Analyze menu The purpose of this option is to view the equations of the particular element junction or bond that is being picked When this menu option is chosen the icon changes to look like an eye The user simply needs to click on a bond graph element junction or bond and the equations for it will be displayed For an example of this see the following picture Fig 5 2 CAMP G session Prise nats rncarrace aretuze opcions mero PPT MTF loading from session bg done v Bprevions session loaded from session and placed Fig 5 2 PEEK display 2
188. t this time using the CAMPGSYM M file 88 3 7 Linear Example Vehicle Crash Test CAMPGSYM and Simulink Every thing that was just done in section 3 7 will be repeated here except this time the CAMPGSYM M file will be used in conjunction with Simulink in place of the other files The entire procedure from above will be repeated for the users benefit PROBLEM The dummy in the figure shown below is driving his new VW Rabbit into a wall Will his shock absorbing bumper k2 b2 and his seat belts k1 b1 prevent him from hitting the windshield without breaking his collar bone DATA ON INJURIES SAE Handbook Seat belts must be tested to 3000 Ibs 1 334 x 10 N Chest can sustain a force of 1500 Ibs distributed over 30 in Seat belt effective area 30 in Shoulder strap seat belt combination 60 in PHYSICAL PARAMETERS M 1500 Kg kj 1x 10 N m b 500 N s m m 100kg k 3 x 10 N m b 8 x 10 N s m OBJECTIVES 1 Generate an engineering model of a physical system 2 Transform the engineering model of reality into a computer model for simulation using the Computer Aided Modeling Program CAMPO 89 Perform interactive simulation and generate numerical and graphical output using Matlab 4 Interpret the results make design decisions and perform simulation of several models in an interactive way PROCEDURE FOR SOLUTION Construct an engineering model of the crash test and consider only the time whe
189. t will be used to illustrate this example will be 2 from above This will be demonstrated in both Simulink and in Matlab Seen below in Fig 3 35 is the bond graph model for this system A SE A0 1 fn UA d d a ELE fa SG ess Fig 3 35 Hydraulic System Bond Graph Model 143 The bond graph from Fig 3 55 above is input into CAMPG as done in earlier methods and then interfaced with Matlab This is seen in Fig 3 36 below CAMP G untitled Prise ecit ancarrace anatuze options meros T E_ move single C 14 marked done move single C 14 marked done move single C_14 marked done BOND FROM P I move single c 14 marked done Fig 3 36 CAMPG Power Plant Bond Graph Model EQUATIONS The equations for this system are as follows C A g rho I rho L A R 1045 H m 2 m 3 sec deltaP1 rho g H1 deltaP2 rho g H2 144 CAMPG Matlab Solution Once the bond graph model was created in CAMPG it was interfaced with Matlab as seen in Fig 3 36 from above Using the CAMPGMOD M and CAMPGEQU M files that were created by CAMPG when interfaced with Matlab the simulation can be run once the physical parameters have been input into these two files The values for the physical elements were input into the files simply by editing them The user can edit these files using the Matlab editor or Notebook or a similar program that will save the file with out any word processing formatting Usin
190. ted matrices 112 MATLAB Simulation Solution of differential equations x 10 Simulation Position angle 6 Fig 3 18 4 Time Domain Simulation s 0 0 0 5 1 1 5 2 2 5 3 x 10 Simulation Velocity of armature and load 2 5 2 1 5 1 0 5 0 0 0 5 1 1 5 2 2 5 3 TF Step Response Angular Velocity of Armature and Load and Angular Velocity of Armature and Load Step Response x 10 2 Fig 3 19 amp E Using the lt Transfer Function s Time Simulation 0 0 5 1 5 2 2 5 3 Time sec n Step Response x 107 2 4 B E 2 0 0 0 5 1 1 5 2 2 5 3 Time sec 113 Fig 3 20 Frequency Response Bode Plot Once the matrices have been defined it is easier to get MATLAB to generate frequency response plots Shown in Figs 3 20 3 21 3 22 and 3 23 seen below is the Bode Plot of the magnitude and face of the torque output at the shaft e7 and position angle theta This variable was chosen to illustrate the fact that this approach will allow the user to obtain transfer functions and simulation results for internal signals of the system since they are calculated during the solution of equations This is a very useful feature of bond graph models generated in CAMPG because not only the time simulation results can be observed plotted for the states but the frequency response and the transfer functions generated for any effort or flow si
191. tes This file is primarily used to determine the transfer functions of the system It can also be used to solve the system and monitor certain outputs as the combination of the other two files did But this file can only be used with linear systems This example listing is the listing for the linear example that is seen in section 3 7 Nothing will be done with this file in section 3 7 In section 3 8 another system will be interfaced with Matlab and will be used to demonstrate how to get the transfer functions of a system This is exactly the way the this file would look just after the interfacing with Matlab has been done As seen here the sections of the file are very clear and straight forward Listing of campgsym m CAMPG MATLAB Symbolic State Space Model TE EE campgsym m CAMPG MATLAB function System symbolic matrices generates transfer functions clear 60 arses citar Initial conditions Q9IN Q3IN P11IN P6IN initial Q9IN Q3IN P11IN P6IN Ti diya System Physical Parameters global C3 R4 I6 C9 R10 I11 Convert system physical parameters and system matrices to symbols syms C3 R4 I6 C9 R10 111 C3 R4 I6 C9 R10 I11 Gis Se eee External inputs se t sf t global SF1 SF1 State variables vector p_q Q9 Q3 P11 P6 System Differential Equations First Order Fo
192. tes the results of the different simulations considering different velocities and physical parameters INITIAL NOF BUMPER SEAT BELTS DUMMY VELOCITY BELTS K2 B2 K1 Bl Ell Q9 N m N s m N m N m N m 25 1 300 000 80 000 10 000 500 9 310 0 8167 25 2 300 000 80 000 20 000 1 000 13 147 0 5144 55 1 300 000 80 000 10 000 500 20 483 1 7968 55 2 300 000 80 000 20 000 1 000 29 035 1 1300 55 1 300 000 80 000 10 000 1 000 25 547 1 3780 55 1 300 000 80 000 10 000 1 500 26 714 1 1100 55 1 300 000 80 000 8 000 1 500 25 990 1 1670 55 1 300 000 80 000 5 000 3 000 36 639 0 7500 55 2 300 000 50 000 5 000 3 000 31 184 0 7810 55 2 300 000 10 000 5 000 3 000 25 426 1 0360 55 2 100 000 10 000 5 000 3 000 15 986 0 8580 55 2 50 000 10 000 5 000 3 000 13 129 0 7440 Table 7 The impact at 55 mph is shown in Fig 4 15 and Fig 4 17 The displacement of the dummy is 1 79m so he hits the windshield in 0 065 sec Chest injury also occurs at 20 483 newtons The values of the shock absorbers can be changed in the bumper and in the seat belts Fig 23 shows what happens if he doesn t use a seat belt The dummy hits the windshield in about 1 sec at 25 mph but in just 0 05 sec at 55 mph without a seat belt 197 This example illustrates the whole process of modeling and simulation using CAMPG ACSL for linear systems The next section will explore other capabilities with non linear systems FORCE ACTING ON THE PASSEMCER 8 O SPLACEMENT 09 AT SPEED 2
193. th are not always in contact and therefore a nonlinear model exists The diagram of this function is shown in Fig 3 25 The position of the gears forces and velocities are of interest in the design of the gear train 117 Nonlinear Dead Space Contact F s a Force between geer teeth slope 200000 1b in Backlash 0 2 in BACKLASH IN GEAR TEETH Fig 3 25 Gear Geometry Discontinuity OBJECTIVES 1 Generate an engineering model of the gear train shown in Fig 3 24 2 Transform the engineering model of the real system into a computer model for simulation using the Computer Aided Modeling Program CAMPG 2 Using computer simulation in an interactive way generates numerical and graphical output using Matlab 4 Interpret the results and make design decisions PROCEDURE FOR SOLUTION 1 GENERATE AN ENGINEERING MODEL The system shown in Fig 3 24 is the engineering model of the real system The stiffness elements are the shafts the inertia element is the flywheel and the gears 118 2 GENERATE THE CORRESPONDING BOND GRAPH Make a Bond Graph model of the gear train Consider the inertia of the gears and the flywheel the compliance effect of the drive shaft and the slack between the gear teeth Fig 3 25 shows this model The backlash is modeled as a nonlinear compliant element C because the constitutive relation between contact force and the relative displacement is defined in Fig 3 25 The force func
194. the default plot command with automatic scaling and noaxis labels PLOT Q2 XTAG SECONDS TAG DISPLACEMENT ft YTAG labels the x axis TAG labels the y axis Since the x axis variable remains the same the label remains until changed with another XI AG Q2 DISPLACEMENT FT 0 02 0 02 0 06 0 06 50 10 o a e a e e SECONDS i Fig 4 4 Use of Axis Labels 170 Q 10 PLOT Q2 XHV 23 0 TAG DISPLACEMENT ft XHI scts the maximum valuc of thc x axis for this plot and subsequi plots 0 06 0 02 Q2 DISPLACEMENT FT 0 02 0 06 0 10 Fig 4 5 Time control of x axis and scaling SET CALPLT FALSE STRPLT TRUE Turns off line plot and turns on strip plot PLOT Q2 TAG DISPLACEMENT ft E3 TAG FORCE 1b Generates two strip plots Q2 and E3 TAC commands follow the respective variables 5 00 E3 FORCE LB 0 00 0 10 5 00 ZoET 82 DISPLACEMENT 0 00 0 10 6p 171 SET TITLE DAMPED OSCILLATOR DAMPED OSCILLATOR Gives title to plots SET STRPLT FALSE CALPLT TRUE Turns off strip plot turns on line plot SET XINCPL 7 0 Sets r aris length to 7 0 inches for line plats PLOT Q2 TAG DISPLACEMENT ft Generates line plot of Q2 with new r aris length Q 10 0 06 0 02 ACEMENT FT Fig 4 7 Plot size control S CALPLT F_STRPLT T Abbreviated way of turning off line plot and
195. the three examples at the end of this chapter These files were completed in the previous step These files can be named any other name that the user wants to use as long as all references in the files reflect the name change Now the user is in a position to enter and take advantage of all the Matlab run time commands The user can issue commands to simulate display and plot the calculated values The SUBPLOT PLOT FPRINTF and DISP commands are used for this purpose Section 3 4 offers more information on this step 6 OPTIMIZE SIMULATION Once familiar with the previous steps and confident to obtain results from Matlab the user can proceed to optimize and speed up the simulation as well as run several different simulations on the model under study Step by Step Explanation A complete step by step explanation of everything that is required of the user from start to finish is listed in each of the examples at the end of this section The examples are in sections 3 7 3 8 and 3 9 72 3 6 Linear Example Vehicle Crash Test MOD and EQU In this example a complete step by step explanation will be given for the entire process from a blank screen in CAMPG to the plotting of the desired outputs and states in Matlab PROBLEM The dummy in the figure shown below is driving his new VW Rabbit into a wall Will his shock absorbing bumper k2 b2 and his seat belts k1 b1 prevent him from hitting the windshield without breaking his col
196. tion is directly related to the relative displacement between the teeth This relative displacement at the gear teeth point of contact is calculated by the integration of the relative velocity between the two gears The relative tangential velocity is obtained by multiplying the angular velocity of the gear by their respective radius and finding the difference in tangential velocities a the point where the gears are in contact This is accomplished by the TF elements that make this transformation between the angular velocity and the tangential velocity The C element performs the integration and controls also the force using the defined DEAD SPACE function that represents the time the gears are in contact as well as when they are not Bond Graph Model GEAR 1 GEAR 2 I a 2 8 1 3 A T 11 SE 1 L rr Y o NT Y 1 I s o jI 1 R gis w R j 2 L d FLY WHEEL c C Fig 3 26 Gear Train Bond Graph Model Bond Graph Model in CAMPG 119 CAMP G session MATLAB MGY loading from session bg done Bprevions session loaded from session and placed OYE SEGMENT FROM cBfmove segment SE 1 marked done Fig 3 27 CAMPG Interface Menu 3 CAMPG Generate a description of the graph using the graphics capabilities of the Computer Aided Modeling Program with Graphical input CAMPG This model is shown in Fig 3 27 In sections 3 7 and 3 8 the linear model was constructed using the
197. transfer functions are not required that section of the file has been remarked out To see this file as Matlab creates it see section 3 3 Listing of CAMPGSYM M CAMPG MATLAB Symbolic State Space Model EE ET TET campgsym m CAMPG MATLAB function System symbolic matrices generates transfer functions clear S 2553 Initial conditions 94 Q9IN Q3IN P11IN P6IN initial Q9IN Q3IN P11IN P6IN T eua System Physical Parameters global C3 R4 I6 C9 R10 I11 global AA BB CC DD IC Convert system physical parameters and system matrices to symbols syms C3 R4 I6 C9 R10 I11 B C3 R4 I6 C9 R10 I11 E External inputs se t sf t global SF1 SF1 State variables vector p_q Q9 Q3 P11 P6 System Differential Equations First Order Form Derivatives vector p qdot dQ9 dQ3 dP11 dP6 System Differential Equations State Space form A B C D symbolic matrices Derivatives dp dq and output variables e f t Generate A B matrices corresponding to states p sand q s dO9 P6 16 P11 I11 A 1 0 0 1 111 1 16 B 1 0 dQ3 SF1 P6 16 A 2 0 0 0 1 16 B 2 1 dP11 09 C9 P6 I6 R10 P11 111 R10 A 3 1 C9 0 1 111 R10 1 16 R10 B 3 0 dP 6 03 C3 SF1 R4 P6 16 R4 09 C9 P6 16 R10 P11 111 R10 A 4 1 C9 1 C3
198. ts wee eee eee eee eee Call to Integration Function and campgequ m Sample Plotting Commands CAMPGEQUUMD are Seeded ed eetec Nei oxy bees pure oE vetere ia Global Declaration oo eee eee eee eee Defining the State Variables Derivative and Output Variable Equations Derivative Vector caviveee esl neccces sev aed Sample for Building Desired Output Vectors CAMPGSYM M anbintivivedoedietacide Pe viele deeieeduex 32 35 38 39 39 40 40 43 45 45 46 50 51 55 55 55 55 55 56 56 57 58 58 59 59 59 ii Converting Physical Parameters to Symbols Creating A and B Matrices in Terms of the States Creating C and D Matrices in Terms of the States Creating an Identity Matrix Creation of the Transfer Function Matrix FOER Creating Transfer functions in Numeric Format 3 4 Useful Runtime Commands used with CAMPG MATLAB SUBPLOT Spree Scie iis y ERR EX i exu tos PEOP D isuepidseytsdsuteste d tob EPRA EPRINTE eiusdem ger ots DISP 3iees xas tes epe eger Rex ER HA SR EHE SYMS gece eu n blunt dv db avem dodo EN GLOBAL keen EXER SAXA RR aS ALABBLE usse here ito YLABBlbL unsteereen Re E Sen 3E ed y e ds MEE osea etta ect as END Xni inten RC OA dS Generate the bond graph 11 core eee e xen Entering the Bond Graph in CAMPG sss Generating a set of usable M files ses
199. u With this option the user can change the color of different aspects of the CAMPG display to match the user s preferences The user has the option of changing the color of the Bond Element Number Marked Grid Ambig Deriv and Others This really allows the user to customize the CAMPG display 226 5 3 Advanced Bond Graph Features LARGE BOND GRAPHS CAMPG allows the user to create very large bond graphs inside the workspace by being able to scroll up down and left right This allows the user to create bond graphs that are much larger than the viewable area This is very useful in many applications in that many applications have bond graphs that are very large An example of this can be seen in the following Fig 5 4 and Fig 5 5 CAMP G session Pete T satz onterrose anmiiza options mer TT sE SYR ame ern ss KS se pop Vn 7 Rig pe SE SE aS RL 3 j a eo o m E X v d F4 a o loading from session bg done previons session loaded from session and placed te fican t locate from element for bond BOND FROM cBstoring to engine8c bg done ALS Fig 5 4 Four cycle internal combustion engine bond graph 227 CAMP G session Prise core feto aratra opcions meros PT ig n e E c c A F F E se d lc r se se Jerboa 5 yr Ese C se zJ R REP m ver B Bum bir T r Ese SE d RESO R se ue T 0 ARE se adn ogni SE loading from session bg
200. uld be accessed automatically RUN ACSL with CAMPSL CSL This option links the ACSL system to the CAMPG generated model file CAMPSL CSL and produces a CAMPSL EXE Execute CAMPSL EXE This option is useful if we are studying a model that has been translated compiled linked and executed previously This may be the case where a simulation may be done with different parameters and different plots on the same model The ACSLCLG CAMPSL command means run ACSL with CAMSPSL CSL as input Note that the CSL file attribute is not necessary 43 44 Chapter 3 CAMPG and Matlab 3 1 Introduction This document is to help the user learn how to use CAMPG in conjunction with Matlab This document will tell and show the user how to create a bond graph in CAMPG and then interface that bond graph with Matlab so the system being modeled can be simulated This document will also help the user get a better understanding of the files that are created when CAMPG is interfaced with Matlab and how to use them to get what is required of the project Using CAMPG in conjunction with Matlab makes for a very powerful set of computer modeling and simulation tools With the proper creation of a bond graph CAMPG can write the files that Matlab will user to run computer simulations of the system that is modeled by the bond graph 3 2 Interfacing CAMPG with Matlab Interfacing CAMPG with Matlab is a very simple procedure that is very fast Before the interfaci
201. unctions Rlocus using numeric Transfer Functior MATLAB Control system tool box operat using numeric transfer funtions wow 0 Ov Oi 4 WN m o Frequency Response using Transfer Func Hm clear 2521 more off lt T campgmod m X campgequ m X campgsym m X campgnum m x script Fig 1 10 CAMPG MATLAB input files display Yet there is another option The bond graph can be displayed using the CAMPG window display and entering a command to rearrange the windows horizontally or vertically we have the following display DOSBox 0 72 Cpu Cycles 3000 Frameskip 0 Progra E x 8 Editor C Campg working campgnum m File Edit Text Cell Tools Debug Desktop Window Help rine cait rmcersace mraryze options L S MF OO BOP BB sexx CAMP G MATLAB Numeric State Space Model b campgnum m CAMP G MATLAB functio m Generates Numeric A B C D matrices Numeric Tranfer Functions Frequency Response using Transfer Rlocus using numeric Transfer Func MAMTAD Central evwekem tant h D J O Oc QN lt campgmodm X campgequm X campgsymm X campgnumm script File Edit Debug Desktop Window Help DE Ro os BN f Locos working Shortcuts Z Howto Add Z What s New Command Window campgmod m Model Parameter Ir File Edit View Favorites Tools Help campgequ m Model Differential Q o P7 J Search E Folders m r campgsym m Symbolic
202. y 2000 Granda J The Role of Bond Graph Modeling and Simulation in Mechatronics Systems An Integrated Software Tool CAMPG Matlab Simulink Published in the Proceedings of MECHATRONICS 2000 Conference Atlanta Georgia September 7 2000 Granda J Computer Generated Transfer Functions CAMPG Interface to MATLAB and SIMULINK Proceedings of the International Conference on Bond Graph Modeling and Simulation ICBGM 99 San Francisco Ca January 1999 Pg 129 Granda J The Role of Physical System Modeling in Industry and Academia Proceedings of the International Conference on Bond Graph Modeling and Simulation ICBGM 99 San Francisco Ca January 1999 Pg 7 Fitsos P Granda J Bond Graph Modeling of Engine Valve and Control System Using Electromechanical Rotary Actuators Proceedings of the International Conference on Bond Graph Modeling and Simulation ICBGM 99 San Francisco Ca January 1999 Pg 353 247 36 3d 38 39 40 4 42 43 Granda J Reus J New developments in Bond Graph Modeling Software Tools The computer Aided Modeling Program CAMPG and MATLAB The IEEE International Conference on Systems man and Cybernetics Orlando Fla October 1997 Granda J Bond Graph Modeling Software Developments CAMPG Computer Aided Modeling Program New Features Proceedings of the International Conference on Bond Graph Modeling and Simulation ICBGM 97 Phoenix Arizona January 1997 Pg 31
203. y is to wait until the bond graph model is converted to the S domain in MATLAB and be treated as the plant and then add a 1 s term to produce the integration Incrementing the state space modifies the system matrices and in this case introduces a zero eigenvalue Here option two was chosen and the state space was increased to include the angular velocity f9 as one of the derivatives so that integration will produce the angle theta What follows are the listings of the files created by CAMPG after the user has edited them to produce the desired output in graphical form In this example there are a few things that are presented in graphical form They are Simulation Position Angle Simulation Velocity of Armature and Load TF Step Response Angular Velocity of Armature and Load TF Step Response Position Angle at Load Bode Plot Load Angular Velocity Bode Plot Motor Shaft Velocity Bode Plot Motor Shaft Torque Bode Plot Position Angle at Load posse ho ES Much of the files were deleted to save space The comments that are meant to help the user understand what that particular section of the file are what were deleted to save space 107 Campgmod m Bie pie T CAMPGMOD M MATLAB MODEL INPUT FILE clear Di Edo Initial conditions P9IN 0 thetain 0 Initial conditions vector initial P9IN thetain SB usse System Physical Parameters global R2 G3x4 R6 T7x8

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