Archangel User`s Manual - the Cal Poly Flight Simulation
Contents
1. CnB yawing moment due to change in sideslip angle non dimensional derivative CndA yawing moment due to aileron deflection non dimensional derivative CndR yawing moment due to rudder deflection non dimensional derivative Cnp yawing moment due to change in roll rate non dimensional derivative Cnr yawing moment due to change in yaw rate non dimensional derivative Ctxl steady state longitudinal axis thrust coefficient Ctxu change in thrust due to change in longitudinal axis velocity non dimensional derivative CyB side force due to change in sideslip angle non dimensional derivative CydA side force due to aileron deflection non dimensional derivative CydR side force due to rudder deflection non dimensional derivative Cyp side force due to change in roll rate non dimensional derivative Cyr side force due to change in yaw rate non dimensional derivative DBCL magnitude of the closed loop frequency response from Mil Std Closed Loop criterion handling qualities rating Dlat Lateral D matrix DlaydADeRes matrix of delayed a 5 transfer function residues DlaydBDaRes matrix of delayed 2 6 transfer function residues DlaydBDrRes matrix of delayed 2 transfer function residues DlaydNzDeRes matrix of delayed Nz 5 transfer function residues DlaydPDaRes matrix of delayed p 6 transfer function residues DlaydPDrRes matrix of delayed p transfer function residues DlaydPhiDaRes matrix of delayed 6 transfer function2. wndr approximate Dutch Roll natural frequency wndract actual Dutch Roll natural frequency wnlev Mil Std dn short period 7 92 criterion assessed FHQ rating level wnp approximated phugoid natural frequency wnpact actual phugoid natural frequency wnsp approximated short period natural frequency wnspact actual short period natural frequency zdr approximate Dutch Roll damping ratio zdract actual Dutch Roll damping ratio zp approximated phugoid damping ratio Zpact actual phugoid damping ratio zsp approximated short period damping ratio zspact actual short period damping ratio 31
3. respectively When you select a transfer function from this menu you need to enter the amount of system delay you want to add it must be positive and not zero Archangel will display two numerical sets of residues associated with the aircraft spiral mode similar to the short period delayed residue display When the Enter key is pressed Archangel will show the graphic comparison of the delayed and undelayed residues as compared to the appropriate spiral root See Figures 19 and 20 for what these displays will resemble Residue and Additional Analyses Option 11 Display Modal Controllability matrix Eigenspace and MatLab calculated residues This option will display each of these matrices in succession These matrices are a new way of calculating and displaying residues and are based on the original state space equation First the A matrix can be written as a combination of its eigenvalue A and eigenvector E matrices As EAE Substituting this into the original state space equation performing several mathematical gymnastics and solving for the general transfer function we get 21 x s _ ay ly pel HO A E b The eigenvector matrix E can be broken down into a series of column vectors e1 Additionally based on mathematical definition the inverse eigenvector matrix can be written as a series of transposed row vectors m m giving us a new form mb e s e s7 A T m b J x s z le
4. MOE Rearranging and consolidating the transfer function takes the same form as the residue eguation x S mb amp Raj Aa Gay N u s izn EF k l This shows the relationship between the transfer function eigenvectors and residues The combination m b above is called the modal controllability vector and it provides insight into the how easily a particular mode of motion is controllable by the system The higher the relative value in this vector for a particular control u the more easily controllable the associated mode of motion will be using that control elevator aileron rudder etc This equation shows the residues R for the transfer function are the eigenvector matrix elements scaled by the modal controllability vector for control u This option will first display the modal controllability vector as in Figure 21 Modal _ Controllability Matrix 1 0e 002 0 1575 0 1792i 0 1575 0 1792i 1 1977 1 61391 1 1977 1 61391 Figure 21 Archangel modal controllability vector display After pressing the Enter key Archangel will present a comparison of the eigenspace analysis residue matrix calculations to those obtained using MatLab tools as shown in Figure 22 22 Eigenspace Residue Matrix 1 0e 002 0 0101 0 0766i 0 0010 0 04441 0 0112 0 0343i 0 1973 0 09361 Calculated Residues 1 0e 002 0 0101 0 0766i 0 0010 0 04441 0 0112 0 0343i 0 1973 0 09361 Fig
5. 4 Archangel display of short period and phugoid parameters Archangel Main Menu Option 13 Longitudinal Handling Qualities Analysis When you select option 13 from the Archangel main menu a warning is displayed regarding the error that occurs in the bandwidth criterion when a low order system s phase does not cross 180 Also enter the amount of delay you want to add to the closed loop system analyses Smith Geddes Neal Smith and Mil Std Bandwidth You must enter a non zero non negative value After making the necessary calculations a new menu is displayed with all the handling quality analyses Each analysis is followed by a calculated flying qualities rating based on the selected criterion See Figure 5 for an example of this menu EEEE EEEE EEE EEEE RR RR RR RR KERR RR RR RR RR RR KERR RR RR RR RR RR KERR RR RR RR RR RR RR RR RR LONGITUDINAL FLYING HANDLING OUALITIES ANALYSIS MENU kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk 1 Smith Geddes Criterion Yields LEVEL 1 2 Neal Smith Criterion Yields LEVEL 1 3 MIL STD Bandwidth Criterion Yields LEVEL 2 4 MIL STD CAP Criterion Yields LEVEL 1 5 MIL STD wnsp ttheta2 Criterion Yields LEVEL 6 MIL STD Closed Loop Criterion Yields LEVEL 1 7 Northrop Criterion Yields LEVEL 1 8 Smith Geddes PIO Criterion Yields LEVEL 1 9 Look at Neal Smith Carpet Plot BW and DROOP Varied 10 Compare Frequency Response of Nominal and Delayed The
6. Ix slug ft 10 Iy slug ft 11 Lz slug ft 12 Ix slug ft Steady State Coefficients 13 C a 14 C D 15 C Ty 16 Cm 17 nr Longitudinal Directional Derivatives 18 Cm u 19 Cm a 20 Cu a NE d 22 C mr 23 Cm a 24 or BYG a 26 C mG q 28 Cp a 29 Cy u 30 C a 31 C Ls ed e 33 Cm e Lateral Directional Derivatives 34 Giy G p 36 C r 37 C ls 38 C ls 39 Cy B 40 Cy p 41 Cy r 42 Cn a 43 C ns If you don t have data for some of the line items enter a zero 0 for these items When you re finished entering the data for standardization purposes save SAD files with a SAD extension That way you will always know what the file contains Archangel Main Help Help is available for Archangel by typing help AAV3 in the MatLab Workspace This help will list the names of most of the variables used for calculation along with their explanation all the variables used throughout Archangel are listed in Appendix A Once calculated you can escape to the MatLab command line and use other MatLab analysis tools on these variables such as those in the Aerocontrols toolbox Start Archangel Now you are ready to begin using Archangel 3 Start it by opening MatLab and typing AAV3 in the MatLab command window Hit the Enter key when it pauses Then enter the full name including file extension of the aircraft SAD
7. altitude above sea level b aircraft wingspan baKs direct term of the 2 6 partial fraction expansion baPoles poles of the 7 6 partial fraction expansion baResidues residues of the f 6 partial fraction expansion bandwidth same as BW above brKs direct term of the 2 partial fraction expansion brPoles poles of the 2 partial fraction expansion brResidues residues of the 2 partial fraction expansion bwlev Mil Std Bandwidth criterion assessed FHQ level category flight phase category C subcategory landing 1 or other than landing 2 cbar aircraft wing mean aerodynamic chord class aircraft class group clooplev Mil Std Closed Loop criterion assessed FHQ level daResMatrix matrix of the 6 aileron dependent transfer function residues dbcl magnitude of the closed loop frequency response from Neal Smith criterion handling qualities rating deResMatrix matrix of the 5 elevator dependent transfer function residues delay user specified delay to add to selected transfer functions drResMatrix matrix of the rudder dependent transfer function residues faKs direct term of the 6 partial fraction expansion faPoles poles of the SA partial fraction expansion faResidues residues of the oe partial fraction expansion frKs direct term of the partial fraction expansion frPoles poles of the partial fraction expansion frResidues residues of the partial fraction expansion freq
8. displayed by Archangel Imag Axis oe oe eee eee ee eee 4 3 5 3 2 5 2 1 5 1 0 5 Real Axis Figure 10 Archangel root locus plot In addition to this root locus plot function you can escape from Archangel and use the Aerocontrols ezrlocus command with any of the calculated transfer functions from Archangel For example if you wish to view the 0 16 transfer function using ezrlocus type ezrlocus tf thtodenum thtodeden at the MatLab command line The tf function turns given numerator and denominator vector matrices into transfer functions for use with other MatLab tools Archangel Main Menu Option 10 Open Loop Step Response This option takes you to the step response plot selection menu Selecting options 1 15 from this menu will display a time step response of the open loop transfer function chosen The transfer functions are listed in the same order as on the Bode plot menu Option 16 will return you to the Archangel main menu The open loop step response can confirm analyses from other tools such as the stability of the system and the system damping It also tells you how long the system will take to respond to an input and how well it will respond See Figure 11 for an example of an open loop response plotted by Archangel 13 Step Response From Ur 18 T T a T T TO YE Amplitude g 50 00 150 200 250 300 Time sec Figure 11 Archangel open loop time respo
9. logarithmic frequency vector spanning 0 1 100 in 400 discrete steps g gravitational acceleration 32 2 ft sec or 9 8 m sec latFREQ transpose of latfreg see below vector 28 Variable Name Description latGAIN di response magnitude latMAG dio oTesponse magnitude in dB latPHASE response phase in degrees latfreq logarithmic frequency vector spanning 0 1 100 in 400 discrete steps latrslev lateral Smith Geddes criterion FHQ level latw lateral logarithmic frequency response vector see latfreg above lead same as LEAD mass aircraft mass northroplev Northrop criterion assessed FHQ level noveralpha variable used to calculate the CAP nslev Neal Smith criterion assessed FHQ level nzKs direct term of the Nz 5 partial fraction expansion nzPoles poles of the Nz 5 partial fraction expansion nzResidues residues of the Nz 5 partial fraction expansion nztodeden vertical acceleration to elevator deflection transfer function denominator nztodenum vertical acceleration to elevator deflection transfer function numerator oneoverTtheta2 numerator time constant for pitch angle short period approximation p wnsp 1 oneoverTtheta2 used to determine Mil Std dn short period T 92 criterion assessment paKs direct term of the p 6 partial fraction expansion paPoles poles of the p 6 partia
10. residues DlaydPhiDrRes matrix of delayed transfer function residues DlaydPsiDaRes matrix of delayed y a transfer function residues DlaydPsiDrRes matrix of delayed y transfer function residues DlaydQDeRes matrix of delayed q o transfer function residues DlaydRDaRes matrix of delayed r 6 transfer function residues DlaydRDrRes matrix of delayed r transfer function residues DlaydThDeRes matrix of delayed 0 5 transfer function residues DlaydUDeRes matrix of delayed u 5 transfer function residues Dlong Longitudinal D matrix FREQ transpose of freq see below vector 25 Variable Name Description GAIN 0 response magnitude Ixx mass moment of inertia about the longitudinal x axis Ixz x z product of inertia lyy mass moment of inertia about the lateral y axis Izz mass moment of inertia about the vertical z axis LEAD Neal Smith criterion resultant required pilot lead in degrees Lb rolling moment due to change in sideslip angle stability derivative Lbs Lo 1 Ixz 2 Ixx Izz LdA rolling moment due to aileron deflection stability derivative LdAs LAA 1 I1xz 2 Ixx Izz LdR rolling moment due to rudder deflection stability derivative Ld
11. 7 0663 350 5027 25 3697 6303 87 1596 271 3630 6370 91 8975 Figure 16 Archangel residue matrix display The first matrix is the magnitude of the corresponding residue while the second is the angle by which it departs the appropriate root In addition to the numerical display of the normalized 17 residues each of these is combined with their appropriate root in a graphical display called the Modal Root Residue Display Figure 17 depicts a typical modal root residue display Normalized Residues for Short Period Root 4 1678 4 4018i 4 5 6 5 5 5 4 5 4 3 5 3 2 5 2 Normalized Residues for Short Period Root 4 1678 4 4018i u de alpha de theta de a de nz de Note alpha de li e may be hidden behind nz de 6 5 5 5 45 4 3 6 3 25 2 Figure 17 Archangel modal root residue display Residue and Additional Analyses Option 5 Display effect of delay on poles Selecting option 5 display effect of delay on poles opens another menu listing all the transfer functions starting with longitudinal in standard order then lateral aileron and lateral rudder both in standard order The last three menu items will return you to the Residue and additional analyses menu escape to the MatLab command line and return to the Archangel main menu respectively When you select a transfer function from this menu you need to enter the amount of system delay you want to add it must be positive and not zero Archa
12. Apynavyehoo Archangel v3 2 for MatLab User s Manual Spring 2001 Prepared by Kenneth D Bole For Dr Daniel Biezad Aerospace Engineering Department California Polytechnic State University San Luis Obispo CA Table of Contents TABEE OFECONTENTS ese een ees Ee scenes de ie ee cove BEG eene Se eed gedek de ee eo se el Ge ee se di eb ee ls Ge eene be bes dee nee be ge genee eb I INFRODUCTION ER EE EE EO EE 1 INSTALLATION AND START UP ies ees ingegee stede ss sesse deed sko Gede ed ige es ok ETTER dese We gee Ge ge deeg ee Ee 2 ADD ARCHANGEL DIRECTORY TO MATLAB PATH cssssssscccecsesesececececsesenecesececsenesecesececsesesasaeseeeesesenaaeeeeeeeesensaaeas 2 STANDARD AIRCRAFT DATA SADY FILES 4 ee see ee SE ee ed ee Ee es es EE a awd eee Ee ee es R Ge Dee oases 3 ARCHANGEIMAIN HELP ee ER EE Ge ee een Ge ee ee GE GE GE GEE cae bac Ge Se ee GN aie EE E Ge ee ee bee ee es 5 STARTAREHANGEI ESE SE E EE GE EE GE Ge GR GE Gee GE EG EE EE ER EE ns Ces ees 5 LONGITUDINAL ANALYSES Se SE ee cock Ee de de ee de Se eea ee aaa de de ee ee Ge TE Ee De ee Ge ee ee Ge ae Ee de oe de ee ee de SE Ee Ee beds ee 7 ARCHANGEL MAIN MENU OPTION 1 LONGITUDINAL STATE SPACE MODEL DISPLAY iese se ese ee ee ee ee ee ese ee ee ee ee ee 7 ARCHANGEL MAIN MENU OPTION 2 LONGITUDINAL TRANSFER FUNCTIONS DISPLAY es se se ee ee ee ee ee ee ee ee ee ee ee ee 7 ARCHANGEL MAIN MENU OPTION 3 LONGITUDINAL PARAMETERS DISPLAY ee ee ee
13. C SAD Learjet_catB_a SAD Learjet_catB_b SAD Learjet_catC SAD Marchetti211 catB a SAD Marchetti211 catB L SAD Marchetti211 catC SAD navion catB SAD STOL catB SAD STOL catC SAD Add Archangel directory to MatLab Path The next step is to add this new directory to the path in MatLab 1 2 3 Open MatLab Under the File menu select Set Path In the Path Browser window under the Path menu select Add to Path On the Add to Path window click the button browse to and select the Archangel3 directory created before Ensure the Add to back radio button is selected then click the OK button Finally under the Path Browser File menu select Save Path Close the Path Browser Standard Aircraft Data SAD files Archangel also needs at least one Standard Aircraft Data SAD file available in any directory contained in the MatLab path This is because the first piece of information Archangel asks for is the name and extension of a SAD file You can either enter one by hand or use one already in existence If you choose to enter the data in a SAD file by hand open a blank text file and enter the data in the following order i e Roskam format Flight Condition 1 Altitude ft 2 Air Density slugs ft 3 Speed fps 4 Initial Attitude 6 in rad Geometry and Inertias 5 Wing Area ft 6 Wing Span ft 7 Wing Mean Aerodynamic Chord c ft 8 Weight Ibs 9
14. ES Neal Smith criterion resultant resonance peak in dB 26 Variable Name Description S aircraft wing area TP estimated equivalent time delay in seconds used in Mil Std Bandwidth criterion assessment U aircraft forward velocity UndlaydADeRes matrix of undelayed a 6 7 transfer function residues UndlaydBDaRes matrix of undelayed 2 6 3 transfer function residues UndlaydBDrRes matrix of undelayed 2 transfer function residues UndlaydNzDeRes matrix of undelayed Nz 8 z transfer function residues UndlaydPDaRes matrix of undelayed p 6 transfer function residues UndlaydPDrRes matrix of undelayed p transfer function residues UndlaydPhiDaRes matrix of undelayed 6 i transfer function residues UndlaydPhiDrRes matrix of undelayed 6 transfer function residues UndlaydPsiDaRes matrix of undelayed wy 6 transfer function residues UndlaydPsiDrRes matrix of undelayed w transfer function residues UndlaydQDeRes matrix of undelayed q 6 transfer function residues UndlaydRDaRes matrix of undelayed r 6 transfer function residues UndlaydRDrRes matrix of undelayed r transfer function residues UndlaydThDeRes matrix of undelayed 0 6 transfer function residues UndlaydUDeRes matrix of undelayed u 5 transfer function residues W aircraft weight WIN Neal Smith criterion resultant frequency ve
15. RR de RR k de ke RR RR EK 1 Smith Geddes Criterion Yields LEVEL 1 2 Compare Frequency Response of Nominal and Delayed Phi DAP 3 RETURN TO MAIN OPTION MENU KKK KKK KKK IKK KEK KKK RR RR KERR RR RR KK RR RR RR RR RR KKK EEE KERK RR RR RR RR RR RR RR KI Select an option number to receive a graphical analysis Figure 8 Lateral flying handling gualities menu As indicated at the bottom of the screen each of the menu items may be selected for graphical analysis upon which each criterion is based Type the number of the desired option and press the Enter key When finished examining any of the graphical analyses press the Enter key to close the graph window and continue Selecting option 1 on this menu will display a graphical analysis of the aircraft on which the Smith Geddes criteria rating is based Option 2 will display a Bode plot comparing the normal and delayed system frequency response When done with these analysis tools select option 3 to return to the Archangel main menu 11 5 Graphical Analyses Archangel Main Menu Option 8 Bode Plots Selecting option 8 from the Archangel main menu will take you to the Bode plot selection menu Selecting options 1 15 from this menu will display a Bode plot of any of the available aircraft transfer functions u a 0 qm B p y 6 E 5 e a a a a r E 9 pY 6 8 8 8 d F rF F rY r r 3 Bode plots allow the student to analyze the frequency and
16. Rs LAR 1 Ixz 2 Ixx Izz Lp rolling moment due to change in roll rate stability derivative Lps Le 1 Ixz 2 Ixx Izz Lr rolling moment due to change in yaw rate stability derivative Lrs heyy l Cae oy ie loz MAG 0 6 response magnitude in dB Mde pitching moment due to elevator deflection stability derivative Mq pitching moment due to change in pitch rate stability derivative Mu pitching moment due to change in longitudinal velocity stability derivative Mw pitching moment due to change in vertical velocity stability derivative Mwd pitching moment due to change in vertical acceleration stability derivative Nb yaw moment due to change in sideslip angle stability derivative Nbs Nb 1 Ixz7 2 IzzxIxx NdA yaw moment due to change aileron deflection stability derivative NdAs NAA 1 Ixz 2 Izz Ixx NdR yaw moment due to change rudder deflection stability derivative NdRs NAR 1 Ixz 2 Izz Ixx Np yaw moment due to change in roll rate stability derivative Nps Np 1 Ixz 2 Izz Ixx Nr yaw moment due to change in yaw rate stability derivative Nrs Nr 1 1xz 2 1zz Ixx Nz_GAIN Nz 6 e response magnitude Nz MAG Nz 6 e Tesponse magnitude in dB Nz_ PHASE Nz response phase in degrees PHASE 0 6 response phase in degrees PHCL phase of the closed loop frequency response from Mil Std Closed Loop criterion handling qualities rating Q flight dynamic pressure R
17. SP residues 0 2958 0 90691 0 6713 0 71271 Figure 19 Archangel numerical display of delayed undelayed short period residues 19 You can see that as delay is added the residue real parts become more negative and their imaginary parts become less negative giving the effect that the residues are moving to the left and down We also know that as delay is increased the system becomes more difficult to handle Therefore as these residues move with increased delay the less stable the aircraft Short period residues from some transfer functions have more effect depending upon the flight condition 6 residues are more important to aircraft handling during category C flight operations while N 6 residues are more important during category B operations Pressing the Enter key will show a graphic comparison of the delayed and undelayed residues an example of which is shown in Figure 20 The residues are shown radiating out from their related short period roots to help the student understand the effect of the residue on the root Normalized Residues for Short Period Root 4 1678 4 4018i 4 4 42 4 3 8 3 6 5 5 5 4 5 4 3 5 Normalized Residues for Short Period Root 4 1678 4 4018i Undelayed Delayed 55 5 4 5 4 3 5 Figure 20 Archangel graphic display of delayed undelayed short period residues Residue and Additional Analyses Option 7 Display effect of delay on phugoid residues Option 7
18. ctor for closed loop response Xde longitudinal force due to elevator deflection stability derivative Xtu longitudinal force due to change in longitudinal thrust stability derivative Xu longitudinal force due to change in longitudinal velocity stability derivative Xw longitudinal force due to change in vertical velocity stability derivative Yb lateral force due to change in sideslip angle stability derivative YdA lateral force due to aileron deflection stability derivative YdR lateral force due to rudder deflection stability derivative Yp lateral force due to change in roll rate stability derivative Yr lateral force due to change in yaw rate stability derivative Zde vertical force due to elevator deflection stability derivative Zq vertical force due to change in pitch rate stability derivative Zu vertical force due to change in longitudinal velocity stability derivative Zw vertical force due to change in vertical velocity stability derivative 27 Variable Name Description aKs direct term of the a partial fraction expansion aPoles poles of the a 6 partial fraction expansion aResidues residues of the a 5 partial fraction expansion alphatodeden angle of attack to elevator deflection transfer function denominator alphatodenum angle of attack to elevator deflection transfer function numerator altitude aircraft
19. display When the Enter key is pressed Archangel will show the graphic comparison of the delayed and undelayed residues as compared to the appropriate Dutch roll roots See Figures 19 and 20 for what these displays will resemble Residue and Additional Analyses Option 9 Display effect of delay on roll residues Option 9 will open a menu listing only the lateral transfer functions in standard order The last three options on this menu will allow return to the Residue and additional analyses menu escape to the MatLab command line and return to the Archangel main menu respectively When you select a transfer function from this menu you need to enter the amount of system delay you want to add it must be positive and not zero Archangel will display two numerical sets of residues associated with the aircraft roll mode similar to the short period delayed residue display When the Enter key is pressed Archangel will show the graphic comparison of the delayed and undelayed residues as compared to the appropriate roll root See Figures 19 and 20 for what these displays will resemble Residue and Additional Analyses Option 10 Display effect of delay on spiral residues Option 10 will open a menu of only the lateral transfer functions in standard order The last three options on this menu will allow return to the Residue and additional analyses menu escape to the MatLab command line and return to the Archangel main menu
20. e category are air to air combat ground attack weapon delivery launch aerial recovery reconnaissance in flight refueling receiver terrain following antisubmarine search and close formation flying Category B Nonterminal flight phases that are normally accomplished using gradual maneuvers and without precision tracking although accurate flight path control may be required Included in the category are climb cruise loiter in flight refueling tanker descent emergency descent emergency deceleration and aerial delivery Terminal flight phases Category C Terminal flight phases are normally accomplished using gradual maneuvers and usually require accurate flight path control Included in this category are takeoff catapult takeoff approach wave off go around and landing Table 2 Flight phase categories Enter the number corresponding to the flight phase of the aircraft Now Archangel will make several calculations then display the main Archangel menu Figure 1 kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk YOUR MAIN OPTIONS ARE 1 Display Longitudinal State Space Model Full State Feedback 2 Display Longitudinal Transfer Functions in Zero Pole Gain Format 3 Display Longitudinal Parameters 4 Display Lateral State Space Model Full State Feedback 5 Display Aileron Lateral Transfer Functions in Zero Pole Gain Forma
21. e of which will include a GUI interface Kenneth Bole CPSLO Spring 2001 2 Installation and Start Up To install Archangel 3 2 copy the file Archangel3 2 exe to the toolbox directory under your main MatLab directory Open the self extracting zip file by double clicking it This will create and copy the following m files to a new toolbox Archangel3_2 directory AAV3 m BANDW m BANDWI1 m BANDW2 m BANDWHEL m da ResMatrixl m damp2 m de ResMatrix m DelayDRResMenu m DelayMenu m DelayPhResMenu m DelayResTF m DelayRollResMenu m DelaySpiralResMenu m DelaySPResMenu m DispDelayTF m DisplayPFE m DLATP m DLATSS m DLATTFA m DLATTFR m DLONGP m DLONGSS m DLONGTF m dr ResMatrix1 m DRResCompare m DSBP m DSNP m DSRLP m DSSIGGY m DSSRP m EigRes m FQA m GRAPHIC m GRAPHIC2 m LAT R SMITH m LATFQA m LATPAR m LatResidues m LATSS m LATTFA m LATTFR m LONG R SMITH m LONGPAR m LongResidues m LONGSS m LONGTF m N SMITH m N SMITHI m NCARPET m newOPTION m NORMALIZE m NSDROOP m NSPEAK m PhResCompare m residudispmenu m residumenu m RollResCompare m SIGGY m SpiralResCompare m SPResCompare m It will also copy the following SAD files to the same directory 747 catB a SAD 747 catB b SAD 747 catC SAD A1 SAD A4 SAD AAD catB SAD AAD catC SAD BeechM 21 catB a SAD BeechM21 catB L SAD BeechM 21 catC SAD c880 catB SAD c880 catC SAD Cessnal 72 catB SAD f104 catB SAD f104 catC SAD F4C catB a SAD F4C_catB_b SAD F4C_catC SAD Jetstar_catB SAD Jetstar_cat
22. ee ee ee ee ee ee ee ee ee ee ee ee ee ee ee ee ee ee ee 8 ARCHANGEL MAIN MENU OPTION 13 LONGITUDINAL HANDLING QUALITIES ANALYSIS ee ees se ee ee ee ee ee ee ee ee ee ee 8 TA TERA ANALYSES is see EES siese seek osse ds Oe ans ca tee T Gee ee Gee Ge SeSe ee SE TEDE SODE DSE EE Re erg ses ge se 10 ARCHANGEL MAIN MENU OPTION 4 LATERAL STATE SPACE MODEL DISPLAY ee se ee ee ee ee ee ee ee ee ee ee ee ee ee ee ee ee ee 10 ARCHANGEL MAIN MENU OPTIONS 5 6 LATERAL TRANSFER FUNCTION DISPLAYS ee ee ee ese ee ee ee ee ee ee ee ee ee ee ee ee ee ee 10 ARCHANGEL MAIN MENU OPTION 7 LATERAL PARAMETERS DISPLAY Mu ee oe ee ee ee ee ee ee ee ee ee ee ee ee ee ee ee ee ee ee ee ee ee ee ee 10 ARCHANGEL MAIN MENU OPTION 14 LATERAL HANDLING QUALITIES ANALYSIS sesse see ees se ee ee ee ee ee ee ee ee ee ee 11 GRAPHICAL ANALYSES iss soek ies ese eed n ens ee oes ge diese doe de ae de Me be ee gee de gee Ge ds ee dien Ge Ge ge Se be Ge de eb oge ei ee ere ee 12 ARCHANGEL MAIN MENU OPTION 8 BODE PLOTS cccccccccccecsessseceeececeessaeceeececsessaaeceeeeecsesssaeceeeeseseseeaeeeeeeeenes 12 ARCHANGEL MAIN MENU OPTION 9 ROOT LOCUS PLOTS 0 ccccccecssscecessececesscececssseeceesseeccssseeceesseeceeseecenseeeeees 12 ARCHANGEL MAIN MENU OPTION 10 OPEN LOOP STEP RESPONSE ees ee ee sees se ee ee se ee ee ee ee ee ee se ee ee ee ee ee ee ge ee ee ee ee 13 ARCHANGEL MAIN MENU OPTION 11 NICHOLS PLOTS ees ee ee ese ee ee ee ee ee ee ee ee
23. ee ese ee ee ee ee ee eke ee ee ee Re Re ee ee ee Re Re ee 14 ARCHANGEL MAIN MENU OPTION 12 SIGGY PLOTS ee ese ee ee ee ee ee ee ee ee eke ee ee ee ee Re Re ee ee ee Re Re ee ee ee Re Re ee ee ee Re Re ee 15 RESIDUE AND ADDITIONAL ANALYSES ee sees ssssssssse se ee es ss ss se se se ee ee es ss se se ese es ee Ge ee ee Ge Ge Ge ee ee Ge 16 RESIDUE AND ADDITIONAL ANALYSES OPTION 1 DISPLAY RESIDUES AND POLES eeuse se see ee se ee ee ee ee ee ee ee ee ee ee 16 RESIDUE AND ADDITIONAL ANALYSES OPTION 2 3 4 POPULATE RESIDUE MATRICES ee ees ee ee ee ee ee ee ee ee ee ee ee 17 RESIDUE AND ADDITIONAL ANALYSES OPTION 5 DISPLAY EFFECT OF DELAY ON POLES eeuse see ee ee ee ee ee ee ee ee ee 18 RESIDUE AND ADDITIONAL ANALYSES OPTION 6 DISPLAY EFFECT OF DELAY ON SHORT PERIOD RESIDUES 19 RESIDUE AND ADDITIONAL ANALYSES OPTION7 DISPLAY EFFECT OF DELAY ON PHUGOID RESIDUES ees se se se ee ee 20 RESIDUE AND ADDITIONAL ANALYSES OPTION 8 DISPLAY EFFECT OF DELAY ON DUTCH ROLL RESIDUES 21 RESIDUE AND ADDITIONAL ANALYSES OPTION 9 DISPLAY EFFECT OF DELAY ON ROLL RESIDUES ie ese see se se se se ee 21 RESIDUE AND ADDITIONAL ANALYSES OPTION 10 DISPLAY EFFECT OF DELAY ON SPIRAL RESIDUES iese see se se ee 21 APPENDIX A ARCHANGEL VARIABLES cccccscscscscscscscscsccccccccccccccccccccccccccccccccsccccecececececececececececcsoreres 24 1 Introduction Where shall we begin At the beginning of course Th
24. en you select option 1 from the Archangel main menu it will display the longitudinal state space model of the aircraft i e A B C and D matrices An example of this display is shown in Figure 2 Longitudinal State Space System Along Blong Clong Dlong A u alpha theta q 0 04422 18 74408 32 20000 0 0 00135 2 20202 0 0 97925 0 0 0 1 00000 0 00244 23 72524 0 6 13122 theta q 1 00000 1 00000 Figure 2 Archangel display of longitudinal state space matrices These matrices come from the state variable equations x Ax Bn y Cx Dn where x is the state vector 7 is the control input vector and y is the output vector The A matrix is the aircraft or plant matrix B is the control input matrix C is the output matrix multiplier of the state vector and D is the output matrix multiplier of the control vector For the longitudinal state space representation x consists of states in the following order u velocity a angle of attack pitch angle and q pitch rate The control input vector 7 only reflects one input 5 which is the elevator deflection Archangel Main Menu Option 2 Longitudinal transfer functions display When you select option 2 from the Archangel main menu it will display all the longitudinal transfer functions for the aircraft in zero pole gain format over two screens The u 5 and al 6 transfer functions are shown first after which Archangel waits for you to press the Enter key Af
25. ess the Enter key to return to the Archangel main menu See Figure 3 for an example of how Archangel displays transfer functions Archangel Main Menu Option 7 Lateral parameters display When you select option 7 from the Archangel main menu it will show the Dutch roll frequency approximate and actual and Dutch roll damping ratio approximate and actual See Figure 7 for an example of this screen 10 Approximate Actual Dutch Roll frequency 3 1973 3 3768 Dutch Roll damping 0 22006 0 20311 Figure 7 Archangel display of Dutch roll parameters When done with this information on this screen type the Enter key to return to the Archangel main menu Archangel Main Menu Option 14 Lateral Handling Qualities Analysis When you select option 14 from the Archangel main menu you will be asked to enter the amount of delay you want to add to the Smith Geddes system analyses You must enter a non zero non negative value After making the necessary calculations a new menu is displayed with all the few lateral flying handling quality analyses The one criteria analysis is followed by a calculated flying qualities rating based on the Smith Geddes criteria See Figure 8 for an example of this menu He ke ke He ke He dede He ke He e He de ke RR ke ke k RR k k k k k k k k k k k k k k k k k k k k k k k k k k k kk kk kkk kkk kkk kkk kkkkk Lateral Flying Handling Qualities Menu KKK IKI RRR KKK RIKKI RK IR KIRK KKK RR RR ER RR
26. file you want to analyze Next it will ask you for the Aircraft Class Group of the aircraft see Table 1 for a breakdown of these classes Class I Small light airplanes such as light utility primary trainer and light observation craft Class I Medium weight low to medium maneuverability airplanes such as heavy utility search and rescue light or medium transport cargo tanker reconnaissance tactical bomber heavy attack and trainer for Class I NOTE A C extension is for aircraft in nonterminal flight phases while an L is for terminal Class III Large heavy low to medium maneuverability airplanes such as heavy transport cargo tanker heavy bomber and trainer for Class III Class IV High maneuverability airplanes such as fighter interceptor attack tactical reconnaissance observation and trainer for Class IV Table 1 Classification of airplanes Archangel has separated the classes into two groups for calculations made during additional analyses Group 1 contains classes I II C and IV group 2 contains classes I L and III Enter the number of the group to which the aircraft you want to analyze belongs Next you will be asked to select the category of flight phase the aircraft was in when the SAD file data was measured see Table 2 for flight phase categories Nonterminal flight phase Category A Nonterminal flight phase that require rapid maneuvering precision tracking or precise flight path control Included in th
27. is is a short history of the development of Archangel as an aircraft design analysis tool for the students of the Aerospace Engineering Department of California Polytechnic State University San Luis Obispo In 1983 student Mark Anderson developed software called Flight f to calculate aircraft plant matrices from aircraft test data This proved very useful to Cal Poly aeronautical engineering students in that it relieved them of the burden of calculating these matrices by hand This software was updated in 1992 By 1993 desktop computers had advanced in computing power to the point where more complex calculations could be rapidly performed So in that year Archangel 1 0 was developed to extend the calculations to include analysis tools Since then Archangel has evolved through several iterations of independent student coding to become a fundamental tool for aerospace engineering students to use in all phases of aircraft and spacecraft design Undergraduate student Mark Morrel originally wrote the MatLab version of Archangel when he became frustrated with the limitations of the burdensome Archangel v2 0 He released his Archangel as version 2 5 Over the past year I optimized and expanded upon v2 5 to such a point as to release it as version 3 0 Several of the original MatLab m files were modified re used This version 3 2 is the final version ready for release to the engineering publicly Stay in touch with Dr Dan Biezad for future updates on
28. kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk 1 Display residues and poles 2 Display normalized longitudinal residue magnitudes 3 Display normalized lateral aileron residue magnitudes 4 Display normalized lateral rudder residue magnitudes 5 Display effect of delay on poles 6 Display effect of delay on short period residues 7 Display effect of delay on phugoid residues 8 Display effect of delay on Dutch roll residues 9 Display effect of delay on roll residues 10 Display effect of delay on spiral residues 11 Display Modal Controllability matrix Eigenspace and MatLab calculated residues 12 Return to MatLab workspace 13 Return to Archangel Main Menu kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk Please Enter A Number Corresponding To An Option Above Figure 14 Residue and Additional Analyses menu All available options are detailed below with the exception of options 12 and 13 As on the other menus these last two options will exit to the MatLab command line and return you to the Archangel Main Menu respectively Residue and Additional Analyses Option 1 Display residues and poles This option takes you to the residue display menu which lists all 15 transfer functions as display options as well as options to return to the Residue and additional analyses menu and to return to the Archangel main menu Each transfer function has its own set of ass
29. l fraction expansion paResidues residues of the p 6 partial fraction expansion phase flight phase category A B C phel same as PHCL phi_ach average Cooper Harper rating for results of the 6 TF analysis phiph bw roll attitude criterion function phase of 6 bandwidth freguency phtodaden roll angle to aileron deflection transfer function denominator phitodadentd delayed roll angle to aileron deflection transfer function denominator phitodanum roll angle to aileron deflection transfer function numerator phitodanumtd delayed roll angle to aileron deflection transfer function numerator phitodrden roll angle to rudder deflection transfer function denominator phitodrnum roll angle to rudder deflection transfer function numerator pio Smith Geddes with PIO criterion assessed FHQ level prKs direct term of the p partial fraction expansion prPoles poles of the p partial fraction expansion 29 Variable Name Description prResidues residues ofthe p partial fraction expansion ptodaden roll rate to aileron deflection transfer function denominator ptodanum roll rate to aileron deflection transfer function numerator ptodrden roll rate to rudder deflection transfer function denominator ptodrnum roll rate to rudder deflection transfer function numerator qKs direct term of the q 6 partial fraction expa
30. nction denominator sitodanum yaw angle to aileron deflection transfer function numerator sitodrden yaw angle to rudder deflection transfer function denominator sitodrnum yaw angle to rudder deflection transfer function numerator stab SAD file input matrix 30 Variable Name Description thKs direct term of the partial fraction expansion thPoles poles of the 0 5 partial fraction expansion thResidues residues of the 5 partial fraction expansion tha_ach average Cooper Harper rating for results of the 0 5 TF analysis thaph_bw pitch attitude criterion function phase of 8 5 bandwidth frequency thetal aircraft pitch angle thtodeden pitch angle to elevator deflection transfer function denominator thtodedentd delayed pitch angle to elevator deflection transfer function denominator thtodenum pitch angle to elevator deflection transfer function numerator thtodenumtd delayed pitch angle to elevator deflection transfer function numerator uKs direct term of the u 5 partial fraction expansion uPoles poles of the u 5 partial fraction expansion uResidues residues of the u 5 partial fraction expansion utodeden velocity to elevator deflection transfer function denominator utodenum velocity to elevator deflection transfer function numerator W logarithmic frequency response vector see freq above win same as WIN
31. ngel will display a root locus plot containing the original red and the delayed blue root loci and their movement as gain is increased see Figure 18 Note that as delay is added the system gets worse as we should expect 18 Imag Axis Real Axis Figure 18 Archangel delayed root locus plot This plot is displayed using the Aerocontrols toolbox To close it press the Enter key you will be returned to the Display effect of delay on roots menu Residue and Additional Analyses Option 6 Display effect of delay on short period residues Option 6 will open a short menu of only the longitudinal transfer functions in standard order The last three options on this menu will allow return to the Residue and additional analyses menu escape to the MatLab command line and return to the Archangel main menu respectively When you select a transfer function from this menu you need to enter the amount of system delay you want to add it must be positive and not zero Archangel will display two numerical sets of residues see Figure 19 Like roots residues come in pairs one in the positive imaginary plane the other in the negative imaginary plane Therefore there are two sets displayed here one for each residue In each set displayed the first is the undelayed residue and the second the delayed residue First Undelayed and Delayed SP residues 0 2958 0 90691 0 6713 0 7127 Second Undelayed and Delayed
32. nse graph Archangel Main Menu Option 11 Nichols Plots This option takes you to the Nichols plot selection menu Selecting options 1 15 from this menu will display a Nichols plot of the selected transfer function The transfer functions are listed in the same order as on the Bode plot menu Option 16 will return you to the Archangel main menu A Nichols plot is an alternate form of the Bode plot that combines all Bode elements onto one graph It allows the student after some practice and experience reading it to analyze the frequency and phase response of a system See Figure 12 for an example of an Archangel Nichols plot 14 g ti Figure 12 Archangel Nichols plot HA r E H Option 17 will return you to the Figure 13 Archangel Siggy plot 15 Re ed KO En ob sees RIRA SET PER This option takes you to the Siggy plot selection menu Selecting options 1 15 from this menu will display a Siggy plot of the transfer function chosen see Figure 13 The transfer functions are listed in the same order as on the Bode plot menu Archangel Main Menu Option 12 Siggy Plots Archangel main menu 6 Residue and Additional Analyses Selecting option 15 from the Archangel main menu will open the Residue and Additional Analyses menu See figure 14 for an example of this menu kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk RESIDUE AND ADDITIONAL ANALYSES MENU kkkkkkkkkk
33. nsion qPoles poles of the g partial fraction expansion qResidues residues of the q 5 partial fraction expansion qtodeden pitch rate to elevator deflection transfer function denominator qtodenum pitch rate to elevator deflection transfer function numerator raKs direct term of the r 6 partial fraction expansion raPoles poles of the r Oy partial fraction expansion raResidues residues of the r 6 partial fraction expansion rho air density at current altitude rks direct term of the r partial fraction expansion rrPoles poles of the r partial fraction expansion rrResidues residues of the r N partial fraction expansion rs nz acceleration criterion function phase of Nz at bandwidth frequency rslev Smith Geddes criterion assessed FHQ level rtodaden yaw rate to aileron deflection transfer function denominator rtodanum yaw rate to aileron deflection transfer function numerator rtodrden yaw rate to rudder deflection transfer function denominator rtodrnum yaw rate to rudder deflection transfer function numerator siaKs direct term of the yw 6 partial fraction expansion siaPoles poles of the y 6 partial fraction expansion siaResidues residues of the w 6 partial fraction expansion sirKs direct term of the y partial fraction expansion sirPoles poles of the y partial fraction expansion sirResidues residues of the w partial fraction expansion sitodaden yaw angle to aileron deflection transfer fu
34. ociated residues as calculated in a partial fraction expansion PFE When displayed in PFE form a transfer function looks as follows R R R A eee es s 4 s A s A where R are the residues and are the eigenvalues of the A matrix as well as the roots of the transfer function Archangel displays the partial fraction expansion as in Figure 15 it is an example of a 5 PFE display 16 theta de Zero pole gain 39 4882 s 2 064 s 0 05974 s 2 0 04192s 0 03269 s 2 8 336s 36 75 theta de 1173 3 4253i 1678 4 4018i 1173 3 4253i 1678 4 4018i 1173 0 18692i 02096 0 17959i 1173 0 18692i 02096 0 17959i Figure 15 Archangel residue partial fraction expansion display Residue and Additional Analyses Option 2 3 4 Display normalized residue matrices Options 2 through 4 display the residue matrices for each of the control surface inputs numerically and graphically The longitudinal residue matrix follows the same order as all other longitudinal displays in Archangel u a g Likewise the lateral residue matrices p y r Figure 16 shows a typical normalized residue matrix numerical display Normalized Longitudinal Residue Magnitudes SP1 SP2 Phl 0384 0384 9993 0000 0000 0072 9540 9540 2999 0000 0000 0094 9998 9998 0204 Normalized Longitudinal Residue Angles SP1 SP2 Phl 262 4676 5324 88 8205 271 3283 6717 268 8577 251 933
35. olling moment due to change in sideslip angle non dimensional derivative Cla lift due to change in angle of attack non dimensional derivative Cladot lift due to change in angle of attack rate of change non dimensional derivative Clat Lateral C matrix CldA rolling moment due to aileron deflection non dimensional derivative CldR rolling moment due to rudder deflection non dimensional derivative Clong Longitudinal C matrix Clp rolling moment due to change in roll rate non dimensional derivative Clq lift due to change in pitch rate non dimensional derivative Clr rolling moment due to change in yaw rate non dimensional derivative Clu lift due to change in velocity non dimensional derivative Cml steady state mass coefficient CmT1 steady state lateral axis thrust coefficient CmTa pitching moment due to thrust along the angle of attack path non dimensional derivative CmTu pitching moment due to thrust along longitudinal axis non dimensional derivative Cma pitching moment due to angle of attack non dimensional derivative Cmadot pitching moment due to angle of attack rate of change non dimensional derivative Cmde pitching moment due to elevator deflection non dimensional derivative Cmq pitching moment due to pitch rate non dimensional derivative 24 Variable Name Description Cmu pitching moment due to velocity non dimensional derivative
36. phase response of a system simultaneously See Figure 9 for an example of a Bode plot displayed by Archangel Option 16 on the Bode plot menu will return you to the Archangel main menu Bode Diagrams Gm Inf Pm 34 041 deg at 4 9195 rad sec 40 at r SAAT Phase deg Magnitude dB 200 4 1 a rarr rare 107 TO 10 10 10 Frequency rad sec Figure 9 Archangel Bode plot In addition to this Bode plot function you can escape from Archangel and use the Aerocontrols ezbode command with any of the calculated transfer functions from Archangel For example if you wish to view the transfer function using ezbode type ezbode tf thtodenum thtodeden at the MatLab command line The tf function turns given numerator and denominator vector matrices into transfer functions for use with other MatLab tools Archangel Main Menu Option 9 Root Locus Plots This option will open the Root Locus plot selection menu Selecting options 1 15 from this menu will display a Bode plot of any of the available aircraft transfer functions Option 16 will return you to the Archangel main menu 12 Root locus plots allow the student to analyze the stability natural frequency and damping ratio of a system based on the locations of transfer function poles marked with an X and zeroes marked with a O on the imaginary plane See Figure 10 for an example of a Root Locus plot
37. t 6 Display Rudder Lateral Transfer Functions in Zero Pole Gain Format 7 Display Lateral Parameters 8 Display Selected Bode Plots With Wc PM and GM Indicated 9 Display Selected Root Locus Plots 10 Display Selected Open Loop Step Responses 11 Display Selected Nichols Plots 12 Display Selected Siggy Plots 13 Longitudinal Handling Qualities Analysis With THETA DEP Transfer Function 14 Lateral Directional Handling Qualities Analysis 15 Residue and additional analyses 16 Select another SAD file 17 To Escape to MatLab command line 18 Exit MatLab kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk Please Enter A Number Correspondina To An Option Above Figure 1 Archangel main menu Archangel 3 2 is a menu driven system Type the number next to the function you want it to perform then hit the Enter key For details on options 1 through 15 see the sections in this manual as listed below Main Menu Options Section 1 2 3 and 13 3 Longitudinal Analyses 4 5 6 7 and 14 4 Lateral Analyses 8 9 10 11 and 12 5 Graphical Analyses 15 6 Residue and Additional Analyses Option 16 resets all the calculation variables and allows you to select a different SAD file for analysis Option 17 allows you to escape to the MatLab command line Option 18 exits MatLab altogether 3 Longitudinal Analyses Archangel Main Menu Option 1 Longitudinal state space model display Wh
38. ta DEP 11 Return to Archangel Main Menu TIT CTT CT TCO e e e e Fe He He He e e e e RE RR ERK e e e ERK He e e e ke ke ER He He ke ke ke e ke RR RR RR ke ke kk ke ke ke ke kekk k k k Please Enter a Number Listed Above to View a Graphical Analysis Figure 5 Longitudinal handling qualities menu Ratings are given on a three level basis and rated by pilots during flight testing A level 1 rated aircraft is clearly adequate for the mission flight phase Aircraft rated level 2 are adequate for the mission flight phase but with some increase in pilot workload degradation in mission effectiveness or both Level 3 aircraft can be safely controlled by the pilot but workload is excessive mission effectiveness is inadequate or both The parameters that each criterion bases its analysis upon differs which leads to the different ratings Generally four of the criteria Smith Geddes Neal Smith Mil Std Bandwidth Mil Std Closed Loop and Smith Geddes w PIO should only be used to analyze closed loop systems The remaining criteria Mil Std CAP Mil Std wnsp ttheta2 Northrop may only be used to analyze open loop systems As indicated at the bottom of the screen each of the menu items may be selected for graphical analysis upon which each criterion is based Type the number of the desired option and press the Enter key When finished examining any of the graphical analyses press the Enter key to close the graph window and contin
39. ter you do the 016 gl 4 and nz 5 transfer functions are displayed whereupon there is another pause Press the Enter key to continue See Figure 3 for an example of how Archangel displays the transfer functions u de Zero pole gain 6 248 s 8 865 st6 95 s 6 868 s 2 0 04192s 0 03269 s 2 8 336s 36 75 alpha de Zero pole gain 0 20446 s 195 2 s 2 0 04309s 0 04329 s 2 0 04192s 0 03269 s 2 8 336s 36 75 Figure 3 Archangel display of longitudinal transfer function Archangel Main Menu Option 3 Longitudinal parameters display When you select option 3 from the Archangel main menu it will display two screens of parameters associated with aircraft longitudinal motion The first screen will show the Control Anticipation Parameter CAP 1 7 9 the pitch rate time constant and n a g s to angle of 2 attack ratio When done with the information on this screen type the Enter key to proceed to the next The second screen will show the short period frequency approximate and actual short period damping ratio approximate and actual the phugoid frequency approximate and actual and the phugoid damping ratio approximate and actual See Figure 4 for an example of this screen Approximate Actual Short Period frequency 5 2686 6 0618 Short Period damping 0 79085 0 68754 Approximate Actual Phugoid frequency 0 2082 0 18081 Phugoid damping 0 0708 0 11592 Figure
40. ue To return to the Archangel main menu select option 11 4 Lateral Analyses Archangel Main Menu Option 4 Lateral state space model display When you select option 4 from the Archangel main menu it will display the lateral state space model of the aircraft i e A B C and D matrices An example of this display is shown in Figure 6 Lateral Directional State Space System Alat Blat Clat Dlat A Beta phi P 0 14740 14703 0 00144 0 0 1 00000 28 74922 0 12 40917 0 0 0 10 11937 0 0 38174 Figure 6 Archangel lateral state space matrices The x vector for the lateral state space representation consists of states in the following order 2 side slip angle roll angle p roll rate y yaw angle and r yaw rate There are two columns in the input vector 7 representing the two input surfaces that affect lateral control These are 6 the aileron deflection and the rudder deflection Archangel Main Menu Options 5 6 Lateral transfer function displays When you select option 5 or 6 from the Archangel main menu it will display the lateral transfer functions for the aircraft dependent upon aileron deflection and rudder deflection respectively As with the longitudinal transfer functions each is displayed one after the next The aileron transfer functions 2 16 AE pi 6 L SE and rlo and rudder transfer functions B l gt g d plo y SE and ri are displayed whereupon there is another pause Pr
41. ure 22 Archangel residue calculation method comparison The first matrix shown is that calculated using the eigenspace analysis method The second is calculated using the native residue command contained within MatLab This validates the use of either method for residue calculation 23 Appendix A Archangel Variables Variable Name Description Alat Lateral A matrix Along Longitudinal A matrix BW Bandwidth lesser of 1 the frequency where gain is 6dB higher than gain where the phase angle 180 or 2 the frequency where phase 135 Blat Lateral B matrix Blong Longitudinal B matrix Btodaden sideslip angle to aileron deflection transfer function denominator Btodanum sideslip angle to aileron deflection transfer function numerator Btodrden sideslip angle to rudder deflection transfer function denominator Btodrnum sideslip angle to rudder deflection transfer function numerator CAP Control Anticipation Parameter CAPlev Control Anticipation Parameter criterion assessed FHQ level CD1 steady state drag coefficient CDde drag due to horizontal tail surface non dimensional derivative CLI steady state lift coefficient CLde lift due to horizontal tail surface non dimensional derivative Cda drag due to change in angle of attack non dimensional derivative Cdu drag due to change in velocity non dimensional derivative CIB r
42. will open a menu listing only the longitudinal transfer functions in standard order The last three options on this menu will allow return to the Residue and additional analyses menu escape to the MatLab command line and return to the Archangel main menu respectively When you select a transfer function from this menu you need to enter the amount of system delay you want to add it must be positive and not zero Archangel will display two numerical sets of residues associated with the aircraft phugoid mode similar to the short period delayed residue display When the Enter key is pressed Archangel will show the graphic comparison of the delayed and undelayed residues as compared to the appropriate phugoid roots See Figures 19 and 20 for what these displays will resemble 20 Residue and Additional Analyses Option 8 Display effect of delay on Dutch roll residues Option 8 will open a menu of only the lateral transfer functions in standard order The last three options on this menu will allow return to the Residue and additional analyses menu escape to the MatLab command line and return to the Archangel main menu respectively When you select a transfer function from this menu you need to enter the amount of system delay you want to add it must be positive and not zero Archangel will display two numerical sets of residues associated with the aircraft Dutch roll mode similar to the short period delayed residue
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