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LabVIEW PID Control Toolkit User Manual

1. Chapter 4 Overview of Fuzzy Logic ulo 4 Negative Negative Negative Feiss Positive Positive Positive Large Medium Small Small Medium Large 1 0 0 8 0 6 0 4 0 2 0 0 gt 30 0 25 0 20 0 15 0 10 00 5 0 0 0 5 0 100 15 0 20 0 25 0 30 0 gf Steering Angle PID Control Toolkit User Manual Figure 4 8 Linguistic Variable Steering Angle and Its Linguistic Terms IF vehicle position x is center AND vehicle orientation B is up THEN adjust steering angle to zero In the above rule of the linguistic control strategy the condition is composed of the linguistic term center from the linguistic variable vehicle position x and the linguistic term up from the linguistic variable vehicle orientation B combined by the AND operator Because there are five terms for vehicle position x and seven terms for vehicle orientation B there are at most N 35 different rules available to form a consistent rule base Because there are only two input variables in this case you can document the complete rule base in matrix form as shown in Figure 4 9 4 10 ni com Chapter 4 Overview of Fuzzy Logic Vehicle Position x m AND Left Left Center Center Right Center Right Negative Negative Negative Negative Negative Let Down Small Medium Medium Large Large Left Positive Negative Negative
2. PID Control Toolkit User Manual yim 4 2 0 Start gt Position 1 0 Target Position 0 0 m gt 2 0 3 0 4 0 5 0 6 0 x m Figure 4 4 Automation of a Maneuvering Process Example 4 6 ni com Chapter 4 Overview of Fuzzy Logic Implementing a Linguistic Control Strategy To automate the truck control an ultrasonic distance sensor monitors the truck position in x direction and an electronic compass monitors the truck orientation Each drive situation is identified by at least two conditions The first condition describes the vehicle position x from the loading ramp and the second condition describes the vehicle orientation P The conditions are combined with the word AND which represents the fact that both conditions must be valid for the respective situation Figure 4 5 shows a description of a vehicle position left from the target center with a left hand orientation B and a large negative steering angle with the steering wheel turned all the way to the left vim 4 2 0 Current 1 0 Position 0 0 2 0 gt 3 0 4 0 5 0 6 0 x m Figure 4 5 Condition Vehicle Position x and Orientation B Action Steering Angle You can then use IF THEN rules such as IF lt situati
3. Chapter 5 Fuzzy Controllers j Negative Zero Positive 4 Negative Zero Positive 1 0 u x 9 8 0 8 0 6 0 6 0 4 0 4 0 2 0 2 0 0 0 0 1 0 0 5 1 0 0 5 0 0 0 5 1 0 y gt Undefined gt Max Min Rule Rule 1 IF x Negative THEN y Negative Inference Base Rule 2 IF x Zero THEN y Zero Rule 3 IF x Positive THEN y Positive Modified CoA 1 0 A 0 8 0 6 y 0 4 p 0 0 0 2 0 4 0 6 0 8 1 0 1 0 0 8 0 6 0 4 0 2 0 0 0 2 0 4 0 6 0 8 1 0 x gt Figure 5 10 1 0 Characteristic of a Fuzzy Controller Undefined Input Term Interval If you use an old output value as a default value undefined intervals or incomplete rule bases can lead to hysteretic effects on the controller characteristic PID Control Toolkit User Manual 5 12 ni com Chapter 5 Fuzzy Controllers You can use nonoverlapping rectangular shaped conclusion terms to obtain an exact linear controller characteristic for a single input controller In this case both area and momentum vary linearly with the degree of truth and overlapping regions of the output terms do not cause any distortion The simplest way to obtain a linear controller characteristic is to use singletons as conclusion terms with entirely overlapping input terms Refer to Figure 5 11 for an example of such a controller Singletons are normalized rectangular membership functions with an infinitely small width National Instruments Corpor
4. Negative Zero Positive Negative Zero Positive 4 1 0 1 0 nog 98 ny 08 0 6 0 6 0 4 0 4 0 2 0 2 0 0 0 0 1 0 0 5 0 0 0 5 1 0 1 0 0 5 0 0 0 5 1 0 x gt y Max Min Rule Rule 1 IF x Negative THEN y Negative Inference Base Rule 2 IF x Zero THEN y Zero Rule 3 IF x Positive THEN y Positive Modified CoA 1 0 0 8 0 6 0 4 0 2 0 0 0 2 0 4 0 6 0 8 1 0 x P gt Figure 5 9 1 0 Characteristic of a Fuzzy Controller Nonoverlapping Input Terms In this case only one rule is active for each input situation that leads to the stepped controller characteristic shown in Figure 5 9 PID Control Toolkit User Manual 5 10 ni com Chapter 5 Fuzzy Controllers If there are undefined intervals within input and output terms or the rule base is incomplete you must tell the fuzzy controller what to do If there is no rule available for a certain situation the output value remains undefined One way to avoid this problem is to leave the current output value unchanged until the controller encounters a situation that is covered by the rules Figure 5 10 shows the resulting effect on the controller characteristic National Instruments Corporation 5 11 PID Control Toolkit User Manual
5. National Instruments Corporation 6 5 PID Control Toolkit User Manual Chapter 6 Design Methodology Defining a Fuzzy Logic Rule Base The fuzzy logic rule base is the main part of a fuzzy system and contains all the engineering knowledge necessary to control a system The rule base supplies all the actions the fuzzy controller should perform in certain situations In a sense the rule base represents the intelligence of the controller Changes to a single rule only have a local influence on the controller characteristic Thus you can selectively change the behavior of the fuzzy controller for a certain input situation by modifying a particular rule Because the modification of a rule is usually carried out in discrete steps through changes to the consequence term modifications to a rule have a much greater influence on the controller characteristic than modifications to the membership functions Implement weight factors which are Degrees of Support for the rules to enhance or reduce the influence of a rule on the controller characteristic To build up a rule base define one rule for each combination of antecedent terms of the input variables used in the IF part of the rule Then select the most plausible conclusion from the output variable to specify the THEN part of each rule Assume that you are building a fuzzy controller with m input variables each of which has p terms each The total number N of possible rules is N p
6. 30 0 1 1 1 1 1 1 1 0 10 20 30 40 50 60 70 80 90 10 0 30 00 3 min to max 0 2 1 0 Figure 7 12 O Characteristic Project Specific Front Panel There is a different parameter control block in the Input Parameter Field of the I O Characteristic front panel for each input variable of the fuzzy controller The Toolkit uses the blocks to set up the desired test conditions for the different controller inputs Suppose you want to vary the vehicle position within the input data range and keep the vehicle orientation constant at 0 to observe how the behavior of the controller output variable steering angle changes with the vehicle position and the vehicle orientation To set up these test conditions first enter the desired test value into the parameter control block for vehicle orientation as shown in Figure 7 13 PID Control Toolkit User Manual 7 16 ni com Chapter 7 Using the Fuzzy Logic Controller Design VI 12 Input Output Characteristic yehicle position vehicle orientation y Fi le 0 0 90 0 270 0 min to max steering angle X to min 30 0 Print 20 0 No Points 10 0 20 0 0 10 0 K 20 0 30 0 1 1 i 1 1 1 1 1 1 00 10 20 30 40 50 60 7 0 80 90 10 0 30 00 a min to max 0 2 1 0 Figure 7 13 Entering a Test Condition into a Parameter Control Block of the I O Characteristic Front Panel Then click the Run button to
7. 0 4 0 2 0 0 gt 95 0 968 986 100 4 102 2 104 0 105 8 107 6 109 4 T F Body Temperature PID Control Toolkit User Manual Figure 4 2 Modeling Uncertainty by Fuzzy Set Membership In Figure 4 2 the graph associates each body temperature with a certain degree of membership u T to the high fever set The function u T is called the degree of membership of the element T BT to the fuzzy set high fever The body temperature is called the characteristic quantity or base variable T of the universe BT Notice that ranges from zero to one the values representing absolutely no membership to the set and complete membership respectively You also can interpret the degree of membership to the fuzzy set high fever as the degree of truth given to the statement that the patient suffers from high fever Thus using fuzzy sets defined by membership functions within logical expressions leads to the notion of Fuzzy Logic As shown in Figure 4 2 a continuous function u T often called a fuzzy set represents the degree of membership Refer to the Defining Linguistic Variables section of Chapter 6 Design Methodology for more information about how to define membership functions for certain applications Notice that a body temperature of 102 F is considered only slightly different from a body temperature of 101 5 F and not considered a threshol
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10. PID Control Toolkit User Manual PID Algorithms Table 2 1 Tuning Formula under P only Control fast Controller K T Ta P 0 5K PI 0 4K 0 8T PID 0 6K 0 5T 0 12T Table 2 2 Tuning Formula under P only Control normal Controller K T Ta P 0 2K PI 0 18K 0 8T PID 0 25K 0 5T 0 12T Table 2 3 Tuning Formula under P only Control slow Controller K T Ta P 0 13K PI 0 13K 0 87 PID 0 15K 0 5T 0 12T Table 2 4 Tuning Formula under PI or PID Control fast Controller K T Ta P T t PI 0 9T t 3 33 _ PID 1 17 2 07 0 5T 2 8 ni com Chapter 2 PID Algorithms Table 2 5 Tuning Formula under PI or PID Control normal Controller K T Ta P 0 447 t PI 0 47 t 5 33T PID 0 53T T 4 07 0 87 Table 2 6 Tuning Formula under PI or PID Control slow Controller K T Ta P 0 267 t PI 0 24T T 5 337 PID 0 32T t 4 0T 0 8T iy Note During tuning the process remains under closed loop PID control You do not need to switch off the existing controller and perform the experiment under open loop conditions In the setpoint relay experiment the SP signal mirrors the SP for the PID controller National Instruments Corporation 2 9 PID Control Tool
11. b Fuzzy Set Editor vehicle position z p specify v lt ling variables ANTECEDENCE define lw NE1 lt ling terms edit NE1 NE1 ZE1 PO1 lw Pana Fas As YW 20 30 40 50 60 70 80 90 10 0 left bottom left top right top right bottom A GA 0 00 amp 2 50 250 amp 5 00 q E Figure 7 7 New Term Added to the Vehicle Position Variable 3 Note Adding a new term to an input variable especially one that is part of an existing project causes significant changes to the rule base Additional rules automatically extend the rule base Each rule has a conclusion that is predefined as none Adding a new consequence term only extends the possibility to select conclusion terms within the Rulebase Editor Remember that each input and output variable can have a maximum of nine linguistic terms To add the second new term between ZE1 and PO1 first select ZE1 from the Term Selector With ZE1 as the active term you can select define add term after to add the new term LabVIEW adds the new term ZE1 to the Term Display National Instruments Corporation 7 9 PID Control Toolkit User Manual Chapter 7 Using the Fuzzy Logic Controller Design VI Before rearranging the linguistic terms according to the desired pattern select specify rename term to assign the correct term identifiers Refer to Figure 4 6 Linguistic Variable Vehicle Position x and Its Linguistic Terms for more information about the de
12. I O Characteristics of Fuzzy Controllers PID Control Toolkit User Manual You can consider a fuzzy controller to be a nonlinear characteristic field controller The rule base and membership functions that model the terms of the linguistic input and output variables for the controller determine the behavior of the controller Because the controller has no internal dynamic aspects the I O characteristics can entirely describe the transient response of the controller To illustrate how the I O characteristics of a fuzzy controller depend on design parameters such as rule base and membership function specification you must first restrict yourself to a single input fuzzy controller Most of these ideas apply directly to fuzzy controllers with two or more inputs Figure 5 7 shows the I O characteristic of a fuzzy controller that has only three linguistic terms for the input variable x and the output variable y The rule base consists of three rules which indicate that the increasing input values cause the output to increase 5 6 ni com Chapter 5 Fuzzy Controllers Negative Zero Positive Negative Zero Positive i 1 0 1 0 hog 98 ny 08 0 6 0 6 0 4 0 4 0 2 0 2 0 0 0 0 1 0 0 5 0 0 0 5 1 0 1 0 0 5 0 0 0 5 1 0 x gt y gt Max Min Rule Rule 1 IF x Negative THEN y Negative Inference Base Rule 2 IF x Zer
13. Gain Scheduling iis oti 3 feiss sss renrep cesses e AERE dean E A 2 4 The Advanced PID Al gorithin iisi ensenis aa E aE E aE 2 4 Error Calculation e e e e setae E TEE O T i 2 4 Proportional Actions gne a e o Ea Ee aie 2 5 Trapezoidal Integration pocnaa 2 6 The Autotuning Algorithii seeni e e a S e E 2 7 Tunne Formulas ege uredna e e aie a e aa air 2 7 National Instruments Corporation V PID Control Toolkit User Manual Contents Chapter 3 Using the PID Software Designing a Control Strate gy suc sec cs scssssevidechssecasneeabcee sung cascdesuqeosteseasigtastesdeuseussb T 3 1 S ttine Timi Gs sss oe ce chk nie ed elm ah ae eae 3 2 Tuning Controllers Manually oo eee eeeeccessceeeeseceeeeseeeseesecseceaeenseeasenseeaes 3 3 Closed Loop Ultimate Gain Tuning Procedure eee 3 4 Open Loop Step Test Tuning Procedure eee ee eeeeeeeteeeeees 3 5 Usine the PUD MIS cs e054 cost oE EE AEE EEE EEE E 3 6 We d iB DTA E E E T E ake hs 3 6 The PUD Advanced V ea TEE aE E E A E TEET 3 7 Bumpless Automatic to Manual Transfer eseeseeeeeeeeeeeeeeeereeseee 3 7 Multi Loop PID Controlar e a E A Pet eats 3 8 Setpoint Ramp Generation cece ceceseseceeeeseceseeseeeseeseceseeeseaeeaesnseeseeeaees 3 9 Filtering Control Inputs ccccceiscsccstepetectests e ar evento i a Re s 3 10 G inSch d lihg t seinn e E E A et 3 11 Control Output Rate Limiting ssns na a 3 12 The PID Lead Lae VI stac ain eithictetantsinin a a A 3 13
14. and output ranges for the PID VIs correspond to percentage of full scale In other words proportional gain K relates percentage of full scale output to percentage of full scale input This is the default behavior of many PID controllers used for process control applications To implement PID in this way you must scale all inputs to percentage of full scale and all controller outputs to actual engineering units for example volts for analog output You can use the PID EGU to VI to convert any input from real engineering units to percentage of full scale and you can use the PID to EGU function to convert the controller output from percentage to real engineering units The PID to EGU VI has an additional input coerce output to range The default value of the coerce output to range input iS TRUE ay Note The PID VIs do not use the setpoint range and output range information to convert values to percentages in the PID algorithm The controller gain relates the output in engineering units to the input in engineering units For example a gain value of 1 produces an output of 10 for a difference between setpoint and process variable of 10 regardless of the output range and setpoint range Using the PID with Autotuning VI and the Autotuning Wizard PID Control Toolkit User Manual To use the Autotuning Wizard to improve your controller performance you must first create your control application and determine PID parameters that p
15. five circled base points xi yi x1 x2 x3 x4 x5 y1 y2 y3 y4 y5 4 1 0 1 0 py O ny 08 0 6 0 6 0 4 0 4 0 2 0 2 0 0 0 0 1 0 0 5 0 0 0 5 1 0 1 0 0 5 0 0 0 5 1 0 y gt Rule 1 IF x x1 THEN y y1 Max Min Rul Rule 1 IF x x2 THEN y y2 Inference e Rule 2 IF x x3 THEN y y3 ase Rule 3 IF x x4 THEN y y4 Modified Rule 3 IF x x5 THEN y y5 CoA x5 y5 io Ri 0 8 0 6 y x4 y4 0 4 lo 0 0 0 2 x3 y3 0 4 0 6 0 8 1 0 1 0 0 8 0 6 0 4 0 2 0 0 0 2 0 4 0 6 0 8 1 0 x1 y1 x2 y2 x gt Figure 5 16 Fuzzy Controller for a Given I O Characteristic To use a single input fuzzy controller to reproduce the given characteristic use five linguistic terms each for the input and output quantities naming PID Control Toolkit User Manual 5 22 ni com Chapter 5 Fuzzy Controllers them x1 x2 x5 and y1 y2 y5 respectively To obtain the stepped linear sections between the base points you must always have exactly two available active rules To implement this entirely overlap the triangular membership functions for the input variable giving each a typical value that corresponds to a certain base point component xi To obtain characteristic sections that are exactly linear you must model the output variable with singl
16. rule 1 0 8 and V rule 2 0 1 for the active rules the possible defuzzification results are out Q negative out 6 1 medium V rule 2 O negative small V rule 1 V tule 2 V tule 1 The defuzzification method CoM is identical to using the CoG method with singleton membership functions Figure 4 15 summarizes the fuzzy inference process for the maneuvering situation describ National Instruments Corporation ed above using the CoA method of defuzzification 4 19 PID Control Toolkit User Manual Chapter 4 Overview of Fuzzy Logic 1 IF vehicle posit THEN steering ion x center AND vehicle orientation B left up angle negative small center 0 0 x vehicle position x m mia 0 90 180 270 vehicle orientation B negative negative medium small i XAW PAX 0 15 30 steering angle 2 IF vehicle position x right center AND vehicle orientation B left up THEN steering angle negative medium Fuzzy Inference max right center 0 0 0 vehicle position x m ma 90 0 90 180 270 vehicle orientation p fi Fuzzification negative medium negative small E min 30 15 0 15 30 steering angle Linguistic Level negative medium negative small 0 15 30 steering angle y Technical
17. 0 Right HXI A Left Center Center Center Right 0 8 0 6 0 4 0 2 0 0 0 0 1 0 2 0 3 0 4 0 5 0 Current Vehicle Position x 5 1 m 6 0 7 0 gt 8 0 9 0 10 0 m Figure 4 11 Fuzzification of the Vehicle Position x 5 1 m The current vehicle position x 5 1 m belongs to the following linguistic terms which are defined by fuzzy sets left left center center right center right with a degree of with a degree of with a degree of with a degree of with a degree of 0 0 0 0 0 8 0 1 0 0 The current vehicle position of 5 1 m is translated into the linguistic value 0 0 0 0 0 8 0 1 0 0 which you can interpret as still center just slightly right center National Instruments Corporation 4 13 PID Control Toolkit User Manual Chapter 4 Overview of Fuzzy Logic B A 1 0 U Left p Right Left Down Left Up Right Up Right Down 0 8 0 6 0 4 0 2 0 0 gt 100 50 0 0 50 100 150 200 250 BI Current Vehicle Orientation 70 Vehicle Orientation Figure 4 12 Fuzzification of the Vehicle Orientation 70 The current vehicle orientation 70 belongs to the following linguistic terms fuzzy sets left down with a degree of 0 0 left with a degree of 0
18. 0 left up with a degree of 1 0 up with a degree of 0 0 right up with a degree of 0 0 right with a degree of 0 0 right down with a degree of 0 0 The current vehicle orientation of 70 is translated into the linguistic value 0 0 0 0 1 0 0 0 0 0 0 0 0 0 which you can interpret as left up Refer to Chapter 6 Design Methodology for more information about defining linguistic terms and memberships PID Control Toolkit User Manual 4 14 ni com Chapter 4 Overview of Fuzzy Logic Using IF THEN Rules in Fuzzy Inference After you convert all physical input values into linguistic values identify all rules from the rule base that apply to the current maneuvering situation Identify these rules so you can calculate the values of the linguistic output variable The fuzzy inference step consists of two components Aggregation involves the evaluation of the IF part condition of each rule Composition involves the valuation of the THEN part conclusion of each rule In the following example notice that the IF part of each rule logically combines two linguistic terms from different linguistic variables with the conjunction AND Because the linguistic terms represent conditions that are partially true the Boolean AND from conventional dual logic is not an appropriate choice to model the conjunction AND You must define new operators that represent logical connections such as AND OR and NOT The three operators used in the majority of fu
19. 11 Block Diagram of the Pattern Recognition Application The application example is complete You can switch back to the front panel from the fuzzy controller and run the VI to start the pattern recognition application Immediately after the application begins a file dialog box prompts you to enter the name of a file that contains the appropriate controller data Open the project file FCPR fc which represents the fuzzy controller you designed earlier When you load the Fuzzy Controller drag the sliders to try different settings for the pattern recognition process You can see how the pattern recognition process changes with different input signal conditions Refer to Figure 8 12 National Instruments Corporation 8 9 PID Control Toolkit User Manual Chapter 8 Implementing a Fuzzy Controller i Pattern Recognition Example File Edit Operate Project Windows Help 8 0 6 0 4 0 205 0 0 sfio SRo input signal def sm EE ain j ae a cee ee ve 30 40 50 60 70 0 90 TH signal min 1 1 1 1 1 a 1 1 1 1 1 1 1 50 60 70 80 90 100 TS 00 10 20 30 40 50 10 00 0 00 Moo TH TS PEE TU TD TS 0 125 l Triangle right 10 375 STOP Figure 8 12 Running the Pattern Recognition Application Selecting the Cancel button rather than selecting the fuzzy controller data file FCPR fc executes the default fuzzy controller repeatedly Without having actual data loaded to the controller it will use
20. B 1 designing control strategies 3 1 to 3 5 manual tracking techniques 3 3 closed loop tuning 3 4 open loop tuning 3 5 National Instruments Corporation l 1 step test 3 5 ultimate gain 3 4 setting timing 3 2 diagnostic tools NI resources B 1 documentation conventions used in this manual ix NI resources B 1 organization of this manual ix related documentation x drivers NI resources B 1 E error calculation 2 2 examples NI resources B 1 G gain scheduling 2 4 H Hagglund T A 1 Hang C C A 1 help technical support B 1 Ho W K A 1 instrument drivers NI resources B 1 K KnowledgeBase B 1 PID Control Toolkit User Manual Index manual See documentation National Instruments support and services B 1 NI support and services B 1 Nichols N B A 2 nonlinear adjustment of integral action 2 2 2 6 0 output limiting 2 3 P partial derivative action 2 2 PID Algorithm 2 1 to 2 4 calculating controller action 2 1 to 2 3 controller output 2 2 error calculation 2 2 nonlinear adjustment of integral action 2 2 2 6 output limiting 2 3 partial derivative action 2 2 proportional action 2 2 2 5 trapezoidal integration 2 2 2 6 gain scheduling 2 4 PID algorithms 2 1 to 2 9 Autotuning Algorithm 2 7 to 2 9 PID Algorithm 2 1 to 2 4 PID software 3 1 to 3 19 with DAQ 3 17 to 3 19 PID Control Toolkit User Manual l 2 PID toolkit using with DAQ 3 17
21. Converting Between Percentage of Full Scale and Engineering Units 3 14 Using the PID with Autotuning VI and the Autotuning Wizard 00 000 3 14 Usine PID with DAQ Devices sa sceccuvee tee iacds E A eeneeenen es ieee 3 17 Software Timed DAQ Control Loop 0 eee ee eeeeceeseeeeeceeeseeseesaeeseeeseeseees 3 17 Implementing Advanced DAQ VIs in Software Timed DAQ Control LOOPS esis eae he eal See ines Bala 3 18 Hardware Timed DAQ Control Loop eee eeeeeeeseeseeeneeneeeseeseeeseseeeeeeeaes 3 19 Part Il Fuzzy Logic Control Chapter 4 Overview of Fuzzy Logic Whiat 1s Fuzzy Logie sonnen Ea Waileieniid da R tea ieee 2k 4 1 EYpes OF Uncertainty sosea r eai e E sucess E EE ESE E AE tebe E 4 2 Modeling Linguistic Uncertainty with Fuzzy Sets eseseesssessesessesrsresrsresesrreesreerseesees 4 2 Linguistic Variables and Terms isnin nane i a E 4 5 Rule Based Systems ansi aonn a Linn a A R 4 6 Implementing a Linguistic Control Strategy e essseesseessereresesrrsresrsresrsresrenrsresreereresr 4 7 Structure of the Fuzzy Logic Vehicle Controller 0 0 eee eeeceeeseeeeeteeseeeseeeees 4 12 Fuzzification Using Linguistic Variables 2 0 0 0 eee eeeeeeseeeseeeeeeeeseeeseeeees 4 13 Using IF THEN Rules in Fuzzy Inference 20 0 eee cece eeeteeeeeeeneeeeees 4 15 Using Linguistic Variables in Defuzzification eee eeeeeseeseeeeeneees 4 17 PID Control Toolkit User Manual vi ni com Contents Chapter 5 Fuzzy Controll
22. LIFE SUPPORT SYSTEMS WHOSE FAILURE TO PERFORM CAN REASONABLY BE EXPECTED TO CAUSE SIGNIFICANT INJURY TO A HUMAN 2 IN ANY APPLICATION INCLUDING THE ABOVE RELIABILITY OF OPERATION OF THE SOFTWARE PRODUCTS CAN BE IMPAIRED BY ADVERSE FACTORS INCLUDING BUT NOT LIMITED TO FLUCTUATIONS IN ELECTRICAL POWER SUPPLY COMPUTER HARDWARE MALFUNCTIONS COMPUTER OPERATING SYSTEM SOFTWARE FITNESS FITNESS OF COMPILERS AND DEVELOPMENT SOFTWARE USED TO DEVELOP AN APPLICATION INSTALLATION ERRORS SOFTWARE AND HARDWARE COMPATIBILITY PROBLEMS MALFUNCTIONS OR FAILURES OF ELECTRONIC MONITORING OR CONTROL DEVICES TRANSIENT FAILURES OF ELECTRONIC SYSTEMS HARDWARE AND OR SOFTWARE UNANTICIPATED USES OR MISUSES OR ERRORS ON THE PART OF THE USER OR APPLICATIONS DESIGNER ADVERSE FACTORS SUCH AS THESE ARE HEREAFTER COLLECTIVELY TERMED SYSTEM FAILURES ANY APPLICATION WHERE A SYSTEM FAILURE WOULD CREATE A RISK OF HARM TO PROPERTY OR PERSONS INCLUDING THE RISK OF BODILY INJURY AND DEATH SHOULD NOT BE RELIANT SOLELY UPON ONE FORM OF ELECTRONIC SYSTEM DUE TO THE RISK OF SYSTEM FAILURE TO AVOID DAMAGE INJURY OR DEATH THE USER OR APPLICATION DESIGNER MUST TAKE REASONABLY PRUDENT STEPS TO PROTECT AGAINST SYSTEM FAILURES INCLUDING BUT NOT LIMITED TO BACK UP OR SHUT DOWN MECHANISMS BECAUSE EACH END USER SYSTEM IS CUSTOMIZED AND DIFFERS FROM NATIONAL INSTRUMENTS TESTING PLATFORMS AND BECAUSE A USER OR APPLICATION DESIGNER MAY USE NATIONAL INSTRUMENTS PRODUCTS IN COMBINA
23. Level Defuzzification F vehicle orientation B 70 vehicle position x 5 1 m A steering angle 9 3 Figure 4 15 Fuzzification Fuzzy Inference and Defuzzification for a Specific Maneuvering Situation Without modification the CoA defuzzification method limits the range of the output value compared to the possible range To solve this problem add a fictitious extension of the left and right side border terms when you compute the center of area With this extension the output variable can realize the complete value range shown in Figure 4 16 In this case the defuzzification method is called modified CoA PID Control Toolkit User Manual 4 20 ni com Chapter 4 Overview of Fuzzy Logic 1 0 0 5 KX 0 0 SZ 1 0 0 5 0 0 ool HF pa p CS T 1 0 0 5 100 100 100 100 1 0 d 05 pu pu 1 0 0 5 0 0 0 0 1 0 0 5 0 0 0 0 k 100 L100 Modified CoA Figure 4 16 Modified CoA for Complete Output Value Range The CoM and CoA defuzzification methods are usually applied to closed loop control applications of fuzzy logic These methods usually lead to continuous output signals because the best compromise can never jump to a different value with a small change to the inputs For pattern rec
24. Negative Negative Small Small Medium Large Large Z Positive Positive Negative Negative Negative T Leit Up Medium Small Small Medium Large z SA P S Up Positive Positive Zoio Negative Negative 5 Medium Medium Medium Medium o 2 Positive Positive Positive Negative Negative gt Right Up Large Medium Small Small Medium Right Positive Positive Positive Positive Negative 9 Large Large Medium Small Small Right Down Positive Positive Positive Positive Negative 9 Large Large Medium Medium Small Figure 4 9 Complete Linguistic Rule Base Each combination of a column and a row describes a specific maneuvering situation the condition of a certain rule The term at the intersection of the column and row is the conclusion As an example the following rule is highlighted in Figure 4 9 IF vehicle position x is left center AND vehicle orientation B is left THEN adjust steering angle to negative small National Instruments Corporation 4 11 PID Control Toolkit User Manual Chapter 4 Overview of Fuzzy Logic Structure of the Fuzzy Logic Vehicle Controller The complete structure of a fuzzy logic controller is shown in Figure 4 10 Linguistic Variables and Terms facts vehicle position x center vehicle orientation B up Fuzzy Inference Linguistic Variables SS and Terms i IF l steering angle zero THEN as conclusions Linguistic Level Fuzz
25. VI will initialize all internal states on the first call to the VI All subsequent calls to the VI will make use of state information from previous calls However you can reinitialize the PID VI to its initial state at any time by passing a value of TRUE to the reinitialize input Use this function if your application must stop and restart the control loop without restarting the entire application The PID Advanced VI The PID Advanced VI has the same inputs as the PID VI with the addition of inputs for setpoint range beta linearity auto and manual control You can specify the range of the setpoint using the setpoint range input which also establishes the range for the process variable The default setpoint range is 0 to 100 which corresponds to values specified in terms of percentage of full scale However you can change this range to one that is appropriate for your control system so that the controller gain relates engineering units to engineering units instead of percentage to percentage The PID Advanced VI uses the setpoint range in the nonlinear integral action calculation and with the linearity input in the nonlinear error calculation The VI uses the beta input in the Two Degree of Freedom algorithm and the linearity input in the nonlinear gain factor calculation Refer to Chapter 2 PID Algorithms for more information about these calculations You can use the auto and manual control inputs to switch between manual and
26. begin calculating the I O characteristic within the parameter control block for vehicle position LabVIEW executes the I O characteristics calculation according to the number of points specified in the No Points control box To animate the calculation process move the slider of the varying input variable 3 Note The controller characteristic is calculated twice varying the activated input variable which is vehicle position in this example from the minimum value up to the maximum value and vice versa This happens because of possible hysteresis effects that occur with incomplete rule bases Definition gaps in the term arrangement of the input variable which cause the controller to use the default output value or the last originally computed value can also cause LabVIEW to calculate the controller characteristic twice As soon as the characteristic calculation completes LabVIEW displays the characteristic curve in the I O Characteristic display This display contains a cursor that you can control with the Cursor Navigation block The cursor can travel along the characteristic curve and identify the active rules for the National Instruments Corporation 7 17 PID Control Toolkit User Manual Chapter 7 Using the Fuzzy Logic Controller Design VI PID Control Toolkit User Manual input situation at each cursor position The I O Characteristic function panel displays the current input values and controller output value The Active Rules di
27. can use the advanced level DAQ VIs to configure the analog input and output only once instead of on each loop iteration Be sure to place the configuration functions outside the loop and pass the task ID to the I O functions inside the loop The AI SingleScan and AO Single Update VIs call the DAQ driver directly instead of through other subVI calls minimizing overhead for DAQ functions This example does not use a timing function to specify the loop speed Thus the control loop runs as fast as possible and LabVIEW maximizes the control loop rates However any other operation in LabVIEW can slow down the loop and vary the speed from iteration to iteration Because Windows NT 2000 is a preemptive multitasking operating system other running applications can affect the loop speed Figure 3 14 Software Timed DAQ Control Loop with Advanced Features PID Control Toolkit User Manual 3 18 ni com Chapter 3 Using the PID Software Hardware Timed DAQ Control Loop Figure 3 15 demonstrates hardware timing In this example a continuous analog input operation controls the loop speed Notice that the intermediate and advanced level DAQ VIs specify the acquisition rate for the analog input scanning operation The analog output VIs are identical to those in the previous example Scan rate Scans sec Figure 3 15 Hardware Timed DAQ Control Loop With each loop iteration the AI SingleScan VI returns one scan of dat
28. center right center and right When you create a linguistic variable first determine how many terms define the linguistic variable In most applications between three and seven terms make up a linguistic variable It makes no sense to use less than three terms because most linguistic concepts have at least two extreme terms with a middle term between them On the other hand linguistic systems that use more than seven terms are difficult to understand because humans use their short term memory to interpret technical quantities and the human short term memory can only compute up to seven symbols simultaneously 6 2 ni com Chapter 6 Design Methodology Linguistic variables usually have an odd number of terms because they are defined symmetrically and they include a middle term between the extremes As a starting point set up the input variables with at least three or five terms and the output variables with five or seven terms Standard Membership Functions The degree of truth to which a measurement value of a technical quantity satisfies the linguistic concept of a certain term of a linguistic variable is called degree of membership You can use a mathematical function to model the degree of membership of a continuous variable You can apply the normalized standard membership functions illustrated in Figure 6 1 to most technical processes These standard functions include Z type A type triangular shape I type trapezoidal shap
29. for example if you are measuring process variable values using a DAQ device As discussed in the Setting Timing section of this chapter the sampling rate of the control system should be at least 10 times faster than the fastest time constant of the physical system Therefore if correctly sampled any frequency components of the measured signal greater than one tenth of the sampling frequency are a result of noise in the measured signal Gains in PID Control Toolkit User Manual 3 10 ni com Chapter 3 Using the PID Software the PID controller can amplify this noise and produce unnecessary wear on actuators and other system components The PID Control Input Filter VI filters out unwanted noise from input signals The algorithm it uses is a low pass fifth order Finite Impulse Response FIR filter The cutoff frequency of the low pass filter is one tenth of the sampling frequency regardless of the actual sampling frequency value You can use the PID Control Input Filter VI to filter noise from input values in the control loop before the values pass to control functions such as the PID VI Gain Scheduling With the PID Gain Schedule VI you can apply different sets of PID parameters for different regions of operation of your controller Because most processes are nonlinear PID parameters that produce a desired response at one operating point might not produce a satisfactory response at another operating point The Gain Schedule VI selects a
30. from a time keeper such as those built into the PID VIs If dt is less than or equal to zero the VI calculates new timing information each time LabVIEW calls it At each call the VI measures the time since the last call and uses that difference in its calculations If you call a VI from a While Loop that uses one of the LabVIEW timing VIs located on the Time amp Dialog palette you can achieve fairly regular timing and the internal time keeper compensates for variations However the resolution of the Tick Count ms function is limited to 1 ms If dt is a positive value in seconds the VI uses that value in the calculations regardless of the elapsed time National Instruments recommends you use this method for fast loops such as when you use acquisition hardware to time the controller input or real time applications Refer to the example library prctlex 11b for examples of using timing with the PID VIs If you installed NI DAQmx you also can view relevant examples in the labview examples daqmx control control 11b According to control theory a control system must sample a physical process at a rate about 10 times faster than the fastest time constant in the physical process For example a time constant of 60 s is typical for a temperature control loop in a small system In this case a cycle time of about 6 s is sufficient Faster cycling offers no improvement in performance 3 2 ni com Chapter 3 Using the PID Software Corripio 19
31. fuzzy system to be designed e Testing and project maintenance utilities Refer to the LabVIEW Help available by selecting Help Search the LabVIEW Help for more information about fuzzy logic control The following restrictions are valid e The maximum number of linguistic variables is four e The maximum number of linguistic terms for each linguistic variable is nine e The types of membership functions are normalized triangular and trapezoidal membership functions Z A T and S Type and singletons National Instruments Corporation 7 1 PID Control Toolkit User Manual Chapter 7 Using the Fuzzy Logic Controller Design VI Project Manager Select Tools Control Design and Simulation Fuzzy Logic Controller Design The Fuzzy Logic Controller Design VI runs immediately when you open it This VI is a stand alone application with a graphical user interface for designing and editing a fuzzy controller Although this VI has no inputs or outputs you can use it as a subVI Place the icon on your application diagram to allow your user to programmatically edit the fuzzy logic controller LabVIEW automatically calls the Fuzzy Set Editor when you create a new fuzzy logic project Figure 7 1 displays the Fuzzy Logic Controller Design VI front panel 12 Fuzzy Logic Controller Design File Edit Test Hele T Description New Open 2 controller untitled developer unknown date Friday June 02 2006 time 12 5
32. integral action when there is a sudden change in PV or SP Use nonlinear adjustment of integral action to counteract overshoot The larger the error the smaller the integral action as shown in the following formula k u k y eee Dai i l Partial Derivative Action Because of abrupt changes in SP only apply derivative action to the PV not to the error e to avoid derivative kick The following formula represents the Partial Derivative Action T p k K X PVWD PV k D PID Control Toolkit User Manual 2 2 ni com Chapter 2 PID Algorithms Controller Output Controller output is the summation of the proportional integral and derivative action as shown in the following formula u k up k u k up k Output Limiting The actual controller output is limited to the range specified for control output If u k 2 upay then u k u max and if u k lt u in then u k umin The following formula shows the practical model of the PID controller K SP P 1 f sp_ pra r 2 u t KJ SP PV p SP PVdt Ta The PID VIs use an integral sum correction algorithm that facilitates anti windup and bumpless manual to automatic transfers Windup occurs at the upper limit of the controller output for example 100 When the error e decreases the controller output decreases moving out of the windup area The integral sum correction algorithm prevents abrupt controller output changes when you switch from manual
33. output in a rule base does not necessarily mean that there is no rule active for a certain input situation The completeness of a rule base is not the only aspect to consider when you deal with large rule bases Avoid contradicting rules rules with the same IF part but different THEN parts because they are illogical Contradicting rules have only a marginal effect on the controller characteristic because of the averaging process that occurs during the defuzzification step A consistent rule base is a rule base that has no contradicting rules If the rule base is small enough to contain all possible rules it is not difficult to detect inconsistencies This is guaranteed for rule bases that can be built in the form of a matrix Refer to Figure 4 9 Complete Linguistic Rule Base for more information about rule bases in matrix form However many rule bases are larger and more complex To build these rule bases begin with just a few rules to operate input quantities and gradually add more rules It is difficult to detect inconsistencies in larger rule bases For fuzzy controllers with only two or three input quantities it is possible to estimate the qualitative controller characteristic just by looking at the rule base Neighboring terms within a rule matrix with strongly differing meanings like positive large and negative small indicate steeply sloped edges in the control surface which usually are not desired This is referred National Ins
34. profile can have two successive array values with the same time value but different setpoint values as shown in Figure 3 8 setpoint profile setpoint profile graph f Jo time s setpoint 100 0 80 0 Hfo oo0 Vo 00 time s setpoint fs 000 Yo 00 time s setpoint i ffs 000 4100 00 20 05 time s setpoint 0 0 1 I 0 0 2 0 4 0 6 0 8 0 10 0 10 000 100 00 Time i 60 0 40 0 Setpoint Figure 3 8 Step Setpoint Profile The PID Setpoint Profile VI outputs a single setpoint value determined from the current elapsed time Therefore you should use this VI inside the control loop The first call to the VI initializes the current time in the setpoint profile to 0 On subsequent calls the VI determines the current time from the previous time and the dt input value If you reinitialize the current time to 0 by passing a value of TRUE to the reinitialize input you can repeat the specified setpoint profile If the loop cycle time is deterministic you can use the input dt to specify its value The default value of dt is 1 so by default the VI uses the operating system clock for calculations involving the loop cycle time The operating system clock has a resolution of 1 ms so specify a dt value explicitly if the loop cycle time is less than 1 ms Filtering Control Inputs You can use the PID Control Input Filter to filter high frequency noise from measured values in a control application
35. signals from a process and one output signal used as a control value National Instruments Corporation 8 7 PID Control Toolkit User Manual Chapter 8 Implementing a Fuzzy Controller Although the Fuzzy Controller VI has many different inputs and outputs at this time you only need those inputs and outputs shown in bold in Figure 8 10 Controller data name 1 in ne mes analog output name 3 output assessment in3 error array name 4 ing Figure 8 10 Fuzzy Controller VI You can connect the input signals TH TS and TU TD TS to the Fuzzy Controller VI inputs inputi and input2 You also can connect the output signal of the Fuzzy Controller VI called analog output to the input side of the NumtoString VI Leave the rest of the inputs unconnected at this time Loading Fuzzy Controller Data You can compare the Fuzzy Controller VI to a microprocessor that does not have an executable program loaded To obtain the specific data for the fuzzy controller you must use the Load Fuzzy Controller VI to load the required data into the Fuzzy Controller VI This VI also is included in the Fuzzy Logic Controls Because the controller data must be loaded into the Fuzzy Controller VI when the pattern recognition application is started place it outside the While Loop as shown in Figure 8 11 PID Control Toolkit User Manual 8 8 ni com Chapter 8 Implementing a Fuzzy Controller E signal minj Figure 8
36. the Fuzzy Logic Controller Design VI vehicle position specify define iv left m edit left left center center right center right LUBERRI 40 50 60 70 80 90 100 left bottom right top right bottom 0 00 ho 4o q yehicle orientation specify lt bles ANTECEDENCE define leFt down ling terms edit left down left left up 0 6 up right up right 0 2 right down 0 45 0 0 1 i 1 i 90 0 50 0 0 0 50 0 100 0 150 0 LTS S13 13h Slee left bottom left top righttop 90 00 i 45 00 a specify iv all O NegBig m lt ling terms edit vl steering angle NegBig NegMed NegSmall Zero PosSmall PosMod PosBig Isisisishsisis i i i i i 10 0 y 20 0 30 0 left bottom left top ight top right bottom 30 00 30 00 0 15 00 a q Figure 7 11 Results of the Complete Editing Session Example National Instruments Corporation 7 13 PID Control Toolkit User Manual Chapter 7 Using the Fuzzy Logic Controller Design VI Rulebase Editor PID Control Toolkit User Manual After you enter all the linguistic information of the application example into your FuzzyTruck project you can begin editing The rule base represents expert knowledge about the vehicle maneuvering process If it is not already active select File Open to load the example project FuzzyTruck Sele
37. the IF condition In this case the first rule results in the action adjust steering angle to negative small with a degree of 0 8 The second rule results in the action adjust steering angle to negative medium with a degree of 0 1 The composition step ensures that the resulting action is composed of the differently weighted THEN conclusions of the active rules The rules of this rule base are defined alternatively which means that they are logically linked by the word OR Because the resulting conclusions of the rules are partially true you cannot use the OR operator from conventional dual logic to calculate the resulting conclusion In fuzzy logic you must use the maximum operator instead For example assume that two rules assert different degrees of truth for the linguistic term positive medium One rule asserts positive medium with a degree of truth of 0 2 while another asserts positive medium with a degree of truth of 0 7 Because the OR operator relates two rules to each other the output of the fuzzy inference for the linguistic term is the maximum value of 0 7 Because the truck example has only one rule asserting a nonzero degree of truth for both negative medium and negative small those values become the maximum values you use 4 16 ni com Chapter 4 Overview of Fuzzy Logic The final result of the fuzzy inference for the linguistic variable steering angle includes the following linguistic terms and their corr
38. to 3 19 hardware timed DAQ control loop 3 19 software timed DAQ control loop 3 17 software timed DAQ control loop with advanced DAQ functions 3 18 programming examples NI resources B 1 proportional action 2 2 2 5 S setpoint relay experiment 2 7 Shinskey F G A 1 software NI resources B 1 support technical B 1 T technical support B 1 timing 3 2 training and certification NI resources B 1 trapezoidal integration 2 2 2 6 troubleshooting NI resources B 1 tuning 3 3 W Web resources B 1 Z Ziegler J G A 2 ni com
39. to use the Variable Selector to access the input variables The Fuzzy Set Editor starts a new project with two input variables each of which has the default data range interval 1 0 1 0 The variable data ranges must be changed for the truck application example The vehicle position ranges from 0 0 to 10 0 meters and the vehicle orientation from 90 0 to 270 0 degrees Select specify edit range to display the Edit Range dialog box from which change the data range of the input variable vehicle position Open the Edit Range dialog box to enter the range boundaries as shown in Figure 7 5 PID Control Toolkit User Manual 7 6 ni com Chapter 7 Using the Fuzzy Logic Controller Design VI 2 Define Range Define variable range current linguistic variable identifier min vehicle position Figure 7 5 Edit Range Dialog Box Close the dialog box Notice that all linguistic terms of the linguistic variable are adapted to the new data range proportionally as shown in Figure 7 6 Eb J Fuzzy Set Editor vehicle position N p specify m lt ling variables ANTECEDENCE define lt ling terms edit NEI iv NE1 ZE1 PO1 40 50 60 70 80 90 10 0 left bottom left top right top right bottom rs Ea F Lon oo oo o0 amp 5 00 Figure 7 6 Current Input Variable Data Range Changed For the application example repeat the steps discussed above to set up the correct data range for
40. 17 Max Min Inference 1 00 1 00 1 00 dx dt PID Control Toolkit User Manual Chapter 5 Fuzzy Controllers Because the minimum operator used in the aggregation step is nonlinear the characteristic field is not exactly linear despite the entirely overlapping membership functions that overlap entirely for both input variables Nonoverlapping membership functions yield a stepped characteristic field with constant planes as shown in Figure 5 18 National Instruments Corporation 5 25 PID Control Toolkit User Manual Chapter 5 Fuzzy Controllers Negative Zero Positive NL NS ZE PS PL ii 1 0 t 1 0 py O ny 8 0 6 0 6 0 4 0 4 0 2 0 2 0 0 0 0 1 0 0 5 0 0 0 5 1 0 1 0 0 5 0 0 0 5 1 0 x gt y A Negative Zero Positive Rule Input x Base Negative Zero Positive g 08 0 6 j Negative NL NS ZE 0 4 z 0 2 Zero NS ZE PS 0 0 1 0 0 5 0 0 0 5 1 0 Positive ZE PS PL dx at gt Max Min Inference Modified CoA y f x dx dt Figure 5 18 1 0 Characteristic Field of a Dual Input Fuzzy Controller Slightly Overlapping Input Terms PID Control Toolkit User Manual 5 26 ni com Design Methodology This chapter provides an overview of the design methodology of a fuzzy controller Design and Implementation Pr
41. 3 PM PID Control Toolkit User Manual Figure 7 1 Project Manager Front Panel You use the menu bar 1 to access options related to fuzzy logic controllers In particular use the File menu 2 to load custom controllers and create new ones Use the Description text box 3 to enter a description of the controller The information area 4 shows information about the controller 7 2 ni com Chapter 7 Using the Fuzzy Logic Controller Design VI Many of the commands in the Fuzzy Logic Control portion of the PID Control Toolkit work similarly to those in LabVIEW Select File Save or File Save as to store the project data to a file with an fc extension Refer to the LabVIEW Help for more information about the Fuzzy Logic controls Fuzzy Set Editor Now consider designing a fuzzy controller for the truck maneuvering example described in the Rule Based Systems section of Chapter 4 Overview of Fuzzy Logic When you begin a new project it is best to enter at least a short project description and the name of the developer into the Project Identification Field Select File New to start the Fuzzy Set Editor If there is an existing project already loaded select Edit Set Editor to open the Fuzzy Set Editor The Fuzzy Set Editor front panel is shown in Figure 7 2 3 Fuzzy Set Editor 3 specify lt ling variables ANTECEDENCE define lt ling terms edit 6 NE1 ZE1 POI 0 0 1 I 10 0 8 6 left bot
42. 90 In fact running all your control VIs too fast degrades the response time of your LabVIEW application All VIs within a loop execute once per iteration at the same cycle time To run several control VIs at different cycle times and still share data between them as for example in a cascade you must separate the VIs into independently timed While Loops Figure 3 3 shows an example of a cascade with two independently timed While Loops Loop A Global Number d Ca Cycle Time A Loop B Stobal Number PID GAE Cycle Time B 0 Figure 3 3 Cascaded Control Functions A global variable passes the output of Loop A to the PV input of Loop B You can place both While Loops on the same diagram In this case they are in separate VIs Use additional global or local variables to pass any other necessary data between the two While Loops If the front panel does not contain graphics that LabVIEW must update frequently the PID Control VIs can execute at kilohertz kHz rates Remember that actions such as mouse activity and window scrolling interfere with these rates Tuning Controllers Manually The following controller tuning procedures are based on the work of Ziegler and Nichols the developers of the Quarter Decay Ratio tuning techniques derived from a combination of theory and empirical observations Corripio 1990 Experiment with these techniques and with one of the process control simul
43. ID Control VIs with LabVIEW math and logic functions to create block diagrams for real control strategies The PID Control VIs use LabVIEW functions and library subVIs without any Code Interface Nodes CINs to implement the algorithms You can modify the VIs for your applications in LabVIEW without writing any text based code Refer to the LabVIEW Help available by selecting Help Search the LabVIEW Help for more information about the VIs Fuzzy logic is a method of rule based decision making used for expert systems and process control that emulates the rule of thumb thought process that human beings use You can use fuzzy logic to control processes that a person manually controls based on expertise gained from experience A human operator who is an expert in a specific process often uses a set of linguistic control rules based on experience that he can describe generally and intuitively Fuzzy logic provides a way to translate these linguistic descriptions to the rule base of a fuzzy logic controller Refer to Chapter 4 Overview of Fuzzy Logic for more information How Do the Fuzzy Logic Vis Work PID Control Toolkit User Manual With the Fuzzy Logic VIs you can design a fuzzy logic controller an expert system for decision making and implement the controller in your LabVIEW applications The Fuzzy Logic Controller Design VI available by selecting Tools Control Design and Simulation Fuzzy Logic Controller Design defines
44. LabVIEW PID Control Toolkit User Manual August 2006 c7 NATIONAL 372192A 01 IE INSTRUMENTS Worldwide Technical Support and Product Information ni com National Instruments Corporate Headquarters 11500 North Mopac Expressway Austin Texas 78759 3504 USA Tel 512 683 0100 Worldwide Offices Australia 1800 300 800 Austria 43 0 662 45 79 90 0 Belgium 32 0 2 757 00 20 Brazil 55 11 3262 3599 Canada 800 433 3488 China 86 21 6555 7838 Czech Republic 420 224 235 774 Denmark 45 45 76 26 00 Finland 385 0 9 725 725 11 France 33 0 1 48 14 24 24 Germany 49 0 89 741 31 30 India 91 80 41190000 Israel 972 0 3 6393737 Italy 39 02 413091 Japan 81 3 5472 2970 Korea 82 02 3451 3400 Lebanon 961 0 1 33 28 28 Malaysia 1800 887710 Mexico 01 800 010 0793 Netherlands 31 0 348 433 466 New Zealand 0800 553 322 Norway 47 0 66 90 76 60 Poland 48 22 3390150 Portugal 351 210 311 210 Russia 7 095 783 68 51 Singapore 1800 226 5886 Slovenia 386 3 425 4200 South Africa 27 0 11 805 8197 Spain 34 91 640 0085 Sweden 46 0 8 587 895 00 Switzerland 41 56 200 51 51 Taiwan 886 02 2377 2222 Thailand 662 278 6777 United Kingdom 44 0 1635 523545 For further support information refer to the Technical Support and Professional Services appendix To comment on National Instruments documentation refer to the National Instruments Web site at ni com info and enter the info code feedback 1996 2006 National Instruments Corporation All rights reserved
45. TION WITH OTHER PRODUCTS IN A MANNER NOT EVALUATED OR CONTEMPLATED BY NATIONAL INSTRUMENTS THE USER OR APPLICATION DESIGNER IS ULTIMATELY RESPONSIBLE FOR VERIFYING AND VALIDATING THE SUITABILITY OF NATIONAL INSTRUMENTS PRODUCTS WHENEVER NATIONAL INSTRUMENTS PRODUCTS ARE INCORPORATED IN A SYSTEM OR APPLICATION INCLUDING WITHOUT LIMITATION THE APPROPRIATE DESIGN PROCESS AND SAFETY LEVEL OF SUCH SYSTEM OR APPLICATION Contents About This Manual Organization of This Manual eee eceseeeceeseceeeeseeseeesecseceaeesesesecseseseceesaesseeeaeesees ix CONVENON S aza an n a N a a oudea aah eye A ees ix Related Documentations m a e a a A E aa NE aa Eia x Chapter 1 Overview of the PID Control Toolkit PID Control sages dosais 358s sesscaaveneked satis seg sethace nba cadendsbasddbed E E 1 1 PUZZy LOSIC ani ED Gea ah Aint E E A E aachaee Baas 1 2 How Do the Fuzzy Logic VIs Work seesessesseeeesessrssrssessrsssessresressessresreseese 1 2 Part PID Control Chapter 2 PID Algorithms FRE RID Al gorithinsse itis oveed steraten EE tre denne tice ico O T E E EEE 2 1 Implementing the PID Algorithm with the PID VIs eee eee eeeeeeeneeeeeeeeaee 2 2 Error Calculat om orenera e a E E ET tees NE 2 2 Proportional ACHO e e AT A Ea TAE E NAE 2 2 Trapezoidal Integration isoen a E A O EEE 2 2 Partial Derivative ACtiOn osipi ee e ans a a aias 2 2 Controller QuUtput presreo e ae rE AE EE E EEES 2 2 Output Limiti ss snn A a Readies 2 3
46. Value error t derror t at H ddt H gt EUA OP zr Rule Base IF AND THEN IF AND THEN IF AND THEN P gt A Fuzzification Fuzzy Inference Defuzzification dy t at K d error t at oh error t Measured Value National Instruments Corporation 5 3 Figure 5 3 Closed Loop Control Structure with Fuzzy P Controller A Fuzzy PI Controller is a fuzzy controller with two inputs and one output The output value increases when the input values increase If you use an error signal and its derivative as input signals the Fuzzy PI Controller is essentially a generalization of the conventional PI controller The benefit of the Fuzzy PI Controller is that it does not have a special operating point The rules evaluate the difference between the measured value and the set value which is the error signal The rules also evaluate the tendency of the error signal to determine whether to increase or decrease the control variable The absolute value of the command variable has no influence The advantage of a Fuzzy PI Controller over a conventional PI controller is that it can implement nonlinear control strategies and that it uses linguistic rules It is possible to consider only the error tendency when the error becomes small Chemical industry and process technology often use the Fuzzy Controller with Underly
47. W windup area Glossary In process instrumentation the value T in minutes in an exponential response term A exp t T or in one of the transform factors such as 1 sT See overshoot A numerical of integration in which the current value and the previous value are used to calculate the addition of the current value to the integral value Volts In process instrumentation the range through which an input signal may be varied upon reversal of direction without initiating an observable change in output signal The time during which the controller output is saturated at the maximum or minimum value The integral action of a simple PID controller continues to increase wind up while the controller is in the windup area National Instruments Corporation G 9 PID Control Toolkit User Manual Index A AND operator 4 10 Astrom K J A 1 Autotuning Algorithm 2 7 to 2 9 tuning formulas 2 7 PI control fast 2 8 PI control normal 2 9 PI control slow 2 9 P only control fast 2 8 P only control normal 2 8 P only control slow 2 8 bumpless transfer 2 3 C calculating controller action 2 1 to 2 3 control strategies 3 1 controller output 2 2 Corripio A B A 1 D DAQ hardware with PID 3 17 to 3 19 hardware timed DAQ control loop 3 19 software timed DAQ control loop 3 17 software timed DAQ control loop with advanced DAQ functions 3 18 Declaration of Conformity NI resources
48. You can use these VIs interchangeably because they all use consistent inputs and outputs where possible The PID VI has inputs for setpoint process variable PID gains dt output range and reinitialize The PID gains input is a cluster of three values proportional gain integral time and derivative time You can use output range to specify the range of the controller output The default range of the controller output is 100 to 100 which corresponds to values specified in terms of percentage of full scale However you can change this range to one that is appropriate for your control system so that the controller gain relates engineering units to engineering units instead of percentage to percentage The PID VI coerces the controller output to the specified range In addition the PID VI implements integrator anti windup when the controller output is saturated at the specified minimum or maximum values Refer to Chapter 2 PID Algorithms for more information about anti windup You can use dt to specify the control loop cycle time The default value is 1 so by default the PID VI uses the operating system clock for 3 6 ni com Chapter 3 Using the PID Software calculations involving the loop cycle time If the loop cycle time is deterministic you can provide this input to the PID VI Note that the operating system clock has a resolution of ms so specify a dt value explicitly if the loop cycle time is less than 1 ms The PID
49. a The Control VI processes data and LabVIEW updates the analog output channels as quickly as the VI can execute If the processing time of the loop subdiagram remains less than the scan interval the scan rate dictates the control rate If the processing of the analog input control algorithm and analog output takes longer than the specified scan interval which is ms in this example the software falls behind the hardware acquisition rate and does not maintain real time If you monitor data remaining when you call AI SingleScan you can determine whether the VI has missed any scans If data remaining remains zero the control is real time National Instruments Corporation 3 19 PID Control Toolkit User Manual Part Il Fuzzy Logic Control This section of the manual describes the Fuzzy Logic portion of the PID Control Toolkit e Chapter 4 Overview of Fuzzy Logic introduces fuzzy set theory and fuzzy logic control e Chapter 5 Fuzzy Controllers describes different implementations of fuzzy controllers and the I O characteristics of fuzzy controllers e Chapter 6 Design Methodology provides an overview of the design methodology of a fuzzy controller e Chapter 7 Using the Fuzzy Logic Controller Design VI describes how to use Fuzzy Logic VIs to design a fuzzy controller e Chapter 8 Implementing a Fuzzy Controller describes how to use Fuzzy Logic VIs to implement the custom controller in your applications Nati
50. a positional algorithm that approximates a true exponential lead lag Feedforward control schemes often use this kind of algorithm as a dynamic compensator You can specify the range of the output using the output range input The default range is 100 to 100 which corresponds to values specified in terms of percentage of full scale However you can change this range to one that is appropriate for your control system so that the controller gain relates engineering units to engineering units instead of percentage to percentage The PID Lead Lag VI coerces the controller output to the specified range The output value on the first call to the VI is the same as the input value You can reinitialize the output to the current input value by passing a value of TRUE to the reinitialize input You can use dt to specify the control loop cycle time The default value is 1 so that by default the VI uses the operating system clock for calculations involving the loop cycle time If the loop cycle time is deterministic you can provide this input to the PID Lead Lag VI Note that the operating system clock has a resolution of ms therefore you should specify dt explicitly if the loop cycle time is less than 1 ms National Instruments Corporation 3 13 PID Control Toolkit User Manual Chapter 3 Using the PID Software Converting Between Percentage of Full Scale and Engineering Units As described above the default setpoint process variable
51. able controller even if you cannot properly tune the controller on your own Figure 2 2 illustrates the autotuning procedure excited by the setpoint relay experiment which connects a relay and an extra feedback signal with the setpoint Notice that the PID autotuning VI directly implements this process The existing controller remains in the loop o gt p KE P I Controller gt Process M e PV Tuning Formulas Figure 2 2 Process under PID Control with Setpoint Relay For most systems the nonlinear relay characteristic generates a limiting cycle from which the autotuning algorithm identifies the relevant information needed for PID tuning If the existing controller is proportional only the autotuning algorithm identifies the ultimate gain Ku and ultimate period Tu If the existing model is PI or PID the autotuning algorithm identifies the dead time t and time constant Tp which are two parameters in the integral plus deadtime model TS En Ts p Gp s This package uses Ziegler and Nichols heuristic methods for determining the parameters of a PID controller When you autotune select one of the following three types of loop performance fast 1 4 damping ratio normal some overshoot and slow little overshoot Refer to the following tuning formula tables for each type of loop performance National Instruments Corporation 2 7 PID Control Toolkit User Manual Chapter 2
52. ap entirely The conclusion term distribution and the rule base remain unchanged for this case PID Control Toolkit User Manual 5 8 ni com Chapter 5 Fuzzy Controllers Negative Zero Positive Negative Zero Positive ii 1 0 1 0 ney S uy 8 0 6 0 6 0 4 0 4 0 2 0 2 0 0 0 0 1 0 0 5 0 0 0 5 1 0 1 0 0 5 0 0 0 5 1 0 x y r Max Min Rule Rule 1 IF x Negative THEN y Negative Inference Base Rule 2 IF x Zero THEN y Zero Rule 3 IF x Positive THEN y Positive Modified CoA 1 0 I i Rules 1 and Rules 2 and 0 8 2 Active 3 Active gt 1 0 0 8 0 6 0 4 0 2 0 0 0 2 0 4 0 6 0 8 1 0 x gt Figure 5 8 1 0 Characteristic of a Fuzzy Controller Entirely Overlapping Input Terms Because the antecedence terms completely overlap there are always two active rules The different conclusion terms weighted by the degree of truth for the different active rules that lead to the nonlinear pass of the controller characteristic determine the output value National Instruments Corporation 5 9 PID Control Toolkit User Manual Chapter 5 Fuzzy Controllers Figure 5 9 shows the controller characteristic that results when nonoverlapping antecedence terms describe the input variable
53. arameters of a controlled process while the setpoint value remains constant Time interval between calls to a control algorithm See gain A quantity or condition that is varied as a function of the actuating error signal so as to change the value of the directly controlled variable Also called controller output Fuzzy inference method using the maximum function for the OR operator and the minimum function for the AND operator Another common inference method is the Max Prod method which uses the product function for the AND operator Megabytes of memory 1 MB is equal to 1 024 KB Method of defuzzification in which the crisp output is determined by selecting a value corresponding to the maximum degree of membership of the composite output membership function If there are multiple maximums the mean of the corresponding values is selected PID Control Toolkit User Manual Glossary membership function noise 0 output limiting overshoot P P partial membership P controller PC PD PD controller PI PI controller PID PID Control Toolkit User Manual A function that defines degree of membership to the fuzzy set over a defined universe of discourse of the variable parameter Milliseconds In process instrumentation an unwanted component of a signal or variable Noise may be expressed in units of the output or in percent of output span Preventing a controller s output from travelling beyond a
54. ariable completely overlapping each other The edit menu also has several other functions for automatically editing membership functions You can change individual membership functions or all of the membership functions to singleton fuzzy sets which are typically used only for controller output The tolerance function changes a trapezoidal membership to a triangular function In addition you can set the overlap between functions and make all functions symmetric This command does not affect the left side of the left most term and the right side of the right most term National Instruments Corporation 7 11 PID Control Toolkit User Manual Chapter 7 Using the Fuzzy Logic Controller Design VI Fuzzy Set Editor vehicle position p specify l lt ling variables ANTECEDENCE define a right center lt ling terms adit left left center 0 8 center 0 6 right center right 0 4 0 2 LUBBERS 0 0 1 1 1 i i i 1 1 1 i 1 0 2 0 3 0 4 0 50 6 0 7 0 8 0 90 100 left bottom right top right bottom 5 00 amp 7 50 10 00 q a a E Figure 7 10 A Term Arrangement of Completely Overlapping Terms With the Fuzzy Set Editor functions described in this section you can edit all linguistic variables including the desired term arrangements for the FuzzyTruck example project Figure 7 11 shows the result of the complete editing session PID Control Toolkit User Manual 7 12 ni com Chapter 7 Using
55. ation 3 15 PID Control Toolkit User Manual Chapter 3 Using the PID Software Figure 3 11 Updating PID Parameters Using a Local Variable To avoid having to manually save the VI each time it runs you can use a datalog file to save the PID gains as shown in Figure 3 12 PID gains ic pid params dat alse case is empt Figure 3 12 Storing PID Parameters in a Datalog File Before the control loop begins the File I O VIs read a datalog file to obtain the PID gains parameters When the autotuning procedure runs a local variable updates the PID gains control After the control loop is complete the VI writes the current PID gains cluster to the datalog file and saves it Each time it runs the control VI uses updated parameters PID Control Toolkit User Manual 3 16 ni com Chapter 3 Using the PID Software Using PID with DAQ Devices The remaining sections in this chapter address several important issues you might encounter when you use the DAQ VIs to implement control of an actual process The following examples illustrate the differences between using easy level DAQ VIs and using advanced DAQ VIs as well as the differences between hardware timing and software timing 3 Note Refer to LabVIEW examples daq solution control 11b for additional examples of control with DAQ VIs Software Timed DAQ Control Loop Figure 3 13 illustrates the basic elements of software control The model assumes you h
56. ation 5 13 PID Control Toolkit User Manual Chapter 5 Fuzzy Controllers Using singleton membership functions for the conclusion terms makes the CoG defuzzification method identical to the CoM method Figure 5 11 shows the controller for the CoG method using singleton membership functions Negative Zero Positive Negative Zero Positive 4 1 0 i 1 0 u x 0 8 uly 0 8 0 6 0 6 0 4 0 4 0 2 0 2 0 0 0 0 1 0 0 5 0 0 0 5 1 0 1 0 0 5 0 0 0 5 1 0 x gt y gt Max Min Rule Rule 1 IF x Negative THEN y Negative Inference Base Rule 2 IF x Zero THEN y Zero Rule 3 IF x Positive THEN y Positive Modified CoA 1 0 4 0 8 0 6 y 0 4 c 0 0 0 2 0 4 0 6 0 8 1 0 1 0 0 8 0 6 0 4 0 2 0 0 0 2 0 4 0 6 0 8 1 0 x Figure 5 11 I O Characteristic of a Fuzzy Controller Singletons as Output Terms Entirely Overlapping Input Terms PID Control Toolkit User Manual 5 14 ni com Chapter 5 Fuzzy Controllers The controller characteristic remains relatively unchanged when you leave the input terms entirely overlapped to vary the overlapping degree of the membership functions for the conclusion terms especially if all the conclusion terms are equal in width Then only the typical values of the conclusion terms are significant Therefore in most closed loop control app
57. ation VIs to compare them For different processes one method might be easier or more accurate than another For National Instruments Corporation 3 3 PID Control Toolkit User Manual Chapter 3 Using the PID Software example some techniques that work best when used with online controllers cannot stand the large upsets described here To perform these tests with LabVIEW set up your control strategy with the PV SP and output displayed on a large strip chart with the axes showing the values versus time Refer to the Closed Loop Ultimate Gain Tuning Procedure and Open Loop Step Test Tuning Procedure sections of this chapter for more information about disturbing the loop and determining the response from the graph Refer to Corripio 1990 as listed in Appendix A References for more information about these procedures Closed Loop Ultimate Gain Tuning Procedure Although the closed loop ultimate gain tuning procedure is very accurate you must put your process in steady state oscillation and observe the PV on a strip chart Complete the following steps to perform the closed loop tuning procedure 1 Set both the derivative time and the integral time on your PID controller to 0 2 With the controller in automatic mode carefully increase the proportional gain K in small increments Make a small change in SP to disturb the loop after each increment As you increase K the value of PV should begin to oscillate Keep making cha
58. automatic control modes The default value of auto is TRUE which means the VI uses the PID algorithm to calculate the controller output You can implement manual control by changing the value of auto to FALSE so that the VI passes the value of manual control through to the output Bumpless Automatic to Manual Transfer The Advanced PID VI cannot implement bumpless automatic to manual transfer In order to ensure a smooth transition from automatic to manual control mode you must design your application so that the manual output value matches the control output value at the time that the control mode is switched from automatic to manual You can do this by using a local variable for the manual control control as shown in Figure 3 5 National Instruments Corporation 3 7 PID Control Toolkit User Manual Chapter 3 Using the PID Software Figure 3 5 Bumpless Automatic to Manual Transfer Although this VI does not support automatic to manual transfer it does support bumpless manual to automatic transfer which ensures a smooth controller output during the transition from manual to automatic control mode Multi Loop PID Control PID Control Toolkit User Manual Most of the PID control VIs are polymorphic VIs for use in multiple control loop applications For example you can design a multi loop PID control application using the PID VI and DAQ functions for input and output A DAQ analog input function returns an array of data when y
59. ave a little less of one quantity This is exactly what the y operator also called the compensatory AND can model Refer to Appendix A References for a list of documents with more information about this topic The standard inference mechanism is the Max Min method Other inference methods have only a marginal influence on the controller characteristic The defuzzification method derives a crisp output value that best represents the linguistic result obtained from the fuzzy inference process As explained in Chapter 4 Overview of Fuzzy Logic there are generally two different linguistic meanings of the defuzzification process calculating the best compromise CoM or CoA and calculating the most plausible result MoM An important aspect of the defuzzification method is the continuity of the output signal Consider a fuzzy logic system with a complete rule base and overlapping membership functions A defuzzification method is 6 8 ni com Chapter 6 Design Methodology continuous if an arbitrary small change of an input value can never cause an abrupt change in the output signal In this respect the defuzzification methods CoM and CoA are continuous because assuming overlapping output membership functions the best compromise can never jump to a different value with a small change to the inputs To the contrary the defuzzification method MoM is discontinuous because there is always a point at which an arbitrary small change in the i
60. ave a plant a real process to control A basic analog input VI reads process variables from sensors that monitor the process In actual applications you might need to scale values to engineering units instead of voltages Process set point Kms Figure 3 13 Software Timed DAQ Control Loop The Control VI represents the algorithm that implements software control The Control VI can be a subVI you write in LabVIEW a PID controller or the Fuzzy Controller VI An analog output VI updates the analog voltages that serve as your controller outputs to the process The Wait Until Next ms Multiple function that controls the loop timing in this example specifies only a minimum time for the loop to execute Other operations in LabVIEW can increase the execution time of the loop functions The time for the first loop iteration is not deterministic Refer to LabVIEW Help for more information about timing control loops National Instruments Corporation 3 17 PID Control Toolkit User Manual Chapter 3 Using the PID Software Implementing Advanced DAQ Vis in Software Timed DAQ Control Loops For faster I O and loop speeds use the advanced level DAQ VIs for analog input and output The easy level VIs shown in Figure 3 13 actually use the advanced level DAQ VIs shown in this example However the easy level VIs configure the analog input and output with each loop iteration which creates unnecessary overhead that can slow your control loops You
61. c Term Center PID Control Toolkit User Manual 6 4 ni com Chapter 6 Design Methodology Sometimes the typical value of a term is an interval rather than a crisp value If for example the position center is characterized by the statement x 5 0 25 m a trapezoidal membership function applies as shown in Figure 6 3 uD A Left 1 0 Left Right Center Center Center Right 0 8 0 6 0 4 0 2 0 0 0 0 1 0 gt 2 0 3 0 4 0 sof 6 0 7 0 8 0 9 0 10 0 m 4 75 5 25 Vehicle Position x Figure 6 3 Definition of a Trapezoidal Membership Function for the Linguistic Term Center If there is no a priori information available begin with terms equally spaced within the range of the associated variable with each term entirely overlapping the neighboring terms Cover the desired stable region of the system with a larger number of linguistic terms that have a small influence interval rather than trying to cover the border regions with a smaller number of linguistic terms that have a large influence interval A term distribution like this makes the controller more sensitive within the stable state region of the system You must take into account disturbance effects such as noise on input values such as noise Do not set up membership functions with an interval of influence that is smaller than the amplitude of the noise signal
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63. ct Edit Rulebase to open the Rulebase Editor Because you have not explicitly entered or modified a rule at this point in the example project the Rulebase Editor begins with a project specific complete default rule base LabVIEW assigns each possible combination of linguistic terms for each of the input variables to a single rule with its consequence part set to none The Rulebase Editor offers a rule base that contains 35 rules because there are five terms for the first input variable vehicle position and seven terms for the second input variable vehicle orientation If there are more than 15 rules available LabVIEW activates a scrollbar to access the rules not currently displayed on the Rulebase Editor front panel Each rule is associated with a weight factor to enhance or reduce the influence of a rule on the controller characteristic The DoS ranges from 0 0 to 1 0 In a default rule base all DoS values are automatically set to 1 0 Use the Utils menu to set weights for all rules Use weight factors in combination with other techniques such as genetic algorithms to optimize controller performance Enter the desired consequence of each rule to begin editing the rule base The consequence part of each rule is implemented as a term selection box containing all possible consequence terms You can select a consequence term from the term selection box to specify the consequence of a particular tule According to the rule base sp
64. ctor Figure 4 1 shows a graphical representation of the set 4 2 ni com Chapter 4 Overview of Fuzzy Logic u T A Membership patients with a high fever 1 0 0 8 0 6 0 4 0 2 0 0 a 95 0 968 986 100 4 102 2 104 0 105 8 107 6 109 4 T F Body Temperature Figure 4 1 Modeling Uncertainty by Conventional Set Membership Even if you measured the body temperature with an accuracy of up to five decimal places the situation remains the same The higher precision does not change the fact that patients with a body temperature below 102 F do not fit into the category of patients with a high fever while all patients with a body temperature of 102 F and higher fully belong to that category Modeling uncertain facts such as high fever sets aside the strict distinction between the two membership values one TRUE and zero FALSE and instead allows arbitrary intermediate membership degrees With respect to conventional set theory you can generalize the set notion by allowing elements to be more or less members of a certain set This type of set is known as a fuzzy set Figure 4 2 shows a graphical representation of the set National Instruments Corporation 4 3 PID Control Toolkit User Manual Chapter 4 Overview of Fuzzy Logic 1 0 u T A Membership patients with a high fever 0 8 0 6 e
65. d 4 4 ni com Chapter 4 Overview of Fuzzy Logic Linguistic Variables and Terms The primary building block of fuzzy logic systems is the linguistic variable A linguistic variable is used to combine multiple subjective categories that describe the same context In the previous example there is high fever and raised temperature as well as normal and low temperature in order to specify the uncertain and subjective category body temperature These terms are called linguistic terms and represent the possible values of a linguistic variable A fuzzy set defined by a membership function represents each linguistic term u T A 1 0 0 8 Low Normal Raised High Fever 0 6 0 4 0 2 0 0 95 0 gt 96 8 98 6 100 4 102 2 104 0 105 8 107 6 109 4 TF Linguistic Variable Body Temperature Figure 4 3 A Linguistic Variable Translates Real Values into Linguistic Values The linguistic variable shown in Figure 4 3 allows for the translation of a crisp measured body temperature given in degrees Fahrenheit into its linguistic description A doctor might evaluate a body temperature of 100 5 F for example as a raised temperature or a slightly high fever The overlapping regions of neighboring linguistic terms are important when you use linguistic variables to model engineering systems National Instruments Corporati
66. d becomes TRUE only on the iteration during which the autotuning finishes The autotuning procedure updates the PID parameters in PID gains out Normally PID gains out passes through PID gains and outputs PID gains out only when the autotuning procedure completes You have several ways to use these outputs in your applications Figure 3 10 shows one possible implementation of the PID with Autotuning VI The shift register on the left stores the initial value of the PID gains PID gains out then passes to the right hand shift register terminal when each control loop iteration completes Although this method is simple it suffers from one limitation The user cannot change PID gains manually while the control loop is running Figure 3 10 Updating PID Parameters Using a Shift Register Figure 3 11 shows a second method which uses a local variable to store the updated PID gains In this example the VI reads the PID gains control on each iteration and a local variable updates the control only when tuning complete is TRUE This method allows for manual control of the PID gains while the control loop executes In both examples you must save PID gains so that you can use the PID gains out values for the next control application run To do this ensure that the PID gains control shows the current updated parameters then choose Make Current Values Default from the Operate menu and then save the VI National Instruments Corpor
67. describe only large numbered phenomena Informal uncertainty results from a lack of information and knowledge about a situation Linguistic uncertainty results from the imprecision of language Much greater too high and high fever describe subjective categories with meanings that depend on the context in which you use them Modeling Linguistic Uncertainty with Fuzzy Sets PID Control Toolkit User Manual One of the basic concepts in fuzzy logic is the use of fuzzy sets to mathematically describe linguistic uncertainty People often must make decisions based on imprecise subjective information Even when the information does not contain precise quantitative elements people can use fuzzy sets to successfully manage complex situations You do not need to have well defined rules to make decisions Most often you can use rules that cover only a few distinct cases to approximate similar rules that apply them to a given situation The flexibility of the rules makes this approximation possible For example if the family doctor agrees to make a house call if a sick child has a high fever of 102 F you would definitely summon the doctor when the thermometer reads 101 5 F However you cannot use conventional dual logic to satisfactorily model this situation because the patient with a body temperature of 101 5 F does not fulfill the criterion for suffering from a high fever and thus conventional dual logic tells you not to call the do
68. desired maximum range The maximum excursion beyond the final steady state value of output as the result of an input change Also called transient overshoot Proportional In fuzzy set theory a condition in which the value of a member partially fulfills the requirements of the membership function of a set A controller which produces proportional control action only that is a controller that has only a simple gain response Pressure controller Proportional derivative A controller that produces proportional plus derivative rate control action Proportional integral A controller that produces proportional plus integral reset control action Proportional integral derivative G 6 ni com PID control PID controller process gain K process variable PV proportional action proportional band PB proportional kick PSI Q Quarter Decay Ratio ramp rate action reentrant execution National Instruments Corporation G 7 Glossary A common control strategy in which a process variable is measured and compared to a desired set point to determine an error signal A proportional gain P is applied to the error signal an integral gain I is applied to the integral of the error signal and a derivative gain D is applied to the derivative of the error signal The controller output is a linear combination of the three resulting values A controller that produces proportional plus integral reset plu
69. e and S type membership function shapes Z type A type I type S type Figure 6 1 Shapes of Standard Membership Functions To establish standard membership functions complete the following steps illustrated in Figure 6 2 1 Define the typical value for each term This is the value that best fits the linguistic meaning of the term and yields the membership degree u l 2 For each term set the membership degree to u 0 at the typical values of neighboring terms 3 Connect the point u 1 with the points u 0 by straight lines creating triangular membership function shapes for all inner terms 4 Because there are no terms beyond the rightmost term and below the leftmost term all values that fall into this region belong to the respective border term with the membership degree u 1 National Instruments Corporation 6 3 PID Control Toolkit User Manual Chapter 6 Design Methodology Typical value for center is 5 0 x Left Right p A Left Center Center Center Right 1 0 M 0 8 0 6 0 4 0 2 0 0 X gt 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 10 0 m Typical values for left center and right center are 4 0 and 6 0 Vehicle Position x Figure 6 2 Definition of a Triangular Membership Function for the Linguisti
70. e controller is the setpoint for another controller PID Control Toolkit User Manual Glossary Center of Area CoA Center of Maximum CoM closed loop composition controller controller output crisp value cycle time D damping DC dead time Ta defuzzification degree of membership PID Control Toolkit User Manual Method of defuzzification in which the crisp output is determined by the geometrical center of the composite output membership function Also known as Center of Gravity CoG Method of defuzzification in which the crisp output is determined by a weighted average of the maximum values of each output membership function This method is equivalent to the Center of Area method using singleton sets A signal path which includes a forward path a feedback path and a summing point and which forms a closed circuit Also called a feedback loop The process by which a fuzzy controller combines all of the fuzzy subsets assigned to each output variable to form a single fuzzy subset for each output variable Hardware and or software used to maintain parameters of a physical process at desired values See manipulated variable A finite single value such as a measured physical quantity for example x 5 3 m The time between samples in a discrete digital control system The progressive reduction or suppression of oscillation in a device or system Direct current The interval of time
71. e the rule base of the previous example to include the following rules Rule 1 IF x negative THEN y negative Rule 2 IF x zero THEN y positive Rule 3 IF x positive THEN y negative 5 20 ni com Chapter 5 Fuzzy Controllers Negative Zero Positive Negative Zero Positive 4 1 0 4 1 0 non 08 ny 8 0 6 0 6 0 4 0 4 0 2 0 2 0 0 0 0 1 0 0 5 0 0 0 5 1 0 1 0 0 5 0 0 0 5 1 0 x gt y gt Max Min Rul Rule 1 IF x Negative THEN y Negative Inference Sas Rule 2 IF x Zero THEN y Positive Rule 3 IF x Positive THEN y Negative Modified CoA 1 0 A 0 8 0 6 y 0 4 E 0 0 0 2 0 4 0 6 0 8 1 0 1 0 0 8 0 6 0 4 0 2 0 0 0 2 0 4 0 6 0 8 1 0 x Figure 5 15 1 0 Characteristic of a Fuzzy Controller with a Changed Rule Base The examples show that you can use a fuzzy controller to perform arbitrary T O operations The number of linguistic input and output terms depends on the desired characteristic type and the precision to which you approximate the given I O characteristic National Instruments Corporation 5 21 PID Control Toolkit User Manual Chapter 5 Fuzzy Controllers Consider for example the stepped linear characteristic curve shown in Figure 5 16 There are four linear sections that you can describe with the
72. ecified in Figure 4 9 Complete Linguistic Rule Base if the vehicle position is left and the vehicle orientation is left down the consequence term is negative small When you select NegSmall from the term selection box of the consequence part the THEN part the first rule of the rule base is IF vehicle position is left AND vehicle orientation is left down THEN set steering angle to negative small 7 14 ni com Chapter 7 Using the Fuzzy Logic Controller Design VI You can enter the complete rule base this way The IF part of the Rulebase Editor panel automatically accommodates the number of input variables used in the fuzzy controller Next select an appropriate defuzzification method Because there must be a continuous output signal for the steering angle control you must select a defuzzification method that calculates the best compromise Follow the guidelines in Table 6 1 Comparison of Different Defuzzification Methods to choose either the CoM method or the CoA method Select the defuzzification method from the appropriate selector from the Defuzzification Method pull down menu You can use the default setting as the default controller output The default setting does not affect the application example because the fuzzy controller has a complete rule base and overlapping term arrangements In the example no input variables have definition gaps or undefined intervals Refer to Figure 5 10 I O Characteristic of a Fuzzy Controller U
73. ely modify the linguistic term activated by the Term Selector The Fuzzy Set Editor controls modifications to terms with respect to plausibility restrictions To prevent the user from making implausible term arrangements LabVIEW dims all input sliders of term points that cannot be modified because of plausibility restrictions When you move a particular point slider to modify a term shape the Fuzzy Set Editor controls and updates all input sliders according to plausibility restrictions too Thus the right top value of the term NE1 might not override the left top value of the term ZE1 When you move the right top slider the Fuzzy Set Editor constantly updates this slider according to the plausibility restriction mentioned above so that this point right top of NE1 cannot exceed the left top of ZE1 As the example in Figure 7 3 illustrates you cannot move the left bottom point or left top point of the term NE1 below the left hand range limit of the input variable 7 4 ni com Chapter 7 Using the Fuzzy Logic Controller Design VI 3 Fuzzy Set Editor specify v lt ling variables ANTECEDENCE define v lt ling terms edit ina NE1 2E1 BES POL noz 0 6 0 4 Dzs 0 0 1 1 0 0 6 left bottom left top right top right bottom a 1 0 0 20 ood 0 20 amp q l q Figure 7 3 Plausibility Checking and Point Slider Movement In the truck maneuvering example in the Rule Based Systems sec
74. email addresses and current events National Instruments Corporation B 1 PID Control Toolkit User Manual Glossary A aggregation algorithm anti reset windup autotuning Autotuning Wizard bias Boolean set theory bumpless transfer C C cascade control National Instruments Corporation G 1 An operation in fuzzy logic in which several fuzzy sets are combined to produce a single fuzzy set A prescribed set of well defined rules or processes for the solution of a problem in a finite number of steps A method that prevents the integral term of the PID algorithm from moving too far beyond saturation when an error persists Automatically testing a process under control to determine the controller gains that will provide the best controller performance An automated graphical user interface provided in the PID with Autotuning VI The Autotuning Wizard gathers some information about the desired control from the user and then steps through the PID autotuning process The offset added to a controller s output Traditional set theory based on strict membership or nonmembership of elements to a set Examples are TRUE or FALSE ON or OFF 1 or 0 and so on A process in which the next output always increments from the current output regardless of the current controller output value therefore transfer from automatic to manual control is always bumpless Celsius Control in which the output of on
75. epresents complete operation time you can extract the following features for the desired pattern recognition TH TS 0 gt Triangle TU TD TS gt 0 gt lefthand shaped 0 lt TH TS gt 1 gt Hexagon TU TD TS 0 gt symmetrical TH TS 1 gt Rectangle TU TD TS lt 0 gt righthand shaped B Note You can use existing functions or functions you can write in LabVIEW to execute all the signal processing steps described above Because the real sensor signal is not an idealized signal as shown above the characteristic features derived from it are not precise You can model them directly by the appropriate linguistic terms for the two linguistic input variables TH TS and TU TD TS Using the Fuzzy Logic Control as described in Chapter 7 Using the Fuzzy Logic Controller Design VI the term arrangements shown in Figures 8 4 and 8 5 exist for the input variables TH TS and TU TD TS Figure 8 4 Linguistic Term Arrangement of Input Variable TH TS National Instruments Corporation 8 3 PID Control Toolkit User Manual Chapter 8 Implementing a Fuzzy Controller Figure 8 5 Linguistic Term Arrangement of Input Variable TU TD TS The linguistic output variable object can be composed of singletons each of which represents a specific shape Figure 8 6 shows the term arrangement and Figure 8 7 shows the rule base PID Control Toolkit User Manual 8 4 ni com Chapter 8 Implementing a Fuzzy Controller Fiz
76. ers Structure of a Fuzzy Controller toc scis cesses casecienecssectscis cas daessgecassveanysciscosiucnaassdestecessasstes 5 1 Closed Loop Control Structures with Fuzzy Controllers 0 eee eee eeeeseeseeeeeeseeeees 5 2 VO Characteristics of Fuzzy Controllers 0 cece ees eeeeseceeceeeseeeseceenseceeesesseeeaeesees 5 6 Chapter 6 Design Methodology Design and Implementation Process Overview 0 scecsseesesseeeseeseeeseceeeaeenseesseneeeaes 6 1 Acquiring Knowledge o0 eee eceeseceeeseesseeseceseeseceeeseceeeeaeceeeseeseeeasensenseeaes 6 1 Optimizin OTM asses ses aS fous cusses cues E EE SERER 6 1 Optimizing Online a ei elke E E A SS 6 2 Trnplementin 8 ea e eera ae a AA E E E AE E ESE 6 2 Defining Linguistic Variables soises so siere k E NE NENS 6 2 Number of Linguistic Temse e a aiea EA 6 2 Standard Membership Functions essssesssesessesrsresrsresreresrssesresteersrrerssrsresrerent 6 3 Defining a Fuzzy Logic Rule Base oo eee are a eA 6 6 Operators Inference Mechanism and the Defuzzification Method ce eeeeeeeeee 6 8 Chapter 7 Using the Fuzzy Logic Controller Design VI COV ELV E W r EAE teens sues RO death et venst E A E E E E eee 7 1 Project Manas OP oenn traen na e a E e E r Se 7 2 F z zy Set Edito o e aot sts r sas cach EE AE E E AAEE EE EA A E POSEE ESE EEA 7 3 Rulebase Editor scx ekecier ats whee hp kien ets oa avec tee eae tes 7 14 Documenting Fuzzy Control Projects eee eecesceseeesesseceseeseesee
77. esecseceaecneessesseeeaeeaees 7 15 Test Bact tes st tevcccet cesstgrerdeslvha eae AA in ue eh Rtas Beats 7 15 Chapter 8 Implementing a Fuzzy Controller Pattern Recognition Application Example 0 0 0 0 cece eeeessceeceeseeeeseseeeeseeeseeseeeeeeaees 8 1 Fuzzy Controller Implementation 00 0 0 eee eceeseescceseeseeeseceeeeseseeeeaeseeeeaeesaeeeeeeeeaees 8 7 Loading Fuzzy Controller Data soiiniconssicei nienia a 8 8 Saving Controller Data with the Fuzzy Controller ccc eeeeceeseceeceeeeeeeseeeeensersees 8 11 Testing the Fuzzy Controller cic ccisssccscecsscesttescasesssbeaseveg coysssesessusisiecescendesesezens scbasasvaseadas 8 13 Appendix A References National Instruments Corporation vii PID Control Toolkit User Manual Contents Appendix B Technical Support and Professional Services Glossary Index PID Control Toolkit User Manual viii ni com About This Manual The LabVIEW PID Control Toolkit User Manual describes the PID Control Toolkit for LabVIEW This toolkit includes the PID Control and Fuzzy Logic Control VIs Organization of This Manual Conventions The LabVIEW PID Control Toolkit User Manual is organized as follows Part I PID Control This section of the manual describes the features functions and operation of PID Control portion of the PID Control Toolkit To use this section you need a basic understanding of process control strategies and algorithms Refer to Appendix A References for ot
78. esponding values negative large to a degree of 0 0 negative medium to a degree of 0 1 negative small to a degree of 0 8 Zero to a degree of 0 0 positive small to a degree of 0 0 positive medium to a degree of 0 0 positive large to a degree of 0 0 This type of fuzzy inference is called Max Min inference Because of certain optimization procedures of fuzzy systems sometimes it is necessary to associate individual weights with each rule Using Linguistic Variables in Defuzzification The fuzzy inference process results in a linguistic value for the output variable In this case you can interpret the linguistic value 0 0 0 1 0 8 0 0 0 0 0 0 0 0 as still negative small or just slightly negative medium To use this linguistic value to adjust the steering wheel you must translate it into a real physical value This step is called defuzzification Refer to Figure 4 10 for a diagram of the different steps The membership functions that describe the terms of the linguistic output variable always define the relationship between the linguistic values and the corresponding real values Refer to Figure 4 8 for more information about membership functions In the example you obtain a fuzzy inference result that is both fuzzy and ambiguous because you acquire the nonzero truth degree of two different actions at the same time You must combine two conflicting actions defined as fuzzy sets to form a crisp real value A solution to this problem
79. eton membership functions each of which has a typical value that corresponds to a certain base point component yi The rule base is then a linguistic enumeration of the five base points In principle these conclusions about I O characteristics are valid for fuzzy controllers with two or more inputs as well However using the AND operation to combine the different input conditions raises an additional nonlinear effect Usually the minimum operator models the AND operation that always prefers as a result the antecedence term of the rule with the lowest degree of truth Refer to Figure 5 16 for an example Figure 5 17 shows the I O characteristic field for a dual input fuzzy controller National Instruments Corporation 5 23 PID Control Toolkit User Manual Fuzzy Controllers oO a L LW n 8 N o a A 2 19 ao o x 28 2 Hlg N w W A a N fo oO 2 w p N W ep wo P Zz Zz N Zz F Zz oO z z E oO o o o t a ol P 3 jo oO x Z N a lt s d y xXp ndu z g Alls a T on no O O a A 9 RRS o og o 3 o N S IN S 9 19 o Q F 2 2 Z z oO oO z 2 2 o o v et a o baa oO lo oO lo fo oO lt lt lt ppp Chapter 5 ni com 1 00 Modified CoA 1 0 Characteristic Field of a Dual Input Fuzzy Controller 5 24 Figure 5
80. example you might want to ramp the setpoint temperature of an oven control system over time and then hold or soak the setpoint at a certain temperature for another period of time You can use the PID Setpoint Profile VI to implement any arbitrary combination of ramp hold and step functions Specify the setpoint profile as an array of pairs of time and setpoint values with the time values in ascending order For example a ramp setpoint profile can be specified with two setpoint profile array values as shown in Figure 3 6 setpoint profile setpoint profile graph 7 time s setpoint 100 0 do ooo 1 40 00 80 0 time s setpoint 60 0 7 7 oO ffs o00 F100 00 B A 40 0 time s setpoint o 000 o 00 20 0 time s setpoint 0 000 10 00 Figure 3 6 Ramp Setpoint Profile A ramp and hold setpoint profile also can have two successive array values with the same setpoint value as shown in Figure 3 7 setpoint profile setpoint profile graph Jo time s setpoint 100 0 Ho oo0 Ho o0 time s setpoint fJs o00 410 00 time s setpoint F10 000 100 00 20 0 0 0 1 1 1 1 0 0 2 0 4 0 6 0 8 0 10 0 Time 80 0 60 0 Setpoint 40 0 time s setpoint 10 000 10 00 Figure 3 7 Ramp and Hold Setpoint Profile National Instruments Corporation 3 9 PID Control Toolkit User Manual Chapter 3 Using the PID Software Alternatively a step setpoint
81. expressed in minutes between initiation of an input change or stimulus and the start of the resulting observable response The process of converting the linguistic output of the rulebase evaluation to a crisp controller output value A value that represents the degree of partial membership of an element to a fuzzy set This value may range from 0 to 1 G 2 ni com degree of support derivative control action deviation derivative kick downstream loop EGU expert F FC feedback control feedback loop fuzzification fuzzy inference National Instruments Corporation G 3 Glossary A weighting value ranging from 0 to 1 that is applied to each rule in the tule base of a fuzzy controller This weighting value represents the relative significance of each rule and allows for fine tuning of the rule base Control response to the time rate of change of a variable Also called rate action Any departure from a desired value or expected value or pattern A sudden change in PID controller output resulting from derivative action applied to the error signal after a change in setpoint value Derivative kick is normally avoided in PID control by applying derivative action only to the process variable and not to the error signal In a cascade the controller whose setpoint is provided by another controller Engineering units A human operator of a system or process that has acquired knowledge related to contro
82. f Freedom PID algorithm Intuitively B is an index of the SP response importance from zero to one For example if you consider load response the most important loop performance set B to 0 0 Conversely if you want the process variable to quickly follow the SP change set B to 1 0 up k K eb k National Instruments Corporation 2 5 PID Control Toolkit User Manual Chapter 2 PID Algorithms Trapezoidal Integration Trapezoidal integration is used to avoid sharp changes in integral action when there is a sudden change in PV or SP Use nonlinear adjustment of integral action to counteract overshoot The larger the error the smaller the integral action as shown in the following formula and in Figure 2 1 k K e i e i 1 1 uk T 2 N e 1o e iy SP rng 0 9 0 8 0 7 0 6 0 5 0 4 0 3 0 2 0 1 0 0 1 l T T T 1 I 1 100 0 75 0 50 0 25 0 0 0 25 0 50 0 75 0 100 0 Error Figure 2 1 Nonlinear Multiple for Integral Action SP ng 100 PID Control Toolkit User Manual 2 6 ni com Chapter 2 PID Algorithms The Autotuning Algorithm Use autotuning to improve performance Often many controllers are poorly tuned As a result some controllers are too aggressive and some controllers are too sluggish PID controllers are difficult to tune when you do not know the process dynamics or disturbances In this case use autotuning Before you begin autotuning you must establish a st
83. ge change in setpoint can cause a very large change in controller output Although in theory this large change in controller output results in fast response of the system it may also cause unnecessary wear on actuators or sudden large power demands In addition the PID controller can amplify noise in the system and result in a constantly changing controller output PID Control Toolkit User Manual 3 12 ni com Chapter 3 Using the PID Software You can use the PID Output Rate Limiter VI to avoid the problem of sudden changes in controller output Wire the output value from the PID VI to the input controller output input of the PID Output Rate Limiter VI This limits the slew or rate of change of the output to the value of the output rate EGU min Assign a value to initial output and this will be the output value on the first call to the VI You can reinitialize the output to the initial value by passing a value of TRUE to the reinitialize input You can use dt to specify the control loop cycle time The default value is 1 so that by default the VI uses the operating system clock for calculations involving the loop cycle time If the loop cycle time is deterministic you can provide this input to the PID Output Rate Limiter VI Note that the operating system clock has a resolution of 1 ms therefore you should specify a dt value explicitly if the loop cycle time is less than ms The PID Lead Lag VI The PID Lead Lag VI uses
84. hat is a placeholder for a word or value that you must supply Text in this font denotes text or characters that you should enter from the keyboard sections of code programming examples and syntax examples This font is also used for the proper names of disk drives paths directories programs subprograms subroutines device names functions operations filenames and extensions Bold text in this font denotes the messages and responses that the computer automatically prints to the screen This font also emphasizes lines of code that are different from the other examples Related Documentation PID Control Toolkit User Manual The following documents contain information you might find helpful as you read this manual e LabVIEW Help availably by launching LabVIEW and selecting Help Search the LabVIEW Help e LabVIEW Real Time Module documentation e LabVIEW Simulation Module documentation e LabVIEW Control Design Toolkit User Manual X ni com Overview of the PID Control Toolkit This chapter describes the PID Control applications PID Control Currently the Proportional Integral Derivative PID algorithm is the most common control algorithm used in industry Often people use PID to control processes that include heating and cooling systems fluid level monitoring flow control and pressure control In PID control you must specify a process variable and a setpoint The process variable is the system paramete
85. her sources of information on process control terminology methods and standards Part II Fuzzy Logic Control This section of the manual describes the features functions and operation of the Fuzzy Logic Control portion of the PID Control Toolkit You can use the Fuzzy Logic Controls to design and implement rule based fuzzy logic systems for process control or expert decision making To use this section effectively you need to be familiar with basic control theory Knowledge of rule based systems and fuzzy logic helps as well bold The following conventions appear in this manual The symbol leads you through nested menu items and dialog box options to a final action The sequence File Page Setup Options directs you to pull down the File menu select the Page Setup item and select Options from the last dialog box This icon denotes a note which alerts you to important information Bold text denotes items that you must select or click in the software such as menu items and dialog box options Bold text also denotes parameter names controls and buttons on the front panel dialog boxes sections of dialog boxes menu names and palette names National Instruments Corporation ix PID Control Toolkit User Manual About This Manual italic monospace monospace bold Italic text denotes variables linguistic terms emphasis a cross reference or an introduction to a key concept Italic text also denotes text t
86. ickly and easily implement process control Most traditional control algorithms require a mathematical model to work on but many physical systems are difficult or impossible to model mathematically In addition many processes are either nonlinear or too complex for you to control with traditional strategies However if an expert can qualitatively describe a control strategy you can use fuzzy logic to define a controller that emulates the heuristic rule of thumb strategies of the expert Therefore you can use fuzzy logic to control a process that a human manually controls with knowledge he gains from experience You can directly translate from the linguistic control rules developed by a human expert to a rule base for a fuzzy logic controller National Instruments Corporation 4 1 PID Control Toolkit User Manual Chapter 4 Overview of Fuzzy Logic Types of Uncertainty Real world situations are often too uncertain or vague for you to describe them precisely Thoroughly describing a complex situation requires more detailed data than a human being can recognize process and understand When you apply fuzzy logic concepts there are the following different types of uncertainty stochastic informal and linguistic Stochastic uncertainty is the degree of uncertainty that a certain event will occur The event itself is well defined and the stochastic uncertainty is not related to when the event occurs This type of uncertainty is used to
87. ification Real Variables measured quantities vehicle position x 5 m vehicle orientation B 90 Technical Level Defuzzification lt Control Variable steering angle 0 PID Control Toolkit User Manual Figure 4 10 Complete Structure of a Fuzzy Controller In the first step you must translate all sensor signals into linguistic variables For example you must translate a measured vehicle position x of 4 8 m to the linguistic value almost center just slightly left center This step is called fuzzification because it uses fuzzy sets to translate real variables into linguistic variables Once you translate all input variable values into their corresponding linguistic variable values use the fuzzy inference step to derive a conclusion from the rule base that represents the control strategy The step results in a linguistic value for the output variable For example the linguistic result for steering angle adjustment might be steering angle a little less than zero 4 12 ni com Chapter 4 Overview of Fuzzy Logic The defuzzification step translates the linguistic result back into a real value that represents the current value of the control variable Fuzzification Using Linguistic Variables For a more detailed look at the fuzzification process consider a maneuvering situation in which the vehicle position x is 5 1 m and the vehicle orientation B is 70 Left 1
88. ing PID Control Loops This application uses PID controllers to control single process parameters Usually human operators supervise the operating point of the entire process PID Control Toolkit User Manual Chapter 5 Fuzzy Controllers For automatic operation of such multivariable control problems you must build a model based controller But for most applications either the process is too complex to model adequately or the mathematical modeling task requires too much time With fuzzy controllers you can often use the experience and the knowledge gained by the supervising operators to form a linguistic rule base with much less effort Figure 5 4 shows the controller structure of the Fuzzy Controller with Underlying PID Control Loops BE Fuzzy Controller Process Set Point Reference Values Fule Bisg Magnitude Signals IF AND THEN e IF AND THEN ml PX D a ts a p PID PID PID Fuzzification Fuzzy Inference Defuzzification Measured Values PID Control Toolkit User Manual Figure 5 4 Fuzzy Controller with Underlying PID Control Loops The next example structure shows how to use a fuzzy controller to automatically tune the parameters of a conventional PID controller For this the fuzzy controller constantly interprets the process reaction and calculates the op
89. inguistic facts like left center or high fever First you must define a linguistic variable for each characteristic quantity of the maneuvering process For example vehicle position x and vehicle orientation B are process or input variables and steering angle is an output variable A linguistic variable consists of a number of linguistic terms that describe the different linguistic interpretations of the characteristic quantity you are modeling The appropriate membership function defines each linguistic term Figures 4 6 4 7 and 4 8 show membership functions for the inputs and output of the truck controller 4 8 ni com Chapter 4 Overview of Fuzzy Logic ux A Left 1 0 Left Right Center Center Center Right 0 8 0 6 0 4 0 2 0 0 gt 0 0 1 0 2 0 30 40 50 60 70 80 90 100 xim Vehicle Position u B LeftDown Figure 4 6 Linguistic Variable Vehicle Position x and Its Linguistic Terms U Left p Right Left Up Right Up Right Down 1 0 0 8 0 6 0 4 0 2 gt 0 0 100 50 0 0 50 100 150 200 250 pIe Vehicle Orientation National Instruments Corporation Figure 4 7 Linguistic Variable Vehicle Orientation B and Its Linguistic Terms 4 9 PID Control Toolkit User Manual
90. is to find the best compromise between the two different goals This compromise represents the best final conclusion received from the fuzzy inference process One of the two most common methods for calculating the best compromise is the Center of Area CoA method also called the Center of Gravity CoG method Following this defuzzification method truncate all membership functions that represent the conclusion terms at the degree of validity of the rule to which the conclusion term belongs The areas under the resulting function of all truncated terms make up the grey area of Figure 4 13 Find the geometric center of this area to determine the crisp compromise value National Instruments Corporation 4 17 PID Control Toolkit User Manual Chapter 4 Overview of Fuzzy Logic 1 0 ufo A Negative Negative Negative Positive Positive Positive Zero Large Medium Small Small Medium Large Validity of Rule 1 0 8 0 6 0 4 0 2 Validity of Rule 2 0 0 30 0 25 0 20 0 gt A 15 0 10 0 5 0 0 0 5 0 100 15 0 20 0 25 0 30 0 f Defuzzified Result 9 3 Steering Angle PID Control Toolkit User Manual Figure 4 13 Defuzzification According to Center of Area CoA The numerical integration necessary to calculate the center of area in this defu
91. kit User Manual Using the PID Software This chapter contains the basic information you need to begin using the PID Control VIs Designing a Control Strategy When you design a control strategy sketch a flowchart that includes the physical process and control elements such as valves and measurements Add feedback from the process and any required computations Then use the VIs in this Toolkit combined with the math and logic VIs and functions in LabVIEW to translate the flowchart into a block diagram Figure 3 1 is an example of a control flowchart and Figure 3 2 is the equivalent LabVIEW block diagram The only elements missing from this simplified VI are the loop tuning parameters and the automatic to manual switching Feedforward jo Surge Tank Figure 3 1 Control Flowchart National Instruments Corporation 3 1 PID Control Toolkit User Manual Chapter 3 Using the PID Software Setting Timing PID Control Toolkit User Manual Figure 3 2 LabVIEW Block Diagram You can handle the inputs and outputs through DAQ devices FieldPoint I O modules GPIB instruments or serial I O ports You can adjust polling rates in real time Potential polling rates are limited only by your hardware and by the number and graphical complexity of your VIs The PID and Lead Lag VIs in this Toolkit are time dependent A VI can acquire timing information either from a value you supply to the cycle time control dt or
92. ler implement the control strategy that you base on engineering experience with respect to a closed loop control application A fuzzy controller has a static and deterministic structure as shown in Figure 5 1 which you can describe with an I O characteristic curve ey e2 n E Rule Base IF AND THEN IF AND THEN IF AND THEN AH IF AND THEN Fuzzification Fuzzy Inference Defuzzification Figure 5 1 Internal Structure of a Fuzzy Controller In principle there are two different implementation forms With the first type of implementation the Offline Fuzzy Controller you transform the three step calculation scheme into a reference table from which you can derive the command values You can use interpolation to calculate National Instruments Corporation 5 1 PID Control Toolkit User Manual Chapter 5 Fuzzy Controllers intermediate command values In the second type of implementation the Online Fuzzy Controller you evaluate the three step calculation scheme online This is the standard implementation form of the Fuzzy Logic Controls Closed Loop Control Structures with Fuzzy Controllers There are many different ways to use fuzzy controllers in closed loop control applications The most basic structure uses the sensor signals from the process as input signals for the fuzzy controller and the output
93. lgorithms The PID Algorithm The PID controller compares the setpoint SP to the process variable PV to obtain the error e e SP PV Then the PID controller calculates the controller action u t where K is controller gain u t c erdp east If the error and the controller output have the same range 100 to 100 controller gain is the reciprocal of proportional band 7 is the integral time in minutes also called the reset time and T is the derivative time in minutes also called the rate time The following formula represents the proportional action u t Ke The following formula represents the integral action Kat u t eat The following formula represents the derivative action d up t Klee National Instruments Corporation 2 1 PID Control Toolkit User Manual Chapter 2 PID Algorithms Implementing the PID Algorithm with the PID VIs This section describes how the PID VIs implement the positional PID algorithm The subVIs used in these VIs are labelled so you can modify any of these features as necessary Error Calculation The following formula represents the current error used in calculating proportional integral and derivative action e k SP PV Proportional Action Proportional Action is the controller gain times the error as shown in the following formula up k K e k Trapezoidal Integration Trapezoidal Integration is used to avoid sharp changes in
94. lications you can use singleton membership functions to sufficiently model the output terms rather than using triangular or other membership function types Figure 5 12 shows that if all the conclusion terms are equal in width the overlapping degree of the membership functions for the conclusion terms has no significant influence on the controller characteristic National Instruments Corporation 5 15 PID Control Toolkit User Manual Chapter 5 Fuzzy Controllers 1 0 w x 0 8 0 6 0 4 0 2 0 0 Negative Zero Positive r 1 0 1 0 Negative Zero Positive Rule Base Rule 1 IF x Negative THEN y Negative Rule 2 IF x Zero THEN y Zero Rule 3 IF x Positive THEN y Positive Max Min Inference Modified CoA 4 0 8 0 6 0 4 0 2 0 0 0 2 0 4 0 6 0 8 1 0 0 8 0 6 0 4 0 2 0 0 0 2 0 4 0 6 x 0 8 1 0 Figure 5 12 1 0 Characteristics of a Fuzzy Controller Different Overlapping Degrees of Membership Functions for the Output Terms PID Control Toolkit User Manual 5 16 ni com Chapter 5 Fuzzy Controllers Instead use output terms that membership functions model with equally distributed typical values but different scopes of influence to significantly influence the controller characteristic The different
95. lling the process through experience Flow controller Control in which a measured variable is compared to its desired value to produce an actuating error signal that is acted upon in such a way as to reduce the magnitude of the error See closed loop The process of evaluating crisp controller input values process parameters using the defined membership functions to determine linguistic input variables for the rulebase evaluation The process by which the rules of the rulebase are evaluated to determine output linguistic variables for defuzzification PID Control Toolkit User Manual Glossary fuzzy set fuzzy set theory gain gain scheduling Instrument Society of America ISA integral action rate integral control action kHz PID Control Toolkit User Manual A set that allows for partial membership of elements Fuzzy sets usually represent linguistic terms and are defined quantitatively by a membership function An extension of traditional Boolean set theory fuzzy set theory is based on the idea that fuzzy sets may be defined such that elements can have partial membership to the set For a linear system or element the ratio of the magnitude amplitude of a steady state sinusoidal output relative to the causal input the length of a phasor from the origin to a point of the transfer locus in a complex plane Also called the magnitude ratio The process of applying different controller gains for differe
96. n affect the signal Figure 8 2 shows some typical voltage drop curves derived from an asymmetric triangle a lefthand shaped triangle National Instruments Corporation 8 1 PID Control Toolkit User Manual Chapter 8 Implementing a Fuzzy Controller U V 9 5 LDR 9 0 8 5 8 0 7 5 15 30 45 60 75 90 105 120 1 Tstep Figure 8 2 Typical Voltage Drop Curves Obtained from a Lefthand Shaped Triangle To obtain a simple but efficient controller abstract the curves shown in Figure 8 2 into the idealized curve outline that is shown in Figure 8 3 PID Control Toolkit User Manual 10 0 genes 8 0 Signal x t Flipped 5 4 Input 6 0 Signal xf t 407 ae an oi ae ade S 0 0 Le Sm a 2 0 4 4 0 5 6 04 he ru 1 8 0 5 160 50 00 com 20 00 i I I I 0 is a0 30 40 Me 0 70 gi a 100 t Tstep gt Figure 8 3 Abstract Voltage Drop Curve for Feature Extraction There are three distinguishable parts of the flipped input signal represented by the dashed curve x t in Figure 8 3 There is a rising curve part a constant part and a falling curve part Differentiation of the flipped input signal yields the dash dotted curve dx t dt from which you can derive the 8 2 ni com Chapter 8 Implementing a Fuzzy Controller time intervals TU up TH hold and TD down When TS signal r
97. n use to adjust the pattern recognition application example Figure 8 9 shows the front panel of the example 8 6 ni com Chapter 8 Implementing a Fuzzy Controller I Pattern Recognition Example File Edit Operate Project Windows Help 15pt Application Font x Fo x te F seo 1 1 1 7 20 30 70 scale xss TU amo 354 input signal def so 380 TD A O a gt i 40 TH a ai Se j 1 j 1 if 50 60 70 80 90 100 7g oo 10 20 30 40 50 sooo 1 00 TH TS Piece Type 0 198 Triangle left STOP Figure 8 9 Front Panel of the Pattern Recognition Application You can use the input signal def sliders to simulate the signal from the reflex light barrier of the real system You also can modify the signal max and signal min sliders to use them to test how the fuzzy controller works despite having a signal with a very small amplitude The scale xss slider models a gain factor towards the signal that the data pre processing step performs You also can use the slider to study how different signal conditions can affect the result of the pattern recognition process Fuzzy Controller Implementation Now incorporate the fuzzy controller into the application block diagram You do not need to program the fuzzy controller just use the pre defined Fuzzy Controller VI available with the Fuzzy Logic Controls shown in Figure 8 10 The pre defined Fuzzy Controller VI can be connected with as many as four input
98. nd outputs one set of PID gains from a gain schedule based on the current value of the gain scheduling value input For example to implement a gain schedule based on the value of the process variable wire the process variable value to the gain scheduling value input and wire the PID gains out output to the PID gains input of the PID VI The PID gain schedule input is an array of clusters of PID gains and corresponding max values Each set of PID gains corresponds to the range of input values from the max value of the previous element of the array to the max value of the same element of the array The input range of the PID gains of the first element of the PID gain schedule is all values less than or equal to the corresponding max value In Figure 3 9 the Gain Schedule Example uses the setpoint value as the gain scheduling variable with a default range of 0 to 100 Table 3 3 summarizes PID parameters National Instruments Corporation 3 11 PID Control Toolkit User Manual Chapter3 Using the PID Software jef 100 00 Figure 3 9 Gain Scheduling Input Example Table 3 3 PID Parameter Ranges Range Parameters 0 lt SP lt 30 Ke 10 Ti 0 02 Td 0 02 30 lt SP lt 70 Kc 12 Ti 0 02 Td 0 01 70 lt SP lt 100 Kc 15 Ti 0 02 Td 0 005 Control Output Rate Limiting Sudden changes in control output are often undesirable or even dangerous for many control applications For example a sudden lar
99. ndefined Input Term Interval for more information about input variables The design work for the example project is complete It is time to save the project and see what documentation features are available for the Fuzzy Logic Controls Documenting Fuzzy Control Projects Test Facilities The File Print submenu offers documentation facilities for printing information about the active project Select Print Complete Documentation to print the complete controller documentation for the example project Before you run a fuzzy controller within a designated system environment study the I O characteristics of the controller within the Toolkit You can use these characteristics to optimize the fuzzy controller and make any necessary modifications The Fuzzy Logic Controls provide an appropriate test environment Select Test I O Characteristics to call the test facility to perform the I O characteristic studies of a fuzzy controller National Instruments Corporation 7 15 PID Control Toolkit User Manual Chapter 7 Using the Fuzzy Logic Controller Design VI For the application example FuzzyTruck previously loaded the 1 O Characteristic test facility starts with a front panel similar to the one shown in Figure 7 12 tb Input Output Characteristic vehicle position vehicle orientation _ gt 0 0 10 0 90 0 min to max steering angle max to min ae Print on No Points 10 0 20 0 0 10 0 K 20 0
100. nges until the oscillation is sustained neither growing nor decaying over time 3 Record the controller proportional band PB as a percent where PB 100 K 4 Record the period of oscillation 7 in minutes 5 Multiply the measured values by the factors shown in Table 3 1 and enter the new tuning parameters into your controller Table 3 1 provides the proper values for a quarter decay ratio If you want less overshoot increase the gain K Table 3 1 Closed Loop Quarter Decay Ratio Values 3 PID Control Toolkit User Manual PB Reset Rate Controller percent minutes minutes P 2 00PB PI 2 22PB 0 83T PID 1 67PB 0 507TT 0 125T 3 4 Note Proportional gain K is related to proportional band PB as K 100 PB ni com Chapter 3 Using the PID Software Open Loop Step Test Tuning Procedure The open loop step test tuning procedure assumes that you can model any process as a first order lag and a pure deadtime This method requires more analysis than the closed loop tuning procedure but your process does not need to reach sustained oscillation Therefore the open loop tuning procedure might be quicker and more reliable for many processes Observe the output and the PV on a strip chart that shows time on the x axis Complete the following steps to perform the open loop tuning procedure 1 Put the controller in manual mode set the output to a nominal o
101. ni com Chapter 5 Fuzzy Controllers When you use the MoM defuzzification method you calculate the most plausible result In other words the typical value of the conclusion term of the most valid rule is taken as a crisp output value which results in stepped output characteristics as shown in Figure 5 14 Negative Zero Positive Negative Zero Positive i 1 0 i 1 0 uo 08 uy 28 0 6 0 6 0 4 0 4 0 2 0 2 0 0 0 0 1 0 0 5 0 0 0 5 1 0 1 0 0 5 0 0 0 5 1 0 x gt y gt Max Min Rule Rule 1 IF x Negative THEN y Negative Inference Base Rule 2 IF x Zero THEN y Zero Rule 3 IF x Positive THEN y Positive Mean of Maximum 1 0 t 0 8 0 6 0 4 lt 0 2 0 0 1 0 0 8 0 6 0 4 0 2 0 0 0 2 0 4 0 6 0 8 1 0 x gt Figure 5 14 1 0 Characteristic of a Fuzzy Controller with Mean of Maximum Entirely Overlapping Membership Functions for Input and Output Terms National Instruments Corporation 5 19 PID Control Toolkit User Manual Chapter 5 Fuzzy Controllers PID Control Toolkit User Manual The rule base itself has the biggest influence on the controller characteristic The rule base determines the principal functionality of the controller Figure 5 15 illustrates how the controller characteristic changes if you chang
102. nput situation of the system will cause a switch to another more plausible result Refer to Table 6 1 for a comparison of different fuzzification methods Table 6 1 Comparison of Different Defuzzification Methods Method Assessment B aa Criteria if Center of Area Center of Maximum Mean of Maximum CoA CoM MoM Linguistic Best Compromise Best Compromise Most Plausible Result Characteristic Fit with Implausible with Good Good Intuition varying membership function shapes and strong overlapping membership functions Continuity Yes Yes No Computational Very High Low Very Low Effort Application Closed loop Control Closed loop Control Pattern Recognition Field Decision Support Decision Support Decision Support Data Analysis Data Analysis Data Analysis National Instruments Corporation 6 9 PID Control Toolkit User Manual Using the Fuzzy Logic Controller Design VI This chapter describes how to use the Fuzzy Logic Controller Design VI to design a fuzzy controller This VI is available by launching LabVIEW and selecting Tools Control Design and Simulation Fuzzy Logic Controller Design Overview The Fuzzy Logic Controller Design VI consists of the following parts e Project Manager Maintains a fuzzy logic project e Fuzzy Set Editor Defines and modifies linguistic variables including their linguistic terms e Rule Base Editor Defines and modifies the rule base of a
103. nt regions of operation of a controller Gain scheduling is most often used in controlling nonlinear physical processes Hertz Cycles per second The organization that sets standards for process control instrumentation in the United States See reset rate Control action in which the output is proportional to the time integral of the input That is the rate of change of output is proportional to the input Process gain Controller gain Kilohertz G 4 ni com L lag linearity factor linguistic term linguistic variable load disturbance loop cycle time magnitude ratio manipulated variable Max Min inference MB Mean of Maximum MoM National Instruments Corporation G 5 Glossary A lowpass filter or integrating response with respect to time A value ranging from 0 to 1 used to specify the linearity of a calculation A value of indicates a linear operation A value of 1 indicates a squared nonlinear operation A word or set of words to describe a quality of a process variable for example hot very low small positive and so on The term is defined quantitatively by the corresponding membership function Defines the state of a process variable by the degree of membership of the parameter to each linguistic term defined for example vehicle position left 0 0 left center 0 0 center 0 8 right center 0 1 right 0 0 The ability of a controller to compensate for changes in physical p
104. ntroller There is another predefined VI available with the Fuzzy Logic Controls that you can use to build or test fuzzy control applications The Test Fuzzy Control VI supplies a fuzzy control test and application environment for as many as four different controller inputs Input assignment is set automatically according to the data being loaded into the controller This VI was created to show the proper use of all input and output signals supplied by the Load Fuzzy Controller VI and the Fuzzy Controller VI Figure 8 15 shows the Test Fuzzy Control VI front panel gt Test Fuzzy Control vi Figure 8 15 Test Fuzzy Control VI Front Panel The controller displays the fuzzy controller project identifier as soon as you load the fuzzy controller data file The input name displays the identifiers of all used inputs The minimum and maximum display the appropriate currently valid data range for each used input variable You can use input value to enter input values to stimulate the controller The controller out displays the output value The lower data range values automatically initialize the corresponding input value National Instruments Corporation 8 13 PID Control Toolkit User Manual Chapter 8 Implementing a Fuzzy Controller Figure 8 16 shows the application front panel immediately after loading the fuzzy controller data file for the pattern recognition example b gt Test Fuzzy Control vi Figure 8 16 Test Fuzzy C
105. o THEN y Zero Rule 3 IF x Positive THEN y Positive Modified CoA 2 rf T Rule1 Rules 1 and Rule 2 Rules2and Rule3 0 8 active 2 Active Active i 3 Active Active Ea gt lt gt lt gt lt i lt Pe 1 0 0 8 0 6 0 4 0 2 0 0 0 2 0 4 0 6 0 8 1 0 x gt Figure 5 7 1 0 Characteristic of a Fuzzy Controller Partially Overlapping Input Terms The resulting controller characteristic shows nonlinear behavior You obtain different intervals within the controller characteristic because the input terms partially overlap There is only one valid rule outside of the overlapping regions so the output has a constant value determined by the National Instruments Corporation 5 7 PID Control Toolkit User Manual Chapter 5 Fuzzy Controllers output term of the output variable which is independent of the degree of truth for that rule The overlapping sections of the antecedence terms lead to the rising intervals of the controller characteristic Within these parts two rules are simultaneously active The different conclusion terms weighted by the degree of truth of the different active rules determine the output value Notice that the overlapping triangular conclusion terms cause the rising edges of the controller characteristic to be nonlinear Figure 5 8 shows the resulting controller characteristic for antecedence terms that overl
106. ocess Overview Acquiring Knowledge Optimizing Offline The knowledge base of a fuzzy controller determines its I O characteristics and thus the dynamic behavior of the complete closed loop control circuit The knowledge base consists of the following parts e Linguistic terms defined by membership functions that describe the input and output quantities of the controller e Rule base that contains engineering knowledge e Operators for both the AND and OR operations e Fuzzy inference method and defuzzification method Within the first system design step you must establish all of the linguistic variables and terms for the given application as the vocabulary of the rule based system Use the rule base to formulate the control strategy then select an appropriate defuzzification method Within this design step you should test the prototype controller and simulate it with either real process data previously recorded from the process or simulation data obtained from a mathematical process model You can perform transfer characteristics analysis and time response analysis to observe the system behavior and optimize the controller LabVIEW supports both types of analysis In this step you also can use Neuro Fuzzy techniques as well as Genetic or Evolutionary Algorithms to optimize your system National Instruments Corporation 6 1 PID Control Toolkit User Manual Chapter 6 Design Methodology Optimizing Online Implementing Wi
107. ognition applications you must apply the Mean of Maximum MoM defuzzification method This defuzzification method calculates the most plausible result Rather than averaging the different inference results MoM selects the typical value of the most valid output term National Instruments Corporation 4 21 PID Control Toolkit User Manual Chapter 4 Overview of Fuzzy Logic In the example situation the output term negative small is the most valid term Refer to Figures 4 13 and 4 14 for more information The typical value of the term is negative small 5 which is the immediate defuzzification result If you want to classify a sensor signal to identify objects for example you are interested in the most plausible result In decision support systems the choice of the defuzzification method depends on the context of the decision you want to calculate with the fuzzy system For quantitative decisions like project prioritization apply the CoM method For qualitative decisions such as an evaluation of credit worthiness MoM is the correct method PID Control Toolkit User Manual 4 22 ni com Fuzzy Controllers This chapter describes various implementations and I O characteristics of fuzzy controllers Structure of a Fuzzy Controller A fuzzy controller is composed of the following three calculation steps fuzzification fuzzy inference and defuzzification Linguistic rules integrated into the rule base of the control
108. oject When LabVIEW prompts you to enter a file name type in FuzzyTruck as the project name Notice that fuzzy controller project files always have the extension fc Use File Open to load an existing project that has not yet been loaded Immediately after the Project Manager loads a project select Edit Set Editor to call the Fuzzy Set Editor Now the input and output variables have the correct names and data ranges The three entirely overlapping default terms NE1 ZE1 and PO1 still set up the input variable vehicle position Because vehicle position must be composed of the five linguistic terms shown in Figure 4 6 Linguistic Variable Vehicle Position x and Its Linguistic Terms you must add two new linguistic terms Refer to the Rule Based Systems section in Chapter 4 Overview of Fuzzy Logic for more information about linguistic variables and linguistic terms All linguistic terms must have the same names and shapes so that the complete term arrangement corresponds to that in Figure 4 6 Select define add term after to add a new linguistic term between the terms NE1 and ZE1 The term identifier of the referred term with a symbol added to its right side composes the new term identifier 7 8 ni com Chapter 7 Using the Fuzzy Logic Controller Design VI NEI is the term identifier of the active term and the new term is NE1 as shown in Figure 7 7 Notice that the new term becomes the active term and you can modify it immediately
109. on 4 5 PID Control Toolkit User Manual Chapter 4 Overview of Fuzzy Logic Rule Based Systems Another basic fuzzy logic concept involves rule based decision making processes You do not always need a detailed and precise mathematical description to optimize operation of an engineering process In other words human operators are often capable of managing complex plant situations without knowing anything about differential equations Their engineering knowledge is perhaps available in a linguistic form such as if the liquid temperature is correct and the pH value is too high adjust the water feed to a higher level Because of fully developed nonlinearities distributed parameters and time constants that are difficult to determine it is often impossible for a control engineer to develop a mathematical system model Fuzzy logic uses linguistic representation of engineering knowledge to implement a control strategy Suppose you must automate the maneuvering process that leads a truck from an arbitrary starting point to a loading ramp The truck should run at a constant low speed and stop immediately when it docks at the loading ramp A human driver is capable of controlling the truck by constantly evaluating the current drive situation mainly defined by the distance from the target position and the orientation of the truck to derive the correct steering angle This is shown in Figure 4 4
110. on gt THEN lt action gt to define a control strategy The above rule format describes the necessary reaction or conclusion to a certain situation or condition National Instruments Corporation 4 7 PID Control Toolkit User Manual Chapter 4 PID Control Toolkit User Manual Overview of Fuzzy Logic An expert driver could tell you the rules of thumb he uses to maneuver the vehicle to the target position Then you can describe those rules with IF THEN rules IF vehicle position x is left center AND vehicle orientation B is left up THEN adjust steering angle to positive small or IF vehicle position x is center AND vehicle orientation B is left up THEN adjust steering angle to negative small or IF vehicle position x is left center AND vehicle orientation B is up THEN adjust steering angle to positive medium or IF vehicle position x is center AND vehicle orientation B is up THEN adjust steering angle to zero Note Uncertain linguistic terms like left center left up and so on compose the conditions of each rule Even the conclusion of each rule contains vague and imprecise facts such as negative small Because there are no precise definitions of the words used in the rules above there is no way to use a text based programming language to directly implement the rules with IF THEN statements You can use fuzzy logic to implement a linguistic control strategy that is capable of using fuzzy sets to model uncertain l
111. onal Instruments Corporation ll 1 PID Control Toolkit User Manual Overview of Fuzzy Logic This chapter introduces fuzzy set theory and provides an overview of fuzzy logic control What is Fuzzy Logic Fuzzy logic is a method of rule based decision making used for expert systems and process control that emulates the rule of thumb thought process human beings use Lotfi Zadeh developed fuzzy set theory the basis of fuzzy logic in the 1960s Fuzzy set theory differs from traditional Boolean set theory in that fuzzy set theory allows for partial membership in a Set Traditional Boolean set theory is two valued in the sense that a member either belongs to a set or does not which is represented by a one or zero respectively Fuzzy set theory allows for partial membership or a degree of membership which might be any value along the continuum of zero to one You can use a a type of fuzzy set called a membership function to quantitatively define a linguistic term A membership function specifically defines degrees of membership based on a property such as temperature or pressure With membership functions defined for controller or expert system inputs and outputs you can formulate a rule base of IF THEN type conditional rules Then with fuzzy logic inference you can use the rule base and corresponding membership functions to analyze controller inputs and determine controller outputs After you define a fuzzy controller you can qu
112. ontrol VI Front Panel with Controller Data Loaded Remember that if there is an input situation not covered by active rules a fuzzy controller uses default values The output assessment displays a message to indicate such a situation PID Control Toolkit User Manual 8 14 ni com Chapter 8 Implementing a Fuzzy Controller If input values exceed the data range assigned to the related input variable the error ring displays an error message and the output value is set to the default output value as shown in Figure 8 17 b gt Test Fuzzy Control vi Figure 8 17 Test Fuzzy Control VI Front Panel with Incorrect Input Value for Input 1 National Instruments Corporation 8 15 PID Control Toolkit User Manual Chapter 8 Implementing a Fuzzy Controller Figure 8 18 shows the proper use of all input and output signals supplied by the Load Fuzzy Controller VI and the Fuzzy Controller VI You can use this program structure as a basis for building your own fuzzy logic applications Test Fuzzy Control vi Diagram Windows Help minimums gt Description Info Controller Name ferror ting l DEL controller out input value 11 8 input value 2 input value 3 input value 4 OBL Figure 8 18 Test Fuzzy Control VI Block Diagram Example ay Note You can connect the inputs and the controller output directly to the outputs and inputs of the DAQ VIs available in Lab VIEW in order to use real process data from senso
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114. ou configure it for multiple channels You can wire this array directly into the process variable input of the PID VI The polymorphic type of the PID VI automatically switches from DBL to DBL Array which calculates and returns an array of output values corresponding to the number of values in the process variable array Note that you also can switch the type of the polymorphic VI manually by right clicking the VI icon and selecting Select Type from the shortcut menu When the polymorphic type is set to DBL Array other inputs change automatically to array inputs as well For example the PID VI inputs setpoint PID gains and output range all become array inputs Each of these inputs can have an array length ranging from to the array length of the process variable input If the array length of any of these inputs is less than the array length of the process variable input the PID VI reuses the last value in the array for other calculations For example if you specify only one set of PID gains in the PID gains array the PID VI uses these gains to calculate each output value corresponding to each process variable input value Other polymorphic VIs included with the PID Control Toolkit operate in the same manner 3 8 ni com Chapter 3 Using the PID Software Setpoint Ramp Generation The PID Setpoint Profile VI located on the PID palette can generate a profile of setpoint values over time for a ramp and soak type PID application For
115. p number of terms for each input variable k m number of input variables For example for three input variables with five terms each the total number of possible rules is 125 The complete rule base for five input variables with seven terms each totals 16 807 rules Notice that for systems with numerous controller inputs you can use cascading fuzzy controllers to avoid large rule bases Outputs from fuzzy controllers serve as the inputs to the next layer of fuzzy controllers PID Control Toolkit User Manual 6 6 ni com Chapter 6 Design Methodology In the case of a fuzzy controller with m input variables each with an individual number of terms p with 1 lt i lt m there are a total of N possible rules according to m p number of terms for input variable i N l l Pi m number of input variables i l This great degree of freedom allows a lot of design flexibility However it is very difficult to implement the complete rule base in large and complex systems In such cases you usually only implement the rules that cover the normal system operation Note A fuzzy controller with an incomplete rule base must have a default action value which is usually the last command value for input situations with no active rule A rule base with at least one active rule for each possible combination of crisp input values is called a complete rule base Because there are overlapping regions of the membership functions an undefined
116. parameters PID Algorithm PID Control Toolkit User Manual Error Calculation The following formula represents the current error used in calculating proportional integral and derivative action SP PY e k SP PY L 1 L 54 range The error for calculating proportional action is shown in the following formula eb k B SP PV L 1 _ ye PSZ range where SP ange is the range of the setpoint B is the setpoint factor for the Two Degree of Freedom PID algorithm described in the Proportional Action section of this chapter and L is the linearity factor that produces a nonlinear gain term in which the controller gain increases with the magnitude of the error If L is 1 the controller is linear A value of 0 1 makes the minimum gain of the controller 10 K Use of a nonlinear gain term is referred to as an Error squared PID algorithm 2 4 ni com Chapter 2 PID Algorithms Proportional Action In applications SP changes are usually larger and faster than load disturbances while load disturbances appear as a slow departure of the controlled variable from the SP PID tuning for good load disturbance responses often results in SP responses with unacceptable oscillation However tuning for good SP responses often yields sluggish load disturbance responses The factor B when set to less than one reduces the SP response overshoot without affecting the load disturbance response indicating the use of a Two Degree o
117. perating value and allow the PV to settle completely Record the PV and output values 2 Make a step change in the output Record the new output value Wait for the PV to settle From the chart determine the values as derived from the sample displayed in Figure 3 4 The variables represent the following values e T Deadtime in minutes e T fTime constant in minutes e K Process gain change in PV change in output 63 2 Max Min PV Min Output ot Td e lt T gt Figure 3 4 Output and Process Variable Strip Chart 4 Multiply the measured values by the factors shown in Table 3 2 and enter the new tuning parameters into your controller The table provides the proper values for a quarter decay ratio If you want less overshoot reduce the gain K National Instruments Corporation 3 5 PID Control Toolkit User Manual Chapter 3 Using the PID Software Table 3 2 Open Loop Quarter Decay Ratio Values PB Reset Rate Controller percent minutes minutes P 1002 T a KT PI 110 3 337 T KT PID 80 2 00T 0 507 Using the PID VIs The PID VI PID Control Toolkit User Manual Although there are several variations of the PID VI they all use the algorithms described in Chapter 2 PID Algorithms The PID VI implements the basic PID algorithm Other variations provide additional functionality as described in the following sections
118. r you want to control such as temperature pressure or flow rate and the setpoint is the desired value for the parameter you are controlling A PID controller determines a controller output value such as the heater power or valve position The controller applies the controller output value to the system which in turn drives the process variable toward the setpoint value You can use the PID Control Toolkit VIs with National Instruments hardware to develop LabVIEW control applications Use I O hardware like a DAQ device FieldPoint I O modules or a GPIB board to connect your PC to the system you want to control You can use the I O VIs provided in LabVIEW with the PID Control Toolkit to develop a control application or modify the examples provided with the Toolkit Using the VIs described in the PID Control section of the manual you can develop the following control applications based on PID controllers e Proportional P proportional integral PI proportional derivative PD and proportional integral derivative PID algorithms e Gain scheduled PID e PID autotuning e Error squared PID e Lead Lag compensation e Setpoint profile generation National Instruments Corporation 1 1 PID Control Toolkit User Manual Chapter 1 Overview of the PID Control Toolkit Fuzzy Logic e Multiloop cascade control e Feedforward control e Override minimum maximum selector control e Ratio bias control You can combine these P
119. roduce stable control of the system You can develop the control application using either the PID VI the PID Gain Schedule VI or the PID with Autotuning VI Because the PID with Autotuning VI has input and output consistent with the other PID VIs you can replace any PID VI with it The PID with Autotuning VI has several additional input and output values to specify the autotuning procedure The two additional input values are autotuning parameters and autotune autotuning parameters is a cluster of parameters that the VI uses for the autotuning process Because the Autotuning Wizard allows you to specify all of these parameters manually you can leave the autotuning parameters input unwired The autotune input takes a Boolean value supplied by a user control Wire a Boolean control on the front panel of your application to this input When the user presses the Boolean control the Autotuning Wizard opens automatically Set the Boolean control mechanical action to Latch When Released so that the Autotuning Wizard does not open repeatedly when the user presses the control The Autotuning Wizard steps the user through the autotuning process Refer to Chapter 2 PID Algorithms for more 3 14 ni com Chapter 3 Using the PID Software information about the autotuning algorithm The PID with Autotuning VI also has two additional output values tuning completed and PID gains out The tuning completed output is a Boolean value It is usually FALSE an
120. rs a survey Control Engineering Practice 1 669 714 Corripio A B 1990 Tuning of industrial control systems Raleigh North Carolina ISA Kahlert J and Frank H Fuzzy Logik und Fuzzy Control Braunschweig Wiesbaden Vieweg 1993 Kahlert J and Frank H Fuzzy Control fuer Ingeniere Braunschweig Wiesbaden Vieweg 1995 Shinskey F G 1988 Process control systems New York McGraw Hill National Instruments Corporation A 1 PID Control Toolkit User Manual Appendix A References Yen J R Langari and L Zadeh eds Industrial Applications of Fuzzy Logic and Intelligent System Piscataway NJ IEEE Press 1995 Ziegler J G and N B Nichols 1942 Optimum settings for automatic controllers Trans ASME 64 759 68 Zimmerman H J Fuzzy Set Theory and Its Applications Second Revised Edition Boston MA Kluwer Academic Publishers 1991 Zimmerman H J Fuzzy Sets Decision Making and Expert Systems Boston Dordrecht London Kluwer Academic Publishers 1987 PID Control Toolkit User Manual A 2 ni com Technical Support and Professional Services Visit the following sections of the National Instruments Web site at ni com for technical support and professional services Support Online technical support resources at ni com support include the following Self Help Resources For answers and solutions visit the award winning National Instruments Web site for software drivers and updates a sear
121. rs instead of the values from the panel controls as shown in Figures 8 16 and 8 17 PID Control Toolkit User Manual 8 16 ni com References This appendix lists the reference material used to produce the VIs in this manual These references contain more information on the theory and algorithms implemented in the fuzzy logic VIs The Instrument Society of America ISA the organization that sets standards for process control instrumentation in the United States offers a catalog of books journals and training materials to teach you the basics of process control programming One particular course Single and Multiloop Control Strategies course number T510 is very helpful Contact the ISA at its Raleigh N C headquarters at 919 549 8411 Corripio 1990 is an ISA Independent Learning Module book It is organized as a self study program covering measurement and control techniques selection of controllers and advanced control techniques Tuning procedures are detailed and yet easily understandable Shinskey 1988 is an outstanding general text covering the application design and tuning of all common control strategies It contains all of the basic algorithms used in the PID control VIs Astr m K J and T Hagglund 1984 Automatic tuning of simple regulators In Proceedings of IFAC 9th World Congress Budapest 1867 72 Astrom K J T Hagglund C C Hang and W K Ho 1993 Automatic tuning and adaption for PID controlle
122. s as command values to drive the actuators of the process A corresponding control loop structure is shown in Figure 5 2 Fuzzy Controller Process 7 Point Command alues ren Variables IF AND THEN IF AND THEN IF AND THEN N Fuzzification Fuzzy Inference Defuzzification i Measured Values PID Control Toolkit User Manual Figure 5 2 Simple Closed Loop Control Structure with Fuzzy Controller Pure fuzzy control applications are more the exception than the rule In most cases the fuzzy controller output serves as reference parameters such as gains that you provide to a conventional controller instead of to driving actuators in the process directly Because you can regard a fuzzy controller as a nonlinear characteristic field controller it has no internal dynamic aspects Thus any dynamic property must be implemented by an appropriate preprocessing of the measured input data 5 2 ni com Chapter 5 Fuzzy Controllers The Fuzzy PI Controller shown in Figure 5 3 uses the error signal e t and its derivative de t dt from the measured data preprocessing step as inputs If the output signal describes the necessary difference toward the current output value you need a subsequent integrator device to build up the command variable value Fuzzy Controller Process Set Point
123. s derivative rate control action For a linear process the ratio of the magnitudes of the measured process response to that of the manipulated variable The measured variable such as pressure or temperature in a process to be controlled Control response in which the output is proportional to the input The change in input required to produce a full range change in output due to proportional control action PB 100 K The response of a proportional controller to a step change in the setpoint or process variable Pounds per square inch A response in which the amplitude of each oscillation is one quarter that of the previous oscillation The total transient plus steady state time response resulting from a sudden increase in the rate of change from zero to some finite value of the input stimulus Also called ramp response Control response to the time rate of change of a variable Also called derivative control action Mode in which calls to multiple instances of a subVI can execute in parallel with distinct and separate data storage PID Control Toolkit User Manual Glossary reset rate reverse acting increase decrease controller RPM rule rule base selector control setpoint SP singleton span stochastic uncertainty PID Control Toolkit User Manual Of proportional plus integral or proportional plus integral plus derivative control action devices for a step input the ratio of the ini
124. sired pattern Figure 7 8 shows an intermediate state and Figure 7 9 shows the final result of this renaming process 3 Note You also can use the specify menu to add or remove linguistic variables E Rename Ling Term Identifiers New Ling Term Identifier Select identifier to be renamed Type in new identifier and click OK left center left center Figure 7 8 Rename Term Dialog Box PID Control Toolkit User Manual 7 10 ni com Chapter 7 Using the Fuzzy Logic Controller Design VI 3 Fuzzy Set Editor vehicle position z e specify lt ling variables ANTECEDENCE define left lt ling terms edit left left center center right center right v v iv Ws AA AA Ws Ws left bottom left top right top right bottom A 0 00 g 0 00 0 00 5 00 amp J Figure 7 9 All Vehicle Position Terms Named Correctly The Fuzzy Set Editor offers many functions that you can use to modify single terms or the whole term arrangement of the active variable It is a good idea to experiment with this function at this point in your project because you must modify the whole term arrangement according to the desired term arrangement shown in Figure 4 6 Linguistic Variable Vehicle Position x and Its Linguistic Terms Figure 7 10 shows the term arrangement you obtain when you select edit full term overlap all which results in a term arrangement with all terms of the active linguistic v
125. splay shows all active rules within the input situation determined by the cursor position including the degree of truth for each antecedence term You can select each active rule by clicking the pull down arrow to the right of the Active Rules display Click the Print button to print out the current situation for documentation purposes 7 18 ni com Implementing a Fuzzy Controller This chapter describes how to implement a fuzzy controller and includes a pattern recognition application example There are several different ways to use the Fuzzy Logic VIs to implement a fuzzy controller The easiest implementation uses the Fuzzy Controller VI Pattern Recognition Application Example Suppose you need to develop and implement a fuzzy controller that identifies the shape of different sized triangular hexagonal and rectangular plastic parts moving on a conveyor belt through a simple reflex light barrier as shown in Figure 8 1 Reflex Light Barrier Conveyor Belt 4o m Figure 8 1 Sensor Facility Moving Direction The plastic parts can be symmetric or asymmetric The reflex light barrier reads a characteristic voltage signal for each plastic part The signal depends on the resistances set up on the light barrier Measuring these signals with a real sensor shows that even the signals of identical plastic parts vary to a certain extent Different environmental conditions such as scattered light ca
126. terms have different areas and thus different weights with respect to the defuzzification process A wide output term has more influence on the inference result than a small neighboring output term This effect is demonstrated in Figure 5 13 National Instruments Corporation 5 17 PID Control Toolkit User Manual Chapter 5 Fuzzy Controllers f u x 0 8 0 6 0 4 0 2 0 0 Negative Zero Positive 0 A 1 0 Negative Zero Positive 0 5 0 0 y gt 0 5 1 0 Rule Base Rule 1 IF x Negative THEN y Negative Rule 2 IF x Zero THEN y Zero Rule 3 IF x Positive THEN y Positive Max Min Inference Modified CoA 1 0 0 8 0 6 0 4 0 2 0 0 0 2 0 4 0 6 0 8 1 0 1 0 0 8 0 6 0 4 0 2 0 0 0 2 0 4 0 6 X 08 1 0 ob Figure 5 13 1 0 Characteristics of a Fuzzy Controller Wide and Small Membership Functions for the Output Terms Using CoA or CoM as the defuzzification method results in continuous controller characteristic functions especially within those intervals of the input values in which two or more rules are active simultaneously This is because of the averaging character of the defuzzification methods described in Chapter 4 Overview of Fuzzy Logic PID Control Toolkit User Manual 5 18
127. th the data acquisition capabilities of LabVIEW you can run the fuzzy controller in conjunction with a process Then you can use online optimization techniques to make modifications to the running system Although you can use the fuzzy controller directly with LabVIEW real time performance constraints might make it necessary to download the fuzzy controller to a fast microcontroller board Defining Linguistic Variables The sensors and actuators of the system to be automated determine the input and output quantities of a fuzzy controller Each additional quantity you measure provides more information about the current process state However although additional sensors can improve accuracy they also can increase cost Fuzzy systems do not require high precision measurement equipment In fact using inexpensive lower precision sensors to obtain many values is better than using expensive higher precision sensors to acquire less data If measuring exact process quantities is too difficult secondary quantities that reveal less specific process information might be sufficient Number of Linguistic Terms PID Control Toolkit User Manual The possible values of a linguistic variable are the linguistic terms which are linguistic interpretations of technical quantities For example the quantity vehicle position x which is usually called the base variable and is measured in meters can have the linguistic interpretations left left center
128. the application front panel to the front 3 Start the application to open the input file dialog box that requests a fuzzy controller data file 4 Select the desired fuzzy controller data file Stop the application 6 Bring the front panel of the Fuzzy Controller VI to the front National Instruments Corporation 8 11 PID Control Toolkit User Manual Chapter 8 Implementing a Fuzzy Controller 9 Select Operate make current values default to make the currently valid controller data the default Choose one of two options Save a copy of the Fuzzy Controller VI if you want it to be available under a unique name Select No when asked to save the original Fuzzy Controller VI Or you can save the original Fuzzy Controller VI which now has the current controller data as default values Only the default values of the original Fuzzy Controller VI have been changed You can still use the VI as a general purpose Fuzzy Controller VI because the VI only uses the default values when you apply the controller without loading specific data into the VI Close the application Now you can use either the new VI or the modified one as a stand alone fuzzy controller as shown in Figure 8 14 PID Control Toolkit User Manual Fuzzy Controller Vl with a data set file being made default Figure 8 14 Application Block Diagram with Stand alone Fuzzy Controller VI 8 12 ni com Chapter 8 Implementing a Fuzzy Controller Testing the Fuzzy Co
129. the default data See the block diagram of the complete pattern recognition application shown in Figure 8 11 Because of security aspects that can occur when running a controller within a real application environment if someone selects the Cancel button the controller should not start To improve your controller design place the While Loop into a Case Structure and connect the selection terminal to the cancel output of the Load Fuzzy Controller VI Figure 8 13 shows the result The TRUE case is empty and the application quits if you click Cancel PID Control Toolkit User Manual 8 10 ni com Chapter 8 Implementing a Fuzzy Controller 2 3 lek J ad BA 3 o x lt signal E ag ae 5 O a f 2 H a Figure 8 13 Improved Controller Application Block Diagram The complete pattern recognition application example also is available within the Fuzzy Logic Controls Saving Controller Data with the Fuzzy Controller You might want to use a fuzzy controller like a predefined VI that you do not have to load to run You might wonder how the currently valid controller data file can be the default for the controller so you can use it as a stand alone controller Complete these steps to build a stand alone Fuzzy Controller VI for the pattern recognition application example 1 Bring the application block diagram to the front and double click the icon of the Fuzzy Controller VI to open the VI 2 Bring
130. the fuzzy membership functions and controller rule base The Controller Design VI is a stand alone VI with a user interface you can use to completely define all controller and expert system components and save all of the parameters of the defined controller to one controller data file You use two additional VIs to implement the fuzzy controller in your LabVIEW application The Load Fuzzy Controller VI loads all the 1 2 ni com Chapter 1 Overview of the PID Control Toolkit parameters of the fuzzy controller previously saved by the Controller Design VI The Fuzzy Controller VI implements the fuzzy logic inference engine and returns the controller outputs To implement real time decision making or control of your physical system you can wire the data acquired by your data acquisition device to the fuzzy controller You also can use outputs of the fuzzy controller with your DAQ analog output hardware to implement real time process control National Instruments Corporation 1 3 PID Control Toolkit User Manual Part I PID Control This section of the manual describes the PID Control portion of the PID Control Toolkit e Chapter 2 PID Algorithms introduces the algorithms used by the PID Control VIs e Chapter 3 Using the PID Software explains how to use the PID Control VIs National Instruments Corporation l 1 PID Control Toolkit User Manual PID Algorithms This chapter explains the PID Advanced PID and Autotuning a
131. the second input variable vehicle orientation and for the output variable steering angle which ranges from 30 0 to 30 0 degree National Instruments Corporation 7 7 PID Control Toolkit User Manual Chapter 7 Using the Fuzzy Logic Controller Design VI PID Control Toolkit User Manual For the next step you must have access to the input variable vehicle position To access the variable switch I O Select to the ANTECEDENCE position and select the desired input variable from the Variable Selector Any modifications made during the Fuzzy Set Editor session can have a significant influence on the rule base It is always a good idea to open the Rulebase Editor immediately after you close the Fuzzy Set Editor Because you started your Fuzzy Set Editor session with a new project the Fuzzy Logic Control VIs automatically call the Rulebase Editor to create a rule base Because you still have to do additional work on the knowledge base you should add and set up all linguistic terms according to the application example You do not need to work with the Rulebase Editor at this point in the project so click Quit to exit the Rulebase Editor LabVIEW does not automatically call the Rulebase Editor when you are working on an existing project and you close the Fuzzy Set Editor Regardless closing the Fuzzy Set Editor as well as closing the Rulebase Editor activates the Project Manager Use the File Save or File Save As command to save your pr
132. tial rate of change of output due to integral control action to the change in steady state output due to proportional control action Of integral control action devices for a step input the ratio of the initial rate of change of output to the input change Also called integral action rate A controller in which the value of the output signal decreases as the value of the input measured variable increases Revolutions per minute A linguistic definition of a specific control action of the form IF condition AND condition THEN action For example IF vehicle position is right center AND vehicle orientation is left up THEN steering angle is negative medium A complete set of rules defined for control of a given system Used during fuzzy inference to determine the linguistic controller output Seconds The use of multiple controllers and or multiple process variables in which the connections may change dynamically depending on process conditions An input variable which sets the desired value of the controlled process variable A normalized membership function with an infinitely small width A singleton is used to model a crisp value with a fuzzy set The algebraic difference between the upper and lower range values The degree of uncertainty of the occurrence of a given future nondeterministic event G 8 ni com T time constant T transient overshoot trapezoidal integration V V valve dead band
133. timal P I and D gains You can apply this control structure to processes that change their characteristics over time Figures 5 5 and 5 6 show this control structure 5 4 ni com Chapter 5 Fuzzy Controllers Fuzzy Controller Set Point Values W is Ea Rule Base IF AND THEN IF AND THEN IF AND THEN av i Fuzzification Fuzzy Inference Defuzzification PID Command Process i E i TE Measured Values Figure 5 5 Fuzzy Controller for Parameter Adaptation of a PID Controller Both the fuzzy controller and the PID controller work in parallel The process adds the output signals from both controllers but the output signal from the fuzzy controller is zero under normal operating conditions The PID controller output leads the process The fuzzy controller intervenes only when it detects abnormal operating conditions such as strong disturbances Set Point Values Fuzzy Controller z BE Rule Base IF AND THEN IF AND THEN Process D gt ie AND by A Fuzzification Fuzzy Inference Defuzzification 3 Measured Values Figure 5 6 Fuzzy Controller for Correction of a PID Controller Output National Instruments Corporation 5 5 PID Control Toolkit User Manual Chapter 5 Fuzzy Controllers
134. tion of Chapter 4 Overview of Fuzzy Logic there are two linguistic input variables vehicle position x and vehicle orientation B and one linguistic output variable steering angle Q It is a good idea to use descriptive variable names instead of the default identifiers offered by the Fuzzy Set Editor Select Specify Rename Variable to display the Rename Variable dialog box Now you can enter the new description identifier vehicle position into the text input box above the OK button to change the selected variable identifier in1 Figure 7 4 shows the dialog box Click the OK button or press lt Enter gt to save the new variable identifier National Instruments Corporation 7 5 PID Control Toolkit User Manual Chapter 7 Using the Fuzzy Logic Controller Design VI T Rename Ling Yariable Identifiers New Ling Variable Identifier Select identifier to be renamed Type in new identifier and click OK int vehicle position in2 Figure 7 4 Rename Variable Dialog Box After this select the variable identifier in2 and enter the description identifier vehicle orientation into the text input box Again click OK or press lt Enter gt to save the new variable identifier Click Exit to close the Rename Variable dialog box Select ANTECEDENCE CONSEQUENCE on the I O Select button to access the output variable Follow the steps listed above to rename the variable Return the button to the ANTECEDENCE position to be able
135. to automatic mode or change any other parameters The default ranges for the parameters SP PV and output correspond to percentage values however you can use actual engineering units Adjust corresponding ranges accordingly The parameters T and T are specified in minutes In the manual mode you can change the manual input to increase or decrease the output You can call these PID VIs from inside a While Loop with a fixed cycle time All the PID control VIs are reentrant Multiple calls from high level VIs use separate and distinct data 3 Note As a general rule manually drive the process variable until it meets or comes close to the setpoint before you perform the manual to automatic transfer National Instruments Corporation 2 3 PID Control Toolkit User Manual Chapter 2 PID Algorithms Gain Scheduling The Advanced Gain scheduling refers to a system where you change controller parameters based on measured operating conditions For example the scheduling variable can be the setpoint the process variable a controller output or an external signal For historical reasons the term gain scheduling is used even if other parameters such as derivative time or integral time change Gain scheduling effectively controls a system whose dynamics change with the operating conditions With the PID Controls you can define unlimited sets of PID parameters for gain scheduling For each schedule you can run autotuning to update the PID
136. tom left top right top right bottom 1 00 1 00 amp 1 00 020 amp a Figure 7 2 Default Fuzzy Controller Settings This dialog box consists of the following components 1 Variable selector 2 Term selector 3 TO select button National Instruments Corporation 7 3 PID Control Toolkit User Manual Chapter 7 PID Control Toolkit User Manual Using the Fuzzy Logic Controller Design VI 4 Editing function selectors 5 Term legend 6 Term display with point slider field A new project has certain default settings Among these are two normalized linguistic input variables with the default description identifiers inl and in2 Each input variable ranges from 1 0 to 1 0 by default Each linguistic input variable is composed of three entirely overlapping linguistic terms For in1 the linguistic terms NE1 negative ZE1 zero and PO1 positive are predefined For in2 the linguistic terms NE2 negative ZE2 zero and PO2 positive are predefined There is one normalized linguistic output variable comprising the three entirely overlapping linguistic terms NEo negative ZEo zero and POo positive The default range of the output variable is 1 0 to 1 0 Term Display shows the linguistic terms of the linguistic variable that the Variable Selector activates while the Term Legend displays the term description identifiers You can adjust the sliders or input controls in the Point Slider Field to interactiv
137. truments Corporation 6 7 PID Control Toolkit User Manual Chapter 6 Design Methodology to as the continuity of a rule base If neighboring rules have the same or similar conclusions the rule base is said to be continuous Within large rule bases it is possible to have multiple definitions of the same rule This is called redundancy It has no influence on the inference result at all if the Max Min inference method is implemented But there are other inference methods which are not discussed in this manual such as the Sum Product method in which multiple rules can effect the inference result Operators Inference Mechanism and the Defuzzification Method PID Control Toolkit User Manual In closed loop control applications that use fuzzy logic the standard common operators for the AND and the OR operation are the Min and Max operators discussed in the Using IF THEN Rules in Fuzzy Inference section of Chapter 5 Overview of Fuzzy Logic Within certain control applications in the field of process technology however it might be necessary to use a compensatory AND operator rather than the pure AND The most important compensatory AND operator is the y operator which is not discussed in detail here The y operator allows a continuous tuning between AND no compensation and OR full compensation In real situations the word AND is sometimes used to combine two antecedences meaning as well as indicating that you can compensate when you h
138. zy Sej EGCG rr Ee T me 1 00 Help Figure 8 7 Complete Rule Base Describing the Pattern Recognition Process National Instruments Corporation 8 5 PID Control Toolkit User Manual Chapter 8 PID Control Toolkit User Manual Implementing a Fuzzy Controller The principal program structure of the pattern recognition facility is a loop structure which repeatedly takes the input signal from a data acquisition board using the easy I O VIs for example and processes the signal Consider the following simulation environment to experiment with the fuzzy controller independent of specific data acquisition equipment The SignalGen VI on the left side of the block diagram shown in Figure 8 8 corresponds to the input side of a process controller You can regard the NumtoString VI on the right side of the diagram as the output side of a process controller The VI supplies all necessary output signals including the signals used for process animation Eke Figure 8 8 Block Diagram of the Pattern Recognition Application Prepared for Entering the Pre Defined Fuzzy Controller VI The SignalGenVI replaces the data acquisition part including all the data pre processing activities which directly supplies the necessary input signals TH TS and TU TD TS for the example application All other input and output signals used in the block diagram are part of the user interface that includes all the controls and indicators you ca
139. zzification method requires a lot of computation The second defuzzification method is called the Center of Maximum CoM method In the first step of this method determine the typical value of each term in the linguistic output variable In the second step calculate the best compromise with a weighted average of typical values of the terms The most common approach to determining the typical value of each term is to find the maximum of the corresponding membership function In the case of trapezoidal membership functions choose the median of the maximizing interval Weight each typical value by the degree to which the action term conclusion is true Then calculate the crisp output value with a weighted average as shown in Figure 4 14 4 18 ni com Chapter 4 Overview of Fuzzy Logic Negative Negative N Hlo i Large Medium egative Zero Positive Positive Positive Small Small Medium Large 0 8 N validity of Rule 0 6 0 4 0 2 0 0 30 0 25 0 20 0 15 0 10 0 Defuzzified Result 6 1 in 0 0 5 0 100 15 0 20 0 25 0 30 0 Steering Angle o Figure 4 14 Defuzzification According to Center of Maximum CoM With negative medium 15 and negative small 5 as typical values of the linguistic terms negative medium and negative small and with the validity values V
140. zzy logic applications are defined as follows AND wAeB min UA UB OR UA B max UA UB NOT u A l uA Notice that these definitions agree with the logical operators used in Boolean logic A truth table uses conventional operators to yield equivalent results The minimum operator represents the word AND Apply AND in the aggregation step to calculate a degree of truth for the IF condition of each rule in the rule base that indicates how adequately each rule describes the current situation National Instruments Corporation 4 15 PID Control Toolkit User Manual Chapter 4 Overview of Fuzzy Logic In the example situation only the following two rules are valid descriptions of the current situation These rules are usually called the active rules All the other rules are called inactive 1 IF vehicle position x is center AND vehicle orientation b is left up degree of truth 0 8 minimum degree of truth 1 0 0 8 THEN adjust steering angle to negative small 2 IF vehicle position x is right center AND vehicle orientation B is left up degree of truth 0 1 minimum degree of truth 1 0 0 1 THEN adjust steering angle to negative small PID Control Toolkit User Manual Each rule defines an action to take in the THEN condition The applicability of the rule to the current situation determines the degree to which the action is valid The aggregation step calculates this adequacy as the degree of truth of

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