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LabVIEW PID Control Toolkit User Manual

1. 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 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
2. Quit National Instruments Corporation Figure 7 11 Results of the Complete Editing Session Example 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 Select Edit Rulebase Editor 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
3. 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 stable 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 SP E e PV Pao T Os P I Controller Process Relay i 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
4. 0 0 1 0 0 5 0 0 0 5 1 0 Positive ZE PS PL dx at a Max Min Inference Modified CoA y f x dx dt 1 00 Figure 5 17 1 0 Characteristic Field of a Dual Input Fuzzy Controller PID Control Toolkit User Manual 5 24 ni com 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 j 1 0 ji 1 0 ney O8 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 gt y gt A Negative Zero Positive Rule Input x 1 0 Base Negative Zero Positive g 08 06 Negative NL NS ZE 0 4 5 0 2 Zero NS ZE PS a 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
5. 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 for more information about the desired pattern Figure 7 8 shows an intermediate state and Figure 7 9 shows the final result of this renaming process nye Note You also can use the specify menu to add or remove linguistic variables PID Control Toolkit User Manual 42 Rename Ling Term Identifiers Select identifier to be renamed left left center ZE1 ZE1 PO1 New Ling Term Identifier Type in new identifier and click OK center Figure 7 8 Rename Dialog Box 7 10 ni com Chapter 7 Using the Fuzzy Logic Controller Design VI 8 Fuzzy Set Editor x vehicle position specify v Y lt ling variables ANTECEDENCE define M left ma aa ling terms edit 1 0 left Fae left center 9 Esa center NA 0 6 right center right ANA 0 4 p 0 2 0 0 1 I 1 1 i 1 1 1 1 i 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 6 0 90 10 0 left bottom left top right top right bottom 000 S 0 00 0 00 amp 5 00 amp 7 fi 7 QUIT 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
6. 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 pom Moving Direction Figure 8 1 Sensor Facility 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 National Instruments Corporation 8 1 PID Control Toolkit User Manual Chapter 8 Implementing a Fuzzy Controller parts vary to a certain extent Different environmental conditions such as scattered light can affect the signal Figure 8 2 shows some typical voltage drop curves derived from an asymmetric triangle a lefthand shaped triangle UI LDR 9 5 9 0 8 5 8 0 7 5 0 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 10 0 Inpu
7. the VI outputs NaN until you pass a value of TRUE to the reinitialize input You can use the Not A Number Path Refnum VI to check for invalid inputs and respond in a way that is appropriate to the application For example the following block diagram uses the Not A Number Path Refnum VI with a Select function and a Feedback Node to reuse the last valid input when the VI receives an invalid input setpoint process variable Derk Not 4 Number Path Refnum Figure 3 5 Fault Protection Refer to the General PID with Fault Protection VI in the labview examples control pid pretrlex 11b directory for an example of a single channel PID implementation that includes fault protection 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 T
8. A controller which produces proportional control action only that is a controller that has only a simple gain response In fuzzy set theory a condition in which the value of a member partially fulfills the requirements of the membership function of a set 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 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 plus 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 G 6 ni com Q quart
9. Controller percent minutes minutes P 2 00PB PI 2 22PB 0 837 PID 1 67PB 0 507T 0 125T 3 Note Proportional gain K is related to proportional band PB as K 100 PB 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 operating 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 National Instruments Corporation 3 5 PID Control Toolkit User Manual Chapter 3 Using the PID Software 3 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 TT Deadtime in minutes e J Time constant in minutes e K Process gain change in PV change in output 63 2 Max Min PV Min Output Figure 3 4 Output an
10. 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 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 lea
11. The Fuzzy Set Editor front panel is shown in Figure 7 2 a Fuzzy Set Editor Xx int specify v lt ling variables ANTECEDENCE define v NE1 lt ling terms edit 1 04 O NE1 ool a 0 6 ree POIRA A 0 6 0 4 os 0 2 0 0 1 i i 1 i i 1 i i 00 08 0 6 0 4 0 2 0 0 0 2 0 4 0 6 0 8 1 0 left bottom left top right top right bottom 1 00 1 00 amp 1 00 0 20 amp Gf 7 QUIT Figure 7 2 Default Fuzzy Controller Settings This dialog box consists of the following components 1 Variable selector 2 Term selector National Instruments Corporation 7 3 PID Control Toolkit User Manual Chapter 7 PID Control Toolkit User Manual Using the Fuzzy Logic Controller Design VI T O select button 3 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 in 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 linguisti
12. 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 10 0 8 0 6 0 4 0 205 o 0 TU 4 20 00 om eae 50 60 70 80 90 100 r5 oO 10 20 30 40 50 scale xss aio spom input signal def 340 soo TD m o 5000 I 30 40 TH 50 60 70 al go 100 il moo es 0 ld ae EEIE TU TDVTS e Figure 8 12 Running the Pattern Recognition Application Clicking the Cancel button rather than selecting the fuzzy controller data file FuzzyTruck fc executes the default fuzzy controller repeatedly Without having actual data loaded to the controller it will use the default data See the block diagram of the complete pattern recognition application shown in Figure 8 11 PID Control Toolkit User Manual 8 10 ni com Chapter 8 Implementing a Fuzzy Controller Because of security aspects that can occur when running a controller within a real application environment if someone clicks the Cancel button the controller should not start To improve your controller design place the While Loop inside 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
13. 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 Linguistic 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 2 0 3 0 4 0 5 0 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 accou
14. 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 the Fuzzy Logic Controller Design VI vehicle position x lt ling variables left ANTECEDENCE iv lt ling terms l 1 00 10 left bottom oo amp 1 i 20 30 40 left top loco 5 0 60 70 right top 1 00 S q specify define edt left left center center right center right LUL BRRR oee vehicle orientation EJ left down lt ling variables ANTEEEDENCE ling terms left bottom 90 00 1 0 0 50 0 left top 90 o f i 100 0 150 0 right top 245 00 E i eee 200 0 270 0 right bottom 20 00 a specify m dfe m let down left left up up right up right right down QUIT i prees steering angle NegBig left bottom 30 0 left top 30 00 e a rk bottom 30 00 15 00 specify _ define edit iv NegBig NegMed NegSmall Zero PosSmall PosMod PosBig wl x R LBBBRREI
15. Control Toolkit User Manual A 2 ni com Glossary A aggregation algorithm anti reset windup autotuning Autotuning Wizard bias Boolean set theory bumpless transfer C cascade control Center of Area CoA 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 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 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 Control in which the output of one controller is the setpoint for another controller Method of defuzzific
16. 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 specified 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 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
17. 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 indicator 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 PID Control Toolkit User Manual Figure 8 16 shows the application front panel immediately after loading the fuzzy controller data file for the pattern recognition example Figure 8 16 Test Fuzzy Control 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 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 Figure 8 17 Test Fuzzy Control VI Front Panel with Incorrect Input Value for Input 1 8 14 ni com Chapter 8 Implementing a Fuzzy Controller Figure 8 18 shows the proper use of all input and
18. Ne medium 757 0 8 ung large praa 0 6 0 4 0 2 0 0 i i i i i i i i i 0 0 0 1 g2 03 0 4 DS 06 07 0 8 0 9 1 0 left bottom left top right top right bottom o0 S o0 S 010 amp o3 10 E i Quit 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 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 tc Fuzzy Set Editor TU TDYTS specify lt ling variables ANTECEDENCE define m lt ling terms Se Fa neg gt zero A7 pos 1 i I 1 i i 0 6 0 4 00 02 04 06 0 8 1 0 left bottom right top __ right bottom 1 00 S 0 50 oo E q 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
19. Negative Zero Positive i 1 0 A 1 0 py O uo 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 Zero THEN y Zero Rule 3 IF x Positive THEN y Positive Modified CoA 18 Tt ara Rule1 Rules1iand Rule 2 Rules2and Rule3 A 0 8 Active 2 Active Active 3 Active Active 0 8 1 0 Figure 5 7 1 0 Characteristic of a Fuzzy Controller Partially Overlapping Input Terms National Instruments Corporation 5 7 PID Control Toolkit User Manual Chapter 5 Fuzzy Controllers 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 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
20. 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 change 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 i 1 0 ji 1 0 uo oS u 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 Max Min Rule Rule 1 IF x Negative THEN y Negative Inference Base Rule 2 IF x Zero THEN y Positive Rule 3 IF x Positive THEN y Negative Modified CoA 1 0 i 0 8 0 6 y 0 4 hes 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 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 t
21. TH TS Piece Tis TU TD TS e 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 preprocessing step performs You also can use the slider to study how different signal conditions can affect the result of the pattern recognition process National Instruments Corporation 8 7 PID Control Toolkit User Manual Chapter 8 Implementing a Fuzzy Controller Fuzzy Controller Implementation PID Control Toolkit User Manual Now incorporate the fuzzy controller into the application block diagram You do not need to program the fuzzy controller Instead use the Fuzzy Controller VI shown in Figure 8 10 The Fuzzy Controller VI can be connected with as many as four input signals from a process and one output signal used as a control value 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 inl name 2 in2 name 3 in3 name 4 in analog output output assessment error array Fig
22. a resolution of 1 ms so specify a dt value explicitly if the loop cycle time is less than 1 ms Filtering Control Inputs Gain Scheduling PID Control Toolkit User Manual You can use the PID Control Input Filter VI to filter high frequency noise from measured values in a control application 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 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 lowpass fifth order finite impulse response FIR filter The cutoff frequency of the lowpass 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 With the PID Gain Schedule VI you can apply different sets of PID parameters for different regions of operation of your controller Because mo
23. by the rules Figure 5 10 shows the resulting effect on the controller characteristic National Instruments Corporation 5 11 PID Control Toolkit User Manual Chapter 5 Fuzzy Controllers Negative Zero Positive Negative Zero Positive ji 1 0 i 1 0 w x 0 8 0 6 0 4 0 2 0 0 i j 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 i 0 8 0 6 y 0 4 r 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 10 1 0 Characteristic of a Fuzzy Controller Undefined Input Term Interval PID Control Toolkit User Manual 5 12 ni com Chapter 5 Fuzzy Controllers 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 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
24. 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 Corporation 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 A io Negative Zero Positive A Negative Zero Positive i 1 0 0 8 0 8 uO uO 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 p 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 i 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 11 1 0 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
25. following three calculation steps fuzzification fuzzy inference and defuzzification Linguistic rules integrated into the rule base of the controller 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 J J es Rule Base IF AND THEN IF AND THEN IF AND THEN IF AND THEN oe 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
26. for all channels To specify unique values for individual channels you must create an initialization loop on the host VI In the initialization loop you might update the parameter values of some channels while other channels retain the initial values you specified in the configuration dialog box In Figure 3 14 the initialization loop initializes the parameters of all channels Initialization Loop Read Write Control b configuration Wait on IRQ gt apply configuration b IRQ Number s e apply reset s b Timeout ms TA R channel s to reset Timed Out gt IRQ s Asserted gt setpoint setpoint L P PID gains x mane E PID gains x zT B range output range 7 Figure 3 14 Initializing PID Parameters on the Host VI Processing Loop on the Host VI After initializing the PID parameters and while running the VI on the FPGA target you might want to modify parameters or reset channels on a per channel basis without affecting the execution of other channels Create a processing loop on the host VI to modify parameters or reset channels asynchronously during execution of the FPGA VI Resetting a PID channel resets the internal channel states to 0 and restarts the PID algorithm while using either the parameter values stored in memory or the parameter values from the host VI To modify different parameters you must specify the channel index which tells the PID algorithm the channe
27. 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 Undefined 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 sub menu 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 t
28. loop control applications The most basic structure uses the sensor signals from the process as input signals for the fuzzy controller and the outputs as command values to drive the actuators of the process A corresponding control loop structure is shown in Figure 5 2 Fuzzy Controller Process Point Command alues A W PB Variables gt IF AND THEN IF AND THEN OX gt l IF AND THEN gt XX Fuzzification Fuzzy Inference Defuzzification Measured Values 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 PID Control Toolkit User Manual 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
29. min 30 15 0 30 vehicle position xim vehicle orientation pII steering angle A A Linguistic Level Technical Level vehicle position x 5 1 m lt lt y Defuzzification H steering angle 9 3 Figure 4 15 Fuzzification Fuzzy Inference and Defuzzification for a Specific Maneuvering Situation PID Control Toolkit User Manual 4 20 ni com Chapter 4 Overview of Fuzzy Logic 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 1 0 0 5 0 0 1 0 0 5 0 0 1 0 0 5 0 0 0 0 1 0 0 5 0 0 o een CoA oo SS Laie 100 100 100 z z 1 0 P Po 1 0 0 5 0 0 0 0 1 0 0 5 0 0 0 0 100 AU iia ae i i ji j li ji 4100 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 le
30. 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 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 variable 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 al __ specify m lt ling variables eS ANTECEDENCE define Io right center lt ling terms edit wl left Va left center center Pota right center A AA right left bottom left top right top right bottom so Sl 750 750 S 10 00 B Figure 7 10 A Term
31. 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 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 n
32. s setpoint fFio 000 4100 00 20 0 time s setpoint 0 i o 000 o 00 ca Figure 3 8 Ramp and Hold Setpoint Profile Alternatively a step setpoint profile can have two successive array values with the same time value but different setpoint values as shown in Figure 3 9 setpoint profile setpoint profile graph gt Jo time s setpoint 100 0 Yo 000 o oo 80 0 time s setpoint 60 0 Hf5 o00 dAfo oo 40 0 time s setpoint aAfs oo0 4100 00 20 05 Setpoint time s setpoint r r 10 000 100 00 spe Hag Figure 3 9 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 National Instruments Corporation 3 11 PID Control Toolkit User Manual Chapter 3 Using the PID Software 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
33. sets left down with a degree of 0 0 left with a degree of 0 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 A
34. terms cause the rising edges of the controller characteristic to be nonlinear Figure 5 8 shows the resulting controller characteristic for antecedence terms that overlap 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 i 1 0 A 1 0 0 8 0 8 u x u y 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 ue I I Rules 1 and Rules 2 and 4 0 8 2 Active 3 Active e gt 0 8 1 0 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
35. 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 applications 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 Negative Zero Positive Negative Zero Positive i 1 0 i 1 0 0 8 0 8 uO u y 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 x Max Min Rule Rule 1 IF x Negative THEN y Negative Inference as Rule 2 IF x Zero THEN y Zero ase Rule 3 IF x Positive THEN y Positive Modified CoA 1 0 i 0 8 0 6 y 0 4 ee 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 xX gt Figure 5 12 1 0 Characteristics of a Fuzzy Controller Different Overlapping Degrees of Members
36. that results when nonoverlapping antecedence terms describe the input variable Negative Zero Positive Negative Zero Positive i 1 0 ji 1 0 uo 0 8 u y 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 Ba n Rule 2 IF x Zero THEN y Zero S Rule 3 IF x Positive THEN y Positive Modified CoA 1 0 l A 0 8 r 0 6 oa Rule 1 Rule 2 Rule 3 Active i Active Active e gt lt ja 0 2 1 0 0 i i 0 2 0 4 T 0 6 0 8 1 0 i 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 PID Control Toolkit User Manual 5 10 ni com Chapter 5 Fuzzy Controllers In this case only one rule is active for each input situation that leads to the stepped controller characteristic shown in Figure 5 9 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
37. the autotuning algorithm identifies the dead time t and time constant Tp which are two parameters in the integral plus deadtime model TS aan Ts pP Gp s National Instruments Corporation 2 7 PID Control Toolkit User Manual Chapter 2 PID Algorithms Tuning Formulas PID Control Toolkit User Manual The LabVIEW PID Control Toolkit 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 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 8T PID 0 15K 0 5T 0 12T 2 8 ni com Table 2 4 Tuning Formula under PI or PID Control Fast Chapter 2 PID Algorithms Controller K T Ta P T t PI 0 9T T 3 337 PID 1 1T 2 01 0 51 Table 2 5 Tuning Formula under PI o
38. the target position and the orientation of the truck to derive the correct steering angle This is shown in Figure 4 4 PID Control Toolkit User Manual yim 2 0 Start Position 1 0 Target Position 0 0 a 20 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 B 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 Cu Position 0 0 a 2 0 3 0 4 0 5 0 6 0 x m National Instru
39. 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 VIs located in the labview examples control pid pretrlex 11b directory for examples of using timing with the PID VIs If you installed NI DAQmx you also can view relevant examples in the labview examples dagmx control control 11b directory 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 3 2 ni com Chapter 3 Using the PID Software 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 Corripio 1990 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 Global Number Cycle Time EET Global Number Cycle Time B E Figure 3 3 Cascaded Control Functions A global variable pa
40. toward the current output value you need a subsequent integrator device to build up the command variable value Set Point Value error t Fuzzy Controller Process derror t dt lt A dat H gt Rule Base IF AND THEN Command IF AND THEN Variable Inc Dec Fuzzification Pape 1 Fuzzy Inference Defuzzification dy t dt K d error t dt 4s 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 I
41. All rights reserved Important Information Warranty The media on which you receive National Instruments software are warranted not to fail to execute programming instructions due to defects in materials and workmanship for a period of 90 days from date of shipment as evidenced by receipts or other documentation National Instruments will at its option repair or replace software media that do not execute programming instructions if National Instruments receives notice of such defects during the warranty period National Instruments does not warrant that the operation of the software shall be uninterrupted or error free A Return Material Authorization RMA number must be obtained from the factory and clearly marked on the outside of the package before any equipment will be accepted for warranty work National Instruments will pay the shipping costs of returning to the owner parts which are covered by warranty National Instruments believes that the information in this document is accurate The document has been carefully reviewed for technical accuracy In the event that technical or typographical errors exist National Instruments reserves the right to make changes to subsequent editions of this document without prior notice to holders of this edition The reader should consult National Instruments if errors are suspected In no event shall National Instruments be liable for any damages arising out of or related to this document or the informat
42. CAL COMPONENTS IN ANY 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 INSTRUMEN
43. 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 Process 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 evolutionar
44. 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 Instrument Society of America The organization that sets standards for process control instrumentation in the United States Process gain Controller gain 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 1 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 G 4 ni com load disturbance loop cycle time magnitude ratio manipulated variable Max Min inference Mean of Maximum MoM membership function noise 0 output limiting overshoot National Instruments Corporation G 5 Glossary The ability of a controller to compensate for changes in physical parameters of a controlled process while the setpoint value remains constant Time interval between calls to a control algorithm See gain A quantity or co
45. LabVIEW PID Control Toolkit User Manual June 2008 c7 NATIONAL 372192C 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 43 662 457990 0 Belgium 32 0 2 757 0020 Brazil 55 11 3262 3599 Canada 800 433 3488 China 86 21 5050 9800 Czech Republic 420 224 235 774 Denmark 45 45 76 26 00 Finland 358 0 9 725 72511 France 01 57 66 24 24 Germany 49 89 7413130 India 91 80 41190000 Israel 972 3 6393737 Italy 39 02 41309277 Japan 0120 527196 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 7 495 783 6851 Singapore 1800 226 5886 Slovenia 386 3 425 42 00 South Africa 27 0 11 805 8197 Spain 34 91 640 0085 Sweden 46 0 8 587 895 00 Switzerland 41 56 2005151 Taiwan 886 02 2377 2222 Thailand 662 278 6777 Turkey 90 212 279 3031 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 2008 National Instruments Corporation
46. Manual 8 4 ni com object TriLeft 0 8 0 6 0 4 0 2 0 0 Chapter 8 lt ling variables CONSEQUENCE lt ling terms left top 1 00 right top 100 Ncemenhtoment i bazi i jozsi I oe Do 0S FO ES 20 207 a0 3S RUAS SSG GS A0 left bottom 1 00 amp right bottom 1 00 q Implementing a Fuzzy Controller specify define edit TriLeft TriSym TriRight HexLeft HexSym HexRight Rect National Instruments Corporation THEN THITS TU TDVTS object Defuzzification Method _ Mean of mal Maximum M small small small medium wont nnk WN neg zero pos neg zero pos neg zero pos TriLeFt TriSym TriRight HexLeft HexSym HexRight Rect Rect Rect TriLeft TriLeft TriLeft TriLeft TriLeft TriLeft x RIR IRK ee RR I Th ararararar default term lt 65535 gt m if no rule is active Take last value v Inference Method MaxMin m Select form of Rulebase normal Rulebase total rules 9 used rules 9 default Dos 1 00 Figure 8 7 Complete Rule Base Describing the Pattern Recognition Process 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 repeatedl
47. ND OR and NOT The three operators used in the majority of fuzzy 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 ag
48. TS PRODUCTS IN COMBINATION 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 GONVENEONS e ees atin eek es esi eke EE TE E en eee ee eee ees 1X Related DoCUMeEntatiONn ccccccccccccesessssesssesessssscscesesceseececeseeeseeseseessenenensssesesseceeeess x Chapter 1 Overview of the PID Control Toolkit PUD Control vss nirin cs Sedu Seed sea a a sdes evade EE A E EA REE E ARRE A E 1 1 UZZY LO a EEE fi vseasea ca vied naked eseadendaeedeasticsSeatnnea ides cabsadejanhesudadvaveaseda E 1 2 How Do the Fuzzy Logic VIs Work ce ceseesceceseceseeeseeeeneeeneeeeaeeesneeeaeenaee 1 2 Chapter 2 PID Algorithms The PID Al Sorithm aei e E Gen eee ain eee a eh ran ais 2 1 Implementing the PID Algorithm with the PID VIs ee ceeeeeeeeeeeeneeeeeeeeaee 2 2 Error Calculation iss tac A e a iio ease 2 2 Proportional ACON er esdvdcecesds cess E E EA E svscusuvestdeaesvecasseancs 2 2 Trapezoidal Int gration eniai REEE EKE E EEES 2 2 Partial Derivative ACtiON 00 0 ec cseeseeseeeeereeesecseeesecseeeaesneeeaeenees 2 2 Controller Outputs cies c
49. ad to continuous output signals because the best compromise can never jump to a different value with a small change to the inputs National Instruments Corporation 4 21 PID Control Toolkit User Manual Chapter 4 Overview of Fuzzy Logic PID Control Toolkit User Manual For pattern recognition 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 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 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
50. application quits if you click the Cancel button i EFE input signa TU TD TS ui Signal mir g o m 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 the application front panel to the front National Instruments Corporation 8 11 PID Control Toolkit User Manual Chapter 8 Implementing a Fuzzy Controller ph Oy ee 9 Start the application to open the input file dialog box that requests a fuzzy controller data file Select the desired fuzzy controller data file Stop the application Bring the front panel of the Fuzzy Controller VI to the front Select Edit 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 availabl
51. are 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 3 24 ni com 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 yo
52. ation in which the crisp output is determined by the geometrical center of the composite output membership function Also known as Center of Gravity CoG PID Control Toolkit User Manual Glossary Center of Maximum CoM closed loop composition controller controller output crisp value cycle time D damping deadtime Ta defuzzification degree of membership degree of support derivative control action PID Control Toolkit User Manual 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 The interval of time expressed in minutes between initiation of an input change or stimulus a
53. ble 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 or process parameters using the defined membership functions to determine linguistic input variables for the rulebase evaluation The process by which the rules of the rule base are evaluated to determine output linguistic variables for defuzzification 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 based on the idea that fuzzy sets may be defined such that elements can have partial membership to the set PID Control Toolkit User Manual Glossary G gain gain scheduling integral control action ISA L lag linearity factor linguistic term linguistic variable PID Control Toolkit User Manual For a linear system or element the ratio of the magnitude or 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 different regions of operation of a controller Gain scheduling is most often used in controlling nonlinear physical processes
54. c terms NEo negative ZEo zero and POo positive The default range of the output variable is 1 0 to 1 0 The 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 interactively 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 NEI 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 fej Fuzzy Set Editor specify ZIR
55. c 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 doctor Figure 4 1 shows a graphical representation of the set 1 0 0 8 0 6 0 4 0 2 0 0 u T A Membership patients with a high fever 95 0 96 8 98 6 100 4 102 2 104 0 105 8 107 6 109 4 TPF 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 Co
56. ction 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 Autotuning Algorithm 2 7 PID Algorithm 2 1 PID software 3 1 with DAQ 3 21 with FPGAs 3 18 PID toolkit using with DAQ hardware timed DAQ control loop 3 24 software timed DAQ control loop 3 22 software timed DAQ control loop with advanced DAQ functions 3 23 PID Control Toolkit User Manual l 2 programming examples NI resources A 1 proportional action 2 2 2 5 R related documentation x S setpoint relay experiment 2 7 Shinskey F G x software NI resources A 1 support technical A 1 T technical support A 1 timing 3 2 training and certification NI resources A 1 trapezoidal integration 2 2 2 6 troubleshooting NI resources A 1 tuning 3 4 W Web resources A 1 Z Ziegler J G x ni com
57. d Tuning 3d ed New York McGraw Hill Yen J R Langari and L Zadeh eds 1995 Industrial Applications of Fuzzy Logic and Intelligent Systems Piscataway NJ IEEE Press Ziegler J G and N B Nichols 1942 Optimum settings for automatic controllers Trans ASME 64 759 68 Zimmerman H J 1991 Fuzzy Set Theory and Its Applications 2d ed Boston MA Kluwer Academic Publishers Zimmerman H J 1987 Fuzzy Sets Decision Making and Expert Systems Boston Dordrecht London Kluwer Academic Publishers 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 parameter 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 VIs with National Instruments hardware
58. d 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 Table 3 2 Open Loop Quarter Decay Ratio Values PB Reset Rate Controller percent minutes minutes P 100824 KT PI 110 3 337 T KT PID 80 77 2 007 0 507 PID Control Toolkit User Manual 3 6 ni com Chapter 3 Using the PID Software Using the PID VIs The PID VI 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 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 sys
59. e ceeeseeseeseeseceeceseeeeesseseeceseeseeeseeeeees 6 3 Defining a Fuzzy Logic Rule Base oo eee eeesceeseceecesececeseeecesesseeeaeeseesseeaeenseeaeenes 6 6 Operators Inference Mechanism and the Defuzzification Method eeeeeeeeeeee 6 8 Chapter 7 Using the Fuzzy Logic Controller Design VI OVERVIEW fei eit iia E hie ae eee Site ate ee ets to pts eat tle fees 7 1 Project Manager naitre Anna a caste cutvecusevestuedePecuteved deevtavdusBevaceevees 7 2 Puzzy Sect Editorascicie 2 hes uote avec eed hes ve ts ante tes 7 3 R lebase Editorsin e EEE EE E E E AEE Beet 7 14 Documenting Fuzzy Control Projects esseseseeseeesesrsresreetsrestsrestsrestesrerrstesrsresesseneees 7 15 Test FacilitieSi in r na a ody eva T E ESERE EEE EE E A EEAO EESE 7 15 Chapter 8 Implementing a Fuzzy Controller Pattern Recognition Application Example sssesssesssesrsseseerseerssrsresrsresresesresresesesesses 8 1 Fuzzy Controller Implementation eseecesececesseceeecseeeaeesesesecseseaeeseseaseneeeaes 8 8 Loading Fuzzy Controller Data 0 eee eeeeeeccesseecceeeeceesecesecseesaeesesesesseeeaecseseaseneeeaes 8 9 Saving Controller Data with the Fuzzy Controller oo eeeeeeseeseceecneeeeseeenseesees 8 11 Testing the Fuzzy Controller crnisss tices thd haiti eae ten 8 13 Appendix A Technical Support and Professional Services Glossary Index National Instruments Corporation vil PID Control Toolkit User Manual About This Manual Conve
60. e 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 you 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 National Instruments Corporation 3 9 PID Control Toolkit User Manual Chapter 3 Using the PID Software 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
61. e 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 ei Fuzzy Set Editor vehicle position specify lt ling variables ANTECEDENCE define NE1 x lt ling terms edit NE1 NE1 n e j ZE1 0 6 POL 1 0 0 4 0 2 FENINNUN TNE 0 0 7 1 i 1 1 1 1 0 0 1 0 2 0 3 0 5 0 6 0 7 0 6 0 90 10 0 left bottom left top right top right bottom 0 00 250 amp 250 amp 5 00 F 3 E Figure 7 7 New Term Added to the Vehicle Position Variable i 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
62. e 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 VI 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 Controller 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 Figure 8 15 Test Fuzzy Control VI
63. ea CoA The numerical integration necessary to calculate the center of area in this defuzzification 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 Negative Zero Positive Positive Positive uig Large Medium Small Small Medium Large 0 N validity of Rule 1 0 6 0 4 0 2 0 0 30 0 25 0 20 0 15 0 10 0 i 0 0 5 0 100 15 0 20 0 25 0 30 0 Defuzzified Result 6 1 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 t
64. ecedence term You can select each active rule by clicking the pull down arrow to the right of the Active Rules display as shown in Figure 7 15 f Input Output Characteristic tg vehicle position yehicle orientation omo t 30 00 i 0 0 10 0 90 0 270 0 15 Rule DoS 1 00 1 00 IF vehicle position center 1 00 AND vehicle orientation left down 1 00 THEN steering angle NegMed controlled result steering angle _ ax to min 30 0 RFA 20 0 N i No Points 10 0 ZS 20 al 00 7 lt gt i 10 0 rat i amp eae PN i min to max 30 0 i I 1 i j i i i 1 00 10 20 30 40 50 60 70 80 90 100 16 67 yehicle position Cursor incr 0 50 characteristic of selected ling variable vehicle position is al QUIT displayed others are constant min to max 5 0 16 7 Figure 7 15 Selecting One of the Active Rules from the Active Rules Display Click the Print button to print out the current situation for documentation purposes National Instruments Corporation 7 19 PID Control Toolkit User Manual 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
65. eeds ee ae hee eb See ey 2 3 OUP UE LIMINE os face Sosshde es Peote yes testtveees Rangeves ah tees sry ctiveeeei de etseeners 2 3 Gain Scheduling 3 2 4 cstiess shee eee ahs eee RA ates i a 2 4 The Advanced PID AlSOrithny s ss sctecsseesecevadeenvectoavevehsebeusutesiteeseutersectueevessavatevievsuceesst 2 4 Error Calculation a e r a E A a E nite ad aia 2 4 Proportional ACHO sarene r e a e E A E A EER E Re 2 5 Trapezoidal Integration nsina na E E aE 2 6 The Autotunins Algorithi e i nean iena E A 2 7 Tuning Formulas sees a ea E E a etd ees 2 8 Chapter 3 Using the PID Software Designing a Control Strateg yeto ta heene a e a a E a ao 3 1 Setting TIMIN Senni a e A A N O A A a S 3 2 Tuning Controllers Manually cccccccccccesesscsecsscsessessesssssessesscsseseeessesseeaes 3 4 Closed Loop Ultimate Gain Tuning Procedure 3 4 Open Loop Step Test Tuning Procedure eee eee eeeeeeeeereeeees 3 5 National Instruments Corporation v PID Control Toolkit User Manual Contents Usitig the PID V1 81 5 tscesszsc2sebnel sates cans Ea eE dees E E NTARE 3 7 The PID V iiinn oa adit es belied aden ives Aves ISG 3 7 Fault Protections aeee A dacl suas EERE 3 8 The PID Adya ced V Lisssssciieas igtss calisuaecheasehtictves eie a a s 3 8 Bumpless Automatic to Manual Transfer eseeeeeeeeeeeeseeeeeeeeeeeee 3 9 Multi Loop PID Control isss iriser sisisi nin irrar inaani 3 9 Setpoint Ramp Generation neseni nemainas 3 10 Filtering Contro
66. ehicle orientation into the text input box Again click OK to save the new variable identifier Click the Exit button to close the Rename dialog box Click the I O Select button to select CONSEQUENCE and access the output variable Follow the steps listed above to rename the output variable to steering angle Return the button to the ANTECEDENCE position to be able 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 Define Range dialog box from which you can change the data range of the input variable vehicle position PID Control Toolkit User Manual 7 6 ni com Chapter 7 Using the Fuzzy Logic Controller Design VI Enter the range boundaries as shown in Figure 7 5 44 Define Range X Define variable range current linguistic variable identifier xmin vehicle position Figure 7 5 Edit Range Dialog Box Click the Exit button to 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 fp Fuzzy Set Editor EJ vehicle position specify lt ling va
67. entation of the PID Control Flowchart FT Flow Transmitter LT Level Transmitter LC Level Control SP Setpoint National Instruments Corporation 3 1 PID Control Toolkit User Manual Chapter 3 Using the PID Software Setting Timing PID Control Toolkit User Manual ontrol valve 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 VI and the PID Lead Lag VI in the LabVIEW PID Control Toolkit are time dependent A VI can acquire timing information either from a value you supply to the cycle time control dt or 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
68. er decay ratio ramp rate action reentrant reset rate rule rule base S selector control singleton National Instruments Corporation G 7 Glossary 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 Execution mode in which calls to multiple instances of a subVI can execute in parallel with distinct and separate data storage Of proportional plus integral or proportional plus integral plus derivative control action devices for a step input the ratio of the initial 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 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 de
69. er 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 input 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 Center of Gravity CoG Assessment Center of Area Center of Maximum Mean of Maximum Criteria 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
70. erms negative medium and negative small and with the validity values V rule 1 0 8 and V rule 2 0 1 for the active rules the possible defuzzification results are Q negative medium e V rule 2 O negative small V rule 1 o out V rule 2 V rule 1 out 6 1 The defuzzification method CoM is identical to using the CoG method with singleton membership functions National Instruments Corporation 4 19 PID Control Toolkit User Manual Chapter 4 Overview of Fuzzy Logic Figure 4 15 summarizes the fuzzy inference process for the maneuvering situation described above using the CoA method of defuzzification 1 IF vehicle position x center AND vehicle orientation B left up THEN steering angle negative small negative negative center 0 0 5 0 vehicle position x m 10 0 90 0 90 180 270 vehicle orientation B medium small 30 15 0 15 KAX steering angle negative negative medium small 0 DOA 30 30 15 0 15 steering angle Fuzzification vehicle orientation B 70 a i Fuzzy 2 IF vehicle position x right center Inference Ma AND vehicle orientation B left up THEN steering angle negative medium i negative negative right center 1 0 medium small ti AIk Zi toa vt N AAA 1 F l We Jot AWA 0 0 5 0 10 0 90 0 90 180 270
71. erss en eseecesscesceecseeeseceeeesecseeeseeseeeaeesseeaseneeeatenes 4 5 Rule Based Systems oreinaren nee age eR an A en 4 6 Implementing a Linguistic Control Strategy 0 ee eeeeseeeeceseeseeeseceeensesseeeaeesees 4 7 Structure of the Fuzzy Logic Vehicle Controller 0 0 eee ees eeeeseeeeeeeeeseeeeeeeees 4 12 Fuzzification Using Linguistic Variables 0 0 eee eee eeeesseeeeeeceeeeeeeseeeees 4 13 Using IF THEN Rules in Fuzzy Inference 00 eee cesses eeeteeeeeeeeeeeees 4 15 Using Linguistic Variables in Defuzzification cee eee eeeeeseeeeeeteeneees 4 17 Chapter 5 Fuzzy Controllers Structure of a Fuzzy Controller oo eee ceeeseeseeeseeseceseeecesecseceseesesesesseseaeeeseaeesees 5 1 Closed Loop Control Structures with Fuzzy Controllers oo cece eee eeeeseeseeeeeees 5 2 I O Characteristics of Fuzzy Controllers 0 0 0 eee ceceseeseeeeeseceseeseeeaeeseeeseeseseeeeaeenaes 5 6 PID Control Toolkit User Manual vi ni com Contents Chapter 6 Design Methodology Design and Implementation Process Overview 0 ccceceseeseeseeeeeseeeseeseeeseeeeeesseneeaes 6 1 ACQUITINE Knowledge cscc6s esses ot e ER E E R 6 1 Optimizing OTe is ceo S E E E cis E 6 1 Optimizing Online sne tects A NE E E ER O RAER 6 2 Implementint ninna a A Gs ee a 6 2 Defining Linguistic Variables ersinnen orror PEE E EEEN A 6 2 Number of Linguistic TEMS isene eecesecesceseeeceseeseceeesseeeaeeseesaeeaeenseeaeenes 6 2 Standard Membership Functions 200 0 cec
72. gly 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 Instruments 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 co
73. gregation step calculates this adequacy as the degree of truth of 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 stee
74. h 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 project 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 NEI ZE1 and PO still set up the input variable vehicle position Because vehicle position must be composed of the five linguistic terms shown in Figure 4 6 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 th
75. he PID gains control shows the current updated parameters then choose Make Current Values Default from the Operate menu and then save the VI 3 16 ni com Chapter 3 Using the PID Software Figure 3 12 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 13 PID gains Lc pid params dat Figure 3 13 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 VI uses updated parameters National Instruments Corporation 3 17 PID Control Toolkit User Manual Chapter 3 Using the PID Software Using PID on FPGA Targets Use the PID FPGA Express VI to implement single channel or multi channel PID on a LabVIEW FPGA target 3 Note The PID FPGA Express VI is available only if you install both the PID Control Toolkit and the LabVIEW FPGA Module PID Control Toolkit User Manual The PID FPGA Express VI implements a fixed point PID algorithm on FPGA targets The PID algorithm features control output range and uses an integrator anti windup calculation to limit the effect of
76. he 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 3 8 ni com Chapter 3 Using the PID Software You can use the auto and manual control inputs to switch between manual and 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 PID Advanced 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 6 anual control Figure 3 6 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 Most of the PID VIs are polymorphic VIs for use in multipl
77. he overlapping regions of neighboring linguistic terms are important when you use linguistic variables to model engineering systems National Instruments Corporation 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
78. hip 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 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 A io Negative Zero Positive 4 Negative Zero Positive i 1 0 uo S uo 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 Rul Rule 1 IF x Negative THEN y Negative Inference Say Rule 2 IF x Zero THEN y Zero ase Rule 3 IF x Positive THEN y Positive Modified CoA 1 0 4 0 8 0 6 y 0 4 pe 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 xX gt 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 contin
79. ht Center Right Negative Negative Negative Negative Negative Eee Down Small Medium Medium Large Large Left Positive Negative Negative Negative Negative Small Small Medium Large Large L Positive Positive Negative Negative Negative a Left Up Medium Small Small Medium Large fo g Pe ai 6 Up Positive Positive Zer Negative Negative 5 Medium Medium Medium Medium 2 o Positive Positive Positive Negative Negative Fight Up Large Medium Small Small Medium Right Positive Positive Positive Positive Negative g Large Large Medium Small Small Positive Positive Positive Positive Negative Pignet Down 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 a a
80. in 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 Control VIs you can define unlimited sets of PID parameters for gain scheduling For each schedule you can run autotuning to update the PID parameters PID Algorithm Error Calculation PID Control Toolkit User Manual 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 18 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 erro
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82. ional Instruments Corporation 3 13 PID Control Toolkit User Manual Chapter 3 Using the PID Software Control Output Rate Limiting Sudden changes in control output are often undesirable or even dangerous for many control applications For example a sudden large 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 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 to specify 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 cloc
83. k has a resolution of 1 ms therefore you should specify a dt value explicitly if the loop cycle time is less than 1 ms The PID Lead Lag VI PID Control Toolkit User Manual The PID Lead Lag VI uses 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 3 14 ni com Chapter 3 Using the PID Software 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 i
84. l IMPutS iisscssiienen aa nai 3 12 Gain Scheduling s sies aeiee inii ea en aee tes rE EE R E E 3 12 Control Output Rate Limiting ee eee ceeceeeeeeeseeseeesecseeesesseeeaeeeenaes 3 14 The PID Lead Lag VE iivis iccesstte tents acct alcetuabcenes evactlevenbeaeestnceteecaentectees vec ieee 3 14 Converting Between Percentage of Full Scale and Engineering Units 3 15 Using the PID Autotuning VI and the Autotuning Wizard ee 3 15 Using PID on FPGA Targets ccccis cise cs sescacks ec susteliscasstbadecsg Septieesk Sovestased cdeasdesessapenssceseass 3 18 Implementing a Single Channel PID on FPGA Targets eee 3 19 Implementing a Multi Channel PID on FPGA Targets n se 3 19 Initialization Loop on the Host VI uu eee ceeeeeeeeeseeeeeeeeeneeeees 3 20 Processing Loop on the Host V1 eee eeeeseeseceeeseeeseeeeseeeeeeees 3 20 Using PID with DAQ Devices issiimti einean N EEA sebeetuleesunes E ea 3 21 Software Timed DAQ Control Loop ss sssessesesssrssesresesresesresresesesresrsresrssesresrs 3 22 Implementing Advanced DAQ VIs in Software Timed DAQ Control Eeto n AEE E 3 23 Hardware Timed DAQ Control Loop sssssssssessssesssrsrrssseesresrsresresrsresrssrsresrsrese 3 24 Chapter 4 Overview of Fuzzy Logic What is Fuzzy LOIC issen n aa e E AOE E EA EEEE aN 4 1 Typesof Uncertainty mtra E R E R E EAE ise aes 4 2 Modeling Linguistic Uncertainty with Fuzzy Sets eeseesesesesessesreresrsrrsresrsresreereeesres 4 2 Linguistic Variables and T
85. l number to which to apply the new parameter values Figure 3 15 shows an example of a processing loop PID Control Toolkit User Manual 3 20 ni com Chapter 3 Using the PID Software Processing Loo True Y dex Array Unbundle By Name p PID gains x 2 8 pom PID gains x 2 8 output range Sty or z setpoint Ae Not Equal setpoint Lv a Replace Array Subset a errr zarra EEE EEEEEEEE eer ieee LEE LEE EEE EEE EEE EEEEEEEEEEEEEEEEEEEEEEEEEEEEEE EEE EEEEEEEEEEEEEEEEEEEEEEEEEEEEEOEEOEEXEEIEEEEEH a Read Write Control Invoke Method Invoke Method Eetpoint Bundle By Name b configuration FIFO Read Wait on IRQ Trier LH setpoint b apply configuration 1024 p Number of Elements EH IRO Number s PID gains x 2 6 PID gains x 26 pa channels to reset Timeout ms b Timeout ms E mas ly output range p f apply reset s Data gt Timed Out butput range channel index Count usec Elements Remaining TRQ S Asserted v ea f Bol pas to Update ly configuration toreset Jf Initialize Array ly reset s p EIE E EE en earner plit Number setpoint Output PY ount uSec To Word Integer e a Figure 3 15 Processing PID Paramete
86. le 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 is a preemptive multitasking operating system other running applications can affect the loop speed Figure 3 17 Software Timed DAQ Control Loop with Advanced Features National Instruments Corporation 3 23 PID Control Toolkit User Manual Chapter 3 Using the PID Software Hardware Timed DAQ Control Loop PID Control Toolkit User Manual Figure 3 18 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 AO pcan rate Kscans sec Real time Figure 3 18 Hardware Timed DAQ Control Loop With each loop iteration the AI SingleScan VI returns one scan of data 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 1 ms in this example the software falls behind the hardw
87. le Vehicle Orientation B and Its Linguistic Terms National Instruments Corporation 4 9 PID Control Toolkit User Manual Chapter 4 Overview of Fuzzy Logic ufo Negative Negative Negative Zero Positive Positive Positive Large Medium Small Small Medium Large 1 0 0 8 0 6 0 4 0 2 0 0 a 30 0 25 0 20 0 15 0 10 0 5 0 0 0 5 0 100 15 0 20 0 25 0 30 0 g 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 Rig
88. ller performance you must first create your control application and determine PID parameters that produce stable control of the system You can develop the control application using either the PID VI the PID Gain Schedule VI or the PID Autotuning VI Because the PID Autotuning VI has input and output consistent with the other PID VIs you can replace any PID VI with it The PID Autotuning VI has several additional input and output values to specify the autotuning procedure The two additional input values are autotuning parameters and autotune The autotuning parameters input 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 National Instruments Corporation 3 15 PID Control Toolkit User Manual Chapter 3 Using the PID Software PID Control Toolkit User Manual 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 information about the autotuni
89. lt ling variables ANTECEDENCE define lt ling terms edit NE1 1 0 0 8 0 6 0 4 0 2 0 0 1 0 left bottom left top right top right bottom 1 00 M ZE1 PO1 LTT Teh 0 8 0 20 od 0 20 i Figure 7 3 Plausibility Checking and Point Slider Movement In the truck maneuvering example in the Rule Based Systems section 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 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 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 inl Figure 7 4 shows the dialog box Click the OK button 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 E Rename Ling Variable 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 v
90. 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 singleton 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 Chapter 5 Fuzzy Controllers Negative Zero Positive NL NS ZE PS PL ii 1 0 i 1 0 u x 0 8 u y 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 A Negative Zero Positive Rule Input x Base Negative Zero Positive g 08 0 6 i Negative NL NS ZE 0 4 z 0 2 Zero NS ZE PS
91. ments Corporation 4 7 Figure 4 5 Condition Vehicle Position x and Orientation B Action Steering Angle You can then use IF THEN rules such as IF lt situation 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 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
92. mpensation 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 have a little less of one quantity This is exactly what the y operator also called the compensatory AND can model Refer to the Related Documentation section of this manual 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 6 8 ni com Chapter 6 Design Methodology 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 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 nev
93. n 7 17 PID Control Toolkit User Manual Chapter 7 Using the Fuzzy Logic Controller Design VI As soon as the characteristic calculation completes LabVIEW displays the characteristic curve in the Input Output Characteristic display as shown in Figure 7 14 43 inp ut Output Characteristic yehicle position vehicle orientation E jo 0 0 10 0 90 0 270 0 15 Rule DoS 1 00 1 00 IF vehicle position center 1 00 AND vehicle orientation left down 1 00 THEN steering angle NegMed v min to max A A controlled result steering angle _ ax to min No Points 1 i T T T i i 20 3 0 40 50 60 70 80 90 10 0 16 67 vehicle position Cursor incr 0 50 characteristic of selected ling variable vehicle position is Hl displayed others are constant min to max 5 0 16 7 Figure 7 14 Controller Characteristic Displayed 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 input situation at each cursor position The Input Output Characteristic panel displays the current input values and controller output value PID Control Toolkit User Manual 7 18 ni com Chapter 7 Using the Fuzzy Logic Controller Design VI The Active Rules display shows all active rules within the input situation determined by the cursor position including the degree of truth for each ant
94. n 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 threshold 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 LIT A 1 0 0 8 Low Normal Raised High Fever 0 6 0 4 0 2 0 0 95 0 L gt 96 8 98 6 100 4 102 2 104 0 105 8 107 6 109 4 TPF 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 T
95. nd Terms i IF steering angle zero THEN conclusions Linguistic Level Fuzzification 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 Q 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 maneuveri
96. nd 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 A weighting value ranging from 0 to 1 that is applied to each rule in the rule 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 G 2 ni com derivative kick deviation downstream loop EGU expert F FC feedback control feedback loop fuzzification fuzzy inference fuzzy set fuzzy set theory National Instruments Corporation G 3 Glossary 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 Any departure from a desired value or expected value or pattern 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 controlling the process through experience Flow controller Control in which a measured varia
97. ndition 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 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 A function that defines degree of membership to the fuzzy set over a defined universe of discourse of the variable parameter 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 output from travelling beyond a 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 PID Control Toolkit User Manual Glossary P P P controller partial membership PC PD PD controller PI PI controller PID PID control PID controller process gain K process variable PV proportional action proportional band PB PID Control Toolkit User Manual Proportional
98. ng algorithm The PID 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 and 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 11 shows one possible implementation of the PID 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 11 Updating PID Parameters Using a Shift Register Figure 3 12 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 t
99. ng situation in which the vehicle position x is 5 1 m and the vehicle orientation B is 70 Left Right ux A Left Center Center Center Right 1 0 0 8 0 6 0 4 0 2 0 0 a 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 10 0 m Current Vehicle Position x 5 1 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 with a degree of 0 0 left center with a degree of 0 0 center with a degree of 0 8 right center with a degree of 0 1 right with a degree of 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 LB A 1 0 U Left o Right Left Down Left Up Right Up Right Down 0 8 0 6 0 4 0 2 0 0 100 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
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101. nt 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 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 or 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
102. ntions This manual describes the LabVIEW PID Control Toolkit The PID Control Toolkit includes VIs for Proportional Integral Derivative PID and Fuzzy Logic control You can use these VIs with input output I O functions such as data acquisition DAQ to implement control of physical processes 3 bold italic monospace 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 Italic text denotes variables linguistic terms emphasis a cross reference or an introduction to a key concept Italic text also denotes text that 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 functi
103. ntrol 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 control strategies 3 1 controller output 2 3 conventions used in this manual ix Corripio A B x D DAQ hardware with PID hardware timed DAQ control loop 3 24 software timed DAQ control loop 3 22 software timed DAQ control loop with advanced DAQ functions 3 23 designing control strategies 3 1 manual tracking techniques 3 4 closed loop tuning 3 4 open loop tuning 3 5 step test 3 5 ultimate gain 3 4 National Instruments Corporation l 1 setting timing 3 2 diagnostic tools NI resources A 1 documentation conventions used in this manual ix NI resources A 1 related documentation x drivers NI resources A 1 E error calculation 2 2 examples NI resources A 1 F FPGAs 3 18 G gain scheduling 2 4 H Hagglund T x Hang C C x help technical support A 1 Ho W K x instrument drivers NI resources A 1 K KnowledgeBase A 1 PID Control Toolkit User Manual Index National Instruments support and services A 1 Nichols N B x nonlinear adjustment of integral action 2 2 2 6 0 output limiting 2 3 P partial derivative action 2 2 PID Algorithm calculating controller action 2 1 controller output 2 3 error calculation 2 2 nonlinear adjustment of integral a
104. o 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 Input Output Characteristic test facility starts with a front panel similar to the one shown in Figure 7 12 fej Input Output Characteristic vehicle position vehicle orientation y S w age w 0 0 10 0 90 0 min to max A maxto min 7 Print steering angle No Points 20 amp 1 j I 1 0 7 0 80 90 10 0 30 00 QUIT 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 Input Output 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 PID Control Toolkit User Manual 7 16 ni com Chapter 7 Using the Fuzzy Logic Controller Design VI To set up these test conditions first enter the desired test value into the parameter con
105. ogic Controller Design VI front panel EE Fuzzy Logic Controller Design File Edit Test Help D New Open D Description controller untitled developer unknown date Friday June 02 2006 time 12 53 PM 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 PID Control Toolkit User Manual 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 LabVIEW 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 c 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
106. ons operations filenames and extensions National Instruments Corporation ix PID Control Toolkit User Manual About This Manual Related Documentation 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 FPGA Module documentation e LabVIEW Real Time Module documentation e LabVIEW Control Design and Simulation Module documentation 3 Note The following resources offer useful background information on the general concepts discussed in this documentation These resources are provided for general informational purposes only and are not affiliated sponsored or endorsed by National Instruments The content of these resources is not a representation of may not correspond to and does not imply current or future functionality in the PID Control Toolkit or any other National Instruments product PID Control Toolkit User Manual Astr m K J and T Hagglund 1984 Automatic tuning of simple regulators In Proceedings of IFAC 9th World Congress Budapest 1867 72 Astr m K J T Hagglund C C Hang and W K Ho 1993 Automatic tuning and adaption for PID controllers a survey Control Engineering Practice 1 669 714 Corripio A B 2000 Tuning of Industrial Control Systems 2d ed Raleigh North Carolina ISA Shinskey F G 1988 Process Control Systems Applicaton Design an
107. or 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 the fuzzy membership functions and controller rule base The Fuzzy Logic Controller Design VI is a stand alone VI with a user interface you can use to define all controller and expert system components completely and save all of the parameters of the defined controller to one controller data file 1 2 ni com Chapter 1 Overview of the PID Control Toolkit You use two additional VIs to implement the fuzzy controller in your LabVIEW application The Load Fuzzy Controller VI loads all the parameters of the fuz
108. ormalized 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 shape and S type membership function shapes Z type A type I type S type Figure 6 1 Shapes of Standard Membership Functions National Instruments Corporation 6 3 PID Control Toolkit User Manual Chapter 6 Design Methodology 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 y 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 pt 1 Typical value for center is 5 0 Ix Left Right H A Left Center Center Center Right 1 0 y 0 8 0 6 0 4 0 2 0 0 gt 0 0 1 0 2 0 3 0 4 0 5 0 6
109. ormation about disturbing the loop and determining the response from the graph Refer to Corripio 1990 as listed in the Related Documentation section of this manual 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 changes 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 PID Control Toolkit User Manual 3 4 ni com Chapter 3 Using the PID Software 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 PB Reset Rate
110. 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 controller out input value 4 PBL Figure 8 18 Test Fuzzy Control VI Block Diagram Example 3 Note You can connect the inputs and the controller output directly to the outputs and inputs of the DAQ VIs available in LabVIEW in order to use real process data from sensors instead of the values from the panel controls as shown in Figures 8 16 and 8 17 National Instruments Corporation 8 15 PID Control Toolkit User Manual Technical Support and Professional Services Visit the following sections of the award winning National Instruments Web site at ni com for technical support and professional services National Instruments Corporation Support Technical support resources at ni com support include the following Self Help Technical Resources For answers and solutions visit ni com support for software drivers and updates a searchable KnowledgeBase product manuals step by step troubleshooting wizards thousands of example programs tutorials application notes instrument drivers and so on Registered users also receive access to the NI Discussion Forums at ni com forums NI Applications Engineers make sure every question submitted online receives an answer Standard Service Program Membership this program entitles member
111. 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 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 TI 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 edit the fuzzy logic controller programmatically LabVIEW automatically calls the Fuzzy Set Editor when you create a new fuzzy logic project Figure 7 1 displays the Fuzzy L
112. ple 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 optimal 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 Process Set Point Values gt X X X A Rule Base D IF AND THEN by IF AND THEN IF AND THEN P gt Command PID D Fuzzification Fuzzy Inference Defuzzification a Measured Values y hve 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 Fuzzy Controller Process Set Point Values Rule Base IF AND THEN IF AND THEN D IF AND THEN J AA Fuzzification Fuzzy Inference Defuzzification
113. polymorphic VIs included with the PID Control Toolkit operate in the same manner Setpoint Ramp Generation The PID Setpoint Profile VI can generate a profile of setpoint values over time for a ramp and soak type PID application For 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 7 setpoint profile setpoint profile graph F J 0 time s setpoint 100 0 i f Yo 000 0 00 20 0 time s setpoint 60 0 t t o H5 o00 Hf100 00 40 0 time s setpoint Yo 000 Yo 00 20 0 time s setpoint 0 0 ni 10 000 10 00 4 Pi Figure 3 7 Ramp Setpoint Profile PID Control Toolkit User Manual 3 10 ni com Chapter 3 Using the PID Software A ramp and hold setpoint profile also can have two successive array values with the same setpoint value as shown in Figure 3 8 setpoint profile setpoint profile graph time s setpoint 100 0 40 00 0 00 ad ad time s setpoint Hf5 o00 Hf100 00 60 0 Setpoint 40 0 time
114. r PID Control Normal Controller K T Ta P 0 447 t PI 0 4T t 5 33T PID 0 53T T 4 07 0 87 Table 2 6 Tuning Formula under PI or PID Control Slow Controller K Ti Ta P 0 26T T PI 0 24T t 5 337 PID 0 32T t 4 0T 0 8T 3 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 Toolkit 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 Surge Tank Figure 3 1 Block Diagram Repres
115. r 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 of 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
116. riables ANTECEDENCE define v NE1 lt ling terms edit NE1 ZE1 PO1 1 0 0 8 0 6 0 4 0 2 0 0 7 1 I i 1 Go TO 20 ssi 4 0 f 6 0 LULLLBEEI left bottom left top right top right bottom 0o00 S oc S oo 5 00 F 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 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 VIs automatically call the Rulebase Editor to create a rule base Because you still have to do additional work on the rule base you should add and set up all linguistic terms according to the application example You do not need to work wit
117. ring angle includes the following linguistic terms and their corresponding 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 fu
118. rithms 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 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 PVk 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
119. rporation 4 3 PID Control Toolkit User Manual Chapter 4 Overview of Fuzzy Logic u T i Membership patients with a high fever 1 0 0 8 0 6 a 0 4 0 2 0 0 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 certai
120. rs on the Host VI Refer to the Template Multichannel PID 1lvproj in the labview examples control pid fpga 11b Template Multichannel directory for an example of a multi channel PID implementation on an FPGA target 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 nye Note Refer to the labview examples daq solution control 11b directory for additional examples of control with DAQ VIs National Instruments Corporation 3 21 PID Control Toolkit User Manual Chapter 3 Using the PID Software Software Timed DAQ Control Loop Figure 3 16 illustrates the basic elements of software control The model assumes you have a plant or 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 Kms Figure 3 16 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 yo
121. s less than 1 ms Converting Between Percentage of Full Scale and Engineering Units As described above the default setpoint process variable 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 Autotuning VI and the Autotuning Wizard To use the Autotuning Wizard to improve your contro
122. s to direct access to NI Applications Engineers via phone and email for one to one technical support as well as exclusive access to on demand training modules via the Services Resource Center NI offers complementary membership for a full year after purchase after which you may renew to continue your benefits For information about other technical support options in your area visit ni com services or contact your local office at ni com contact Training and Certification Visit ni com training for self paced training eLearning virtual classrooms interactive CDs and Certification program information You also can register for instructor led hands on courses at locations around the world System Integration If you have time constraints limited in house technical resources or other project challenges National Instruments Alliance Partner members can help To learn more call your local NI office or visit ni com alliance A 1 PID Control Toolkit User Manual Appendix A Technical Support and Professional Services If you searched ni com and could not find the answers you need contact your local office or NI corporate headquarters Phone numbers for our worldwide offices are listed at the front of this manual You also can visit the Worldwide Offices section of ni com niglobal to access the branch office Web sites which provide up to date contact information support phone numbers email addresses and current events PID
123. sses 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 National Instruments Corporation 3 3 PID Control Toolkit User Manual Chapter 3 Using the PID Software 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 simulation VIs to compare them For different processes one method might be easier or more accurate than another For 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 inf
124. st 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 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 stron
125. st 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 PID Gain Schedule VI selects and 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 3 12 ni com Chapter 3 Using the PID Software 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 10 the Gain Scheduling Input example uses the setpoint value as the gain scheduling variable with a default range of 0 to 100 Table 3 3 summarizes PID parameters 100 00 Figure 3 10 Gain Scheduling Input Example Table 3 3 PID Parameter Ranges Range Parameters 0 lt SP lt 30 Kc 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 Nat
126. statements You can use fuzzy logic to implement a linguistic control strategy that is capable of using fuzzy sets to model uncertain linguistic 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 4 8 ni com Chapter 4 Overview of Fuzzy Logic Figures 4 6 4 7 and 4 8 show membership functions for the inputs and output of the truck controller Left Right ux A Left Center Center Center Right 1 0 0 8 0 6 0 4 0 2 0 0 gt 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 10 0 x m Vehicle Position Figure 4 6 Linguistic Variable Vehicle Position x and Its Linguistic Terms U u B Left P Right A Left Down LeftUp Right Up Right Down 1 0 0 8 0 6 0 4 0 2 0 0 gt 100 50 0 0 50 100 150 200 250 Bie Vehicle Orientation Figure 4 7 Linguistic Variab
127. t 0 i 4 Signal x t p N 8 0 Pots 6 0 d nput Signal xf t 5 407 a wis KONG 20 oa Se re ene 4 0 0 Le Mf 2 2 0 q I 4 0 4 F i 6 0 5 TU gt it gt lt TD 8 0 4 TU TH TD 50 00 10 00 20 00 l 0 0 q I I I I 0 10 20 30 40 50 60 70 80 90 100 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 PID Control Toolkit User Manual 8 2 ni com Note You can Chapter 8 Implementing a Fuzzy Controller signal yields the dash dotted curve dx t dt from which you can derive the time intervals TU up TH hold and TD down When TS signal represents 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 use existing functions or functions you can write in LabVIEW to execute all the signal processing steps described above a Fuzzy Set Editor TH TS v a specify v lt ling variables ANTECEDENCE define SA small ive lt ling terms edit was small
128. t is possible to consider only the error tendency when the error becomes small Chemical industry and process technology often use the fuzzy controller with underlying 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 However 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 often can 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 Fuzzy Controller Process Set Point Reference Values f 1 Bona Magnitude IF AND THEN Signals T IF AND THEN p PID IF AND THEN p Dy he gt Pip n gt z Fuzzification Fuzzy Inference Defuzzification Measured Values PID Control Toolkit User Manual Figure 5 4 Fuzzy Controller with Underlying PID Control Loops The next exam
129. tem 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 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 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 National Instruments Corporation 3 7 PID Control Toolkit User Manual Chapter 3 Using the PID Software The PID Advanced PID Control Toolkit User Manual Fault Protection If the PID VI receives an invalid input such as NaN Not a Number
130. termine the linguistic controller output The use of multiple controllers and or multiple process variables in which the connections may change dynamically depending on process conditions A normalized membership function with an infinitely small width A singleton is used to model a crisp value with a fuzzy set PID Control Toolkit User Manual Glossary SP span stochastic uncertainty T time constant T transient overshoot trapezoidal integration W windup area PID Control Toolkit User Manual Setpoint An input variable which sets the desired value of the controlled process variable The algebraic difference between the upper and lower range values The degree of uncertainty of the occurrence of a given future nondeterministic event 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 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 G 8 ni com Index A AND operator 4 10 Astrom K J x Autotuning Algorithm tuning formulas 2 8 PI control fast 2 9 PI co
131. 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 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 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 PID Control Toolkit User Manual 4 2 ni com Chapter 4 Overview of Fuzzy Logic However you cannot use conventional dual logi
132. the integral action during transients The PID algorithm also features bumpless controller output for PID gain changes The PID FPGA Express VI represents the PID proportional integral and derivative gains as signed fixed point numbers with word length 16 and integer word length 8 Given the proportional gain K integral time T minutes and derivative time T4 minutes respectively this Express VI normalizes the gains according to the following formulas K K KXT i T x 60 _ K X Ty x 60 2 T S Ky where T is the sampling period in seconds at which the PID loop runs The PID controller compares the setpoint SP to the process variable PV at a given sample instant k and produces the error e which is defined as the following e k SP k PV k The PID controller operates on this error and tries to drive it to zero The PID controller produces an output u k also known as a control action according to the following formula u k u k uk u k 3 18 ni com Chapter 3 Using the PID Software where u k is the control output due to the proportional term u k is the control output due to the integral term and u k is the control output due to the derivative term The PID controller calculates these control outputs according to the following formulas u k K e k k gt e i e i 1 uk KK a i 1 ug k K KLPV k PV k 1 Finally the PID controller limits the outp
133. 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 LabVIEW PID Control Toolkit to develop a control application or modify the examples provided with the toolkit Use the PID VIs to 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 FError 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 Moulti loop cascade control e Feedforward control e Override minimum maximum selector control e Ratio bias control You can combine these PID VIs with LabVIEW math and logic functions to create block diagrams for real control strategies The PID VIs use LabVIEW functions and library sub VIs 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 f
134. trol block for vehicle orientation as shown in Figure 7 13 bi Input Output Characteristic yehicle position yvehicle orientation 0 00 amp 90 00 0 0 10 0 90 0 270 0 C min to max A steering angle Maxtomin 30 0 Print 20 0 No Points 10 0 20 E 0 0 10 0 K 20 0 30 0 1 CO Snor S205 0 40 S03 e 07 er 0 6 0 9 0 S10 0 30 00 5 QUIT min to max 0 2 1 0 Figure 7 13 Entering a Test Condition into a Parameter Control Block of the Input Output Characteristic Front Panel Then click the Run button to 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 ys 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 also can cause LabVIEW to calculate the controller characteristic twice National Instruments Corporatio
135. u 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 quickly 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
136. 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 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 Ga
137. uous controller characteristic functions especially within those intervals of the input values in which two or more rules are active simultaneously This behavior results from the averaging character of the defuzzification methods described in Chapter 4 Overview of Fuzzy Logic PID Control Toolkit User Manual 5 18 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 A ao A 10 ney 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 eo 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 A 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 0 8 1 0 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
138. ur 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 the LabVIEW Help available by selecting Help Search the LabVIEW Help for more information about timing control loops PID Control Toolkit User Manual 3 22 ni com 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 16 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 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 possib
139. ure 8 10 Fuzzy Controller VI You can connect the input signals TH TS and TU TD TS to the Fuzzy Controller VI inputs in1 and in2 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 8 8 ni com Chapter 8 Implementing a Fuzzy Controller 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 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 Figure 8 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 FuzzyTruck fc which represents the fuzzy controller you designed earlier National Instruments Corporation 8 9 PID Control Toolkit User Manual Chapter 8 Implementing a Fuzzy Controller
140. ut within an output range that you specify If u k 2 yas u k Umax If u k S U miw u k Umin implementing a Single Channel PID on FPGA Targets To configure the PID FPGA Express VI for a single channel implementation enter 1 in the Number of channels control on the configuration dialog box For single channel PID implementations any changes you make to the PID parameters on the host VI take effect immediately on the FPGA target Refer to the Using Discrete PID cRIO lvproj inthe labview examples control pid fpga 11b CompactRIO0 directory for an example of a single channel PID implementation on an FPGA target You also can refer to the Using Discrete PID R Series lvproj inthe labview examples control pid fpga 11b R Series directory Implementing a Multi Channel PID on FPGA Targets To configure the PID FPGA Express VI for a multi channel implementation enter a number greater than 1 in the Number of channels control on the configuration dialog box To handle the values for each channel the host VI can include an initialization loop and processing loop which you can use to modify parameters or reset channels The following sections provide information about these loops National Instruments Corporation 3 19 PID Control Toolkit User Manual Using the PID Software Initialization Loop on the Host VI The initial parameter values you enter on the configuration dialog box for the PID FPGA Express VI set the initial values
141. y algorithms to optimize your system National Instruments Corporation 6 1 PID Control Toolkit User Manual Chapter 6 Design Methodology Optimizing Online Implementing With 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
142. y 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 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 can 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 A 10 0 8 0 6 0 4 0 2 0 0 0 1 scale xss Ty F 354 input signal def E EEUN IE m se ee 19 30 40 50 60 70 80 90 100 signal meee TH signal min S 1 1 1 1 i 2 1 1 1 1 1 50 60 70 80 90 100 TS OSS Sst ao
143. ype 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 five circled base points xi yi x1 x2 x3 x4 x5 y1 y2 y3 y4 y5 ii 1 0 ji 1 0 no 98 wy 8 0 6 0 6 0 4 0 4 0 2 0 2 Rule 1 IF x x1 THEN y y1 Max Min Rule Rule 1 1F x x2 THEN y y2 Inference Base Rule 2 IF x x3 THEN y y3 Rule 3 IF x x4 THEN y y4 Modified Rule 3 IF x x5 THEN y y5 CoA x5 y5 a6 x5 y5 A 0 8 0 6 y x4 y4 0 4 a 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 e Figure 5 16 Fuzzy Controller for a Given I O Characteristic PID Control Toolkit User Manual 5 22 ni com Chapter 5 Fuzzy Controllers To use a single input fuzzy controller to reproduce the given characteristic use five linguistic terms each for the input and output quantities naming 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
144. zy controller previously saved by the Fuzzy Logic 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 PID Algorithms This chapter explains the PID advanced PID and autotuning algorithms 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 Algo
145. zzy sets to form a crisp real value A solution to this problem 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 National Instruments Corporation 4 17 PID Control Toolkit User Manual Chapter 4 Overview of Fuzzy Logic 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 ulo A Negative Large 1 0 Negative Medium Positive Large Positive Medium Positive Small Negative Small oe T Validity of Rule 1 0 8 0 6 0 4 0 2 Validity of Rule 2 0 0 30 0 25 0 20 0 a 3 10 0 15 0 5 0 0 0 5 0 10 0 15 0 20 0 25 0 Defuzzified Result 9 3 30 0 f Steering Angle PID Control Toolkit User Manual Figure 4 13 Defuzzification According to Center of Ar

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