Fuzzy Logic Control Lect 6 Fuzzy PID Controller

Fuzzy Logic Control Lect 6 Fuzzy PID Controller Basil Hamed Islamic University of Gaza

Contents PID Fuzzy Example Supervisory PID Fuzzy Control Basil Hamed 2

PID § PID: Proportional Integral Derivative § More than 90% of controllers used in industries are PID or PID type controllers (the rest are PLC) § PID controllers are simple, reliable, effective § For lower order linear system PID controllers have remarkable set-point tracking performance and guaranteed stability. Basil Hamed 3

Convectional PID Controller Basil Hamed 4

Convectional PID Controller § Time Domain § Frequency Domain Basil Hamed 5

PID Controller Basil Hamed 6

PID Controller Time Domain Frequency Domain Basil Hamed 7

A comparison of different controller types Basil Hamed 8

General tips for designing a PID controller Obtain an open-loop response and determine what needs to be improved Add a proportional control to improve the rise time Add a derivative control to improve the overshoot Add an integral control to eliminate the steady-state error Adjust each of Kp, Ki, and Kd until you obtain a desired overall response. You can always refer to the table shown to find out which controller controls what characteristics you do not need to implement all three controllers (proportional, derivative, and integral) into a single system, if not necessary. Keep the controller as simple as possible. Basil Hamed 9

General tips for designing a PID controller Basil Hamed 10

Tuning of PID Controller There are methods for tuning PID controllers, for example: § Hand-Tuning, § Ziegler–Nichols Tuning, § Optimal Design, § Pole Placement Design, and § Auto-Tuning (A° stro¨m and H¨agglund 1995). There is much to gain, if these methods are carried forward to fuzzy controllers. Basil Hamed 11

A simple example for PID control • We plot y(t) for step reference r(t ) with • • • P controller PID controller Basil Hamed 12

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Types of Fuzzy Controllers: - Direct Controller The Outputs of the Fuzzy Logic System Are the Command Variables of the Plant: Fuzzy Rules Output Absolute Values ! Slide 16

Types of Fuzzy Controllers: - PID Adaptation Fuzzy Logic Controller Adapts the P, I, and D Parameter of a Conventional PID Controller: The Fuzzy Logic System Analyzes the Performance of the PID Controller and Optimizes It ! Slide 17

Types of Fuzzy Controllers: - Fuzzy Intervention Fuzzy Logic Controller and PID Controller in Parallel: Intervention of the Fuzzy Logic Controller into Large Disturbances ! Slide 18

Supervisory Control Systems Most controllers in operation today have been developed using conventional control methods. There are, however, many situations where these controllers are not properly tuned and there is heuristic knowledge available on how to tune them while they are in operation. There is then the opportunity to utilize fuzzy control methods as the supervisor that tunes or coordinates the application of conventional controllers. Basil Hamed 19

Fuzzy PID Control Because PID controllers are often not properly tuned (e. g. , due to plant parameter variations or operating condition changes), there is a significant need to develop methods for the automatic tuning of PID controllers. While there exist many conventional methods for PID auto-tuning, here we will strictly focus on providing the basic ideas on how you would construct a fuzzy PID auto-tuner. Basil Hamed 20

Fuzzy PID Control Basil Hamed 21

Fuzzy PID Control Fuzzy PID controllers are similar to PID controllers under certain assumptions about the shape of the membership functions and the inference method (Siler and Ying 1989, Mizumoto 1992, Qiao and Mizumoto 1996, Tso and Fung 1997). A design procedure for fuzzy controllers of the PID type, based on PID tuning, is the following: Procedure Design fuzzy PID 1. Build and tune a conventional PID controller first. 2. Replace it with an equivalent fuzzy controller. 3. Fine-tune it. Basil Hamed 22

Fuzzy PID Control The procedure is relevant whenever PID control is possible, or already implemented. Our starting point is the ideal continuous PID controller The control signal u is a linear combination of the error e, its integral and its derivative. The parameter Kp is the proportional gain, Ti is the integral time, and Td the derivative time. Basil Hamed 23

Fuzzy PID Control To implement fuzzy PID control on the computer, one first needs a digital version of analog one. Discretization of PID controller: To digitize the analog controller, the following can be used: Basil Hamed 24

Fuzzy PID Control In digital controllers, the equation must be approximated. Replacing the derivative term by a backward difference and the integral by a sum using rectangular integration, and given a constant – preferably small – sampling time Ts , the simplest approximation is, Index n refers to the time instant. By tuning we shall mean the activity of adjusting the parameters Kp, Ti , and Td in order to achieve a good closed-loop performance. Basil Hamed 25

Example Basil Hamed 26

Example Basil Hamed 27

Example Basil Hamed 28

Example Basil Hamed 29

Example Simulation result are shown , where red is system output, and green is error signal Basil Hamed 30

Supervisory Control Systems § Human operators in the process industry are faced with nonlinear and time-varying behaviour, many inner loops, and much interaction between the control loops. Owing to sheer complexity it is impossible, or at least very expensive, to build a mathematical model of the plant, and furthermore the control is normally a combination of sequential, parallel, and feedback control actions. § Operators, however, are able to control complicated plants using their experience and training, and thus fuzzy control is a relevant method within supervisory control. Basil Hamed 31

Supervisory Control Systems Supervisory control is a multilayer (hierarchical) controller with the supervisor at the highest level, as shown in Figure Basil Hamed 32

Supervisory Control Systems § The supervisor can use any available data from the control system to characterize the system’s current behavior so that it knows how to change the controller and ultimately achieve the desired specifications. § In addition, the supervisor can be used to integrate other information into the control decision-making process. It can incorporate certain user inputs, or inputs from other subsystems. § Supervisory control is a type of adaptive control since it seeks to observe the current behavior of the control system and modify the controller to improve the performance Basil Hamed 33

Supervisory Control Systems For example, in an automotive cruise control problem, inputs from the driver (user) may indicate that she or he wants the cruise controller to operate either like a sports car or more like a sluggish family car. The other subsystem information that a supervisor could incorporate for supervisory control for an automotive cruise control application could include data from the engine that would help integrate the controls on the vehicle (i. e. , engine and cruise control integration). Given information of this type, the supervisor can seek to tune the controller to achieve higher performance operation or a performance that is more to the liking of the driver. Basil Hamed 34

Supervisory Control Systems Conceptually, the design of the supervisory controller can then proceed in the same manner as it did for direct fuzzy controllers: either via the gathering of heuristic control knowledge or via training data that we gather from an experiment. The form of the knowledge or data is, however, somewhat different than in the simple fuzzy control problem. Basil Hamed 35

Supervisory Control Systems the type of heuristic knowledge that is used in a supervisor may take one of the following two forms: 1. Information from a human control system operator who observes the behavior of an existing control system (often a conventional control system) and knows how this controller should be tuned under various operating conditions. 2. Information gathered by a control engineer who knows that under different operating conditions controller parameters should be tuned according to certain rules. Basil Hamed 36

High-level control configurations Fuzzy controllers are combined with other controllers in various configurations. The PID block consists of independent or coupled PID loops, and the fuzzy block employs a high-level control strategy. Normally, both the PID and the fuzzy blocks have more than one input and one output. Basil Hamed 37

Supervisory Fuzzy Control There are four types of Fuzzy supervisory control: 1. Fuzzy replaces PID 2. Fuzzy replaces operator 3. Fuzzy adjusts PID parameters 4. Fuzzy adds to PID control Basil Hamed 38

Fuzzy replaces PID In this configuration, the operator may select between a high-level control strategy and conventional control loops. The operator has to decide which of the two most likely produces the best control performance. Basil Hamed 39

Fuzzy replaces operator This configuration represents the original high level control idea, where manual control carried out by a human operator is replaced by automatic control. Normally, the existing control loops are still active, and the high-level control strategy makes adjustments of the controller set points in the same way as the operator does. Again it is up to the operator to decide whether manual or automatic control will result in the best possible operation of the process, which, of course, may create conflicts. Basil Hamed 40

Fuzzy replaces operator Basil Hamed 41

Fuzzy adjusts PID parameters In this configuration, the high-level strategy adjusts the parameters of the conventional control loops. A common problem with linear PID control of highly nonlinear processes is that the set of controller parameters are satisfactory only when the process is within a narrow operational window. Outside this, it is necessary to use other parameters or set points, and these adjustments may be done automatically by a high-level strategy. Basil Hamed 42

Fuzzy adjusts PID parameters Basil Hamed 43

Fuzzy adds to PID control Normally, control systems based on PID controllers are capable of controlling the process when the operation is steady and close to normal conditions. However, if sudden changes occur, or if the process enters abnormal states, then the configuration may be applied to bring the process back to normal operation as fast as possible. For normal operation, the fuzzy contribution is zero, whereas the PID outputs are compensated in abnormal situations, often referred to as abnormal situation management (ASM). Basil Hamed 44

Fuzzy adds to PID control Basil Hamed 45

Example Design of Self Tuning PID Controller Using Fuzzy Logic for DC Motor Speed International Journal of Social Science and Technology Vol. 2 No. 4; August 2017 DC Motor Mathematical Model Basil Hamed 46

Example The overall transfer function Basil Hamed 47

Example PID Controller (Ziegler-Nichols) PID controllers are tuned in terms of Kp, KI and KD. Ziegler-Nichols is a type of controller tuning. Basil Hamed 48

Example kp is then increased (from zero) until it reaches the ultimate gain ku, at which the output of the control loop has stable and consistent oscillations. ku and the oscillation period Tu are used to set the P, I, and D gains depending on the type of controller used Basil Hamed 49

Example Fuzzy Logic Controller Basil Hamed 50

Example Basil Hamed 51

Example Fuzzy-PID Controller Basil Hamed 52

Example Basil Hamed 53

Example Basil Hamed 54

Example Title Basil Hamed PID Fuzzy PID Peak Time . 0742 (s) . 25 . 29 % overshoot 48. 3 4. 5 0 Settling time . 571 . 36 . 2 Rise time . 03 . 15 . 11 55

Fuzzy PID Controllers Using FPGA Technique for Real Time DC Motor Speed Control Intelligent Control and Automation, 2011 Basil Hamed, Moayed Almobaied DC Motor Basil Hamed 56

Fuzzy PID Controllers Using FPGA Technique for Real Time DC Motor Speed Control Basil Hamed 57

Fuzzy PID Controllers Using FPGA Technique for Real Time DC Motor Speed Controllers Design: PID Controller It’s required to build a digital PID controller in the FPGA card. There are many approaches are available to convert from analogue to digital. In this proper we used the Tus- tin approach. The equation which represents the PID controller is: Basil Hamed 58

Fuzzy PID Controllers Using FPGA Technique for Real Time DC Motor Speed Control Field Programmable Gate Arrays (FPGAs) • FPGAs shown in Figure 5, stands for Field Programma- ble Gate Arrays are one type of programmable logic de - vices (PLDs). It is based on an integrated circuit that can be configured by the user in order to implement digital logic functions of varying complexities. • FPGAs can be very effectively used for control purposes in processes demanding very high loop cycle time. One of the funda- mental advantage of FPGA over DSP or other micro- processors is the freedom of programming parallelism Basil Hamed 59

Fuzzy PID Controllers Using FPGA Technique for Real Time DC Motor Speed Control Basil Hamed 60

Fuzzy PID Controllers Using FPGA Technique for Real Time DC Motor Speed Control Fuzzy Logic Controller “FLC” • FLC has been constructed Using VHDL and embedded Pico. Balze processor in FPGA. The block diagram for the FLC for the DC motor is shown in Figure 11. • FLC has two inputs, which are: Error (E) and the Error change (CE), and one output feeding to the plant speed register of the PWM. Basil Hamed 61

Fuzzy PID Controllers Using FPGA Technique for Real Time DC Motor Speed Control Figure 12 illustrates the method used in reaching the desired speed value. For example, at stage A the Error is positive (desired speed – actual speed) and the Change Error (Error - last Error) is negative, which mean that the response is heading in the right di- rection; hence, the FLC will go forward in this direction. Using the same criteria at stage B, the Error is negative and CE is big negative; hence, the response is heading in wrong direction so FLC will change its direction to enter Stage C, until reaching the desired speed. Basil Hamed 62

Fuzzy PID Controllers Using FPGA Technique for Real Time DC Motor Speed Control Basil Hamed 63

Fuzzy PID Controllers Using FPGA Technique for Real Time DC Motor Speed Control Fuzzy Logic Controller “FLC” Basil Hamed 64

Fuzzy PID Controllers Using FPGA Technique for Real Time DC Motor Speed Control Fuzzy-PID Controller A complete de- sign of the system is shown in Figure 19. The Fuzzy sets for the output: Kp, Ki, and Kd is shown in Figure 20, practically there are three different Fuzzy sets for these parameters. The inputs of the controller used are the error and change of error as presented in the previous section. Basil Hamed 65

Fuzzy PID Controllers Using FPGA Technique for Real Time DC Motor Speed Control Table 3 presents the base rules of Fuzzy-PID control- ler (Kp). Practically there are three base rules tables for Kp, Ki, and Kd Basil Hamed 66

Fuzzy PID Controllers Using FPGA Technique for Real Time DC Motor Speed Control Simulink block diagram for the Fuzzy-PID speed con- troller for DC motor is shown in Figure 21. Basil Hamed 67

Fuzzy PID Controllers Using FPGA Technique for Real Time DC Motor Speed Control Results Comparison Basil Hamed 68

Fuzzy PID Controllers Using FPGA Technique for Real Time DC Motor Speed Control All three controllers presented in this paper are implemented in hardware using the FPGA card; then these controllers have been tested with real time experiments. An auxiliary program in the FPGA is implemented to test the step response of these controllers. Then our program displays the results on the LCD using the Pico. Blaze processor technique as a real time tester the desired speed, the overshoot, the settling time, and the PID parameters for each controller as shown in Figures 23 and 24. Basil Hamed 69

Fuzzy PID Controllers Using FPGA Technique for Real Time DC Motor Speed Control Modelsim Results Basil Hamed 70

Fuzzy PID Controllers Using FPGA Technique for Real Time DC Motor Speed Control The control scheme was modeled and designed in VHDL. It was simulated and synthesized using the Xilinx Foundation package and implemented into a Xilinx Spartan 3 -A FPGA (Figure 27). Basil Hamed 71