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**Lect 6 Fuzzy PID Controller Basil Hamed Islamic University of Gaza**

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

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**Contents PID PID Fuzzy Example Supervisory PID Fuzzy Control**

Basil Hamed

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**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

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**Convectional PID Controller**

Basil Hamed

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**Convectional PID Controller**

Time Domain Frequency Domain Basil Hamed

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PID Controller Basil Hamed

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PID Controller Time Domain Frequency Domain Basil Hamed

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**A comparison of different controller types**

Basil Hamed

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**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

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**General tips for designing a PID controller**

Basil Hamed

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**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

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Why use fuzzy with PID Although PID controllers are able to provide adequate control for simple systems, they are unable to compensate for disturbances. We will use Fuzzy Logic controllers to improve the PID controllers ability to handle disturbances. PID Control works well for linear processes PID control has poor performance in nonlinear processes. Fairly complex systems usually need human control operators for operation and supervision Basil Hamed

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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 13 Basil Hamed

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**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 14 Basil Hamed

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**Types of Fuzzy Controllers: - Fuzzy Intervention -**

Fuzzy Logic Controller and PID Controller in Parallel: Intervention of the Fuzzy Logic Controller into Large Disturbances ! Slide 15 Basil Hamed

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**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

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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

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Fuzzy PID Control A fuzzy PID controller is a fuzzified proportional-integral-derivative (PID) controller. It acts on the same input signals, but the control strategy is formulated as fuzzy rules. If a control engineer changes the rules, or the tuning gains, it is difficult to predict the effect on rise time, overshoot, and settling time of a closed-loop step response, because the controller is generally nonlinear and its structure is complex. In contrast, a PID controller is a simple, linear combination of three signals: the P action proportional to the error e, the I-action proportional to the integral of the error 𝑒𝑑𝑡 , and the D-action proportional to the time derivative of the error de/dt, or ˙e for short. Basil Hamed

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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

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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

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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

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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

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Example Basil Hamed

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Example Basil Hamed

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Example Basil Hamed

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Example Basil Hamed

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

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**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

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**Supervisory Control Systems**

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

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**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

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**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

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**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

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**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

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**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

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**Supervisory Fuzzy Control**

There are four types of Fuzzy supervisory control: Fuzzy replaces PID Fuzzy replaces operator Fuzzy adjusts PID parameters Fuzzy adds to PID control Basil Hamed

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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

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**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

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**Fuzzy replaces operator**

Basil Hamed

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**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

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**Fuzzy adjusts PID parameters**

Basil Hamed

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**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

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**Fuzzy adds to PID control**

Basil Hamed

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Homework 13.2, 13.4, 13.5 Due 20/11/2011 Basil Hamed

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© Goodwin, Graebe, Salgado, Prentice Hall 2000 Chapter7 Synthesis of SISO Controllers.

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