Fuzzy Logic Control 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

Contents

PIDPID FuzzyExampleSupervisory PID Fuzzy Control

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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.

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Convectional PID Controller

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Convectional PID Controller Time Domain

Frequency Domain

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PID Controller

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PID Controller

Time Domain

Frequency Domain

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A comparison of different controller types

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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.

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General tips for designing a PID controller

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Tuning of PID ControllerThere 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.

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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

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Types of Fuzzy Controllers:- Direct Controller - Types of Fuzzy Controllers:- Direct Controller -

Slide 13

The Outputs of the Fuzzy Logic System Are the Command Variables of the Plant: The Outputs of the Fuzzy Logic System Are the Command Variables of the Plant:

Fuzzification Inference Defuzzification

IF temp=lowAND P=highTHEN A=med

IF ...

Variables

Measured Variables

Plant

Command

Fuzzy Rules Output Absolute Values !

Types of Fuzzy Controllers:- PID Adaptation - Types of Fuzzy Controllers:- PID Adaptation -

Slide 14

Fuzzy Logic Controller Adapts the P, I, and D Parameter of a Conventional PID Controller:Fuzzy Logic Controller Adapts the P, I, and D Parameter of a Conventional PID Controller:

Fuzzification Inference Defuzzification

IF temp=lowAND P=highTHEN A=med

IF ...

P

Measured Variable

PlantPID

ID

Set Point Variable

Command Variable

The Fuzzy Logic System Analyzes the Performance of the PID Controller and Optimizes It !

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

Slide 15

Fuzzy Logic Controller and PID Controller in Parallel:Fuzzy Logic Controller and PID Controller in Parallel:

Fuzzification Inference Defuzzification

IF temp=lowAND P=highTHEN A=med

IF ...

Measured Variable

PlantPID

Set Point Variable

Command Variable

Intervention of the Fuzzy Logic Controller into Large Disturbances !

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.

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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.

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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 , and the D-action proportional to the time derivative of the error de/dt, or ˙e for short.

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Fuzzy PID ControlFuzzy 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 PID1. Build and tune a conventional PID controller first.2. Replace it with an equivalent fuzzy controller.3. Fine-tune it.

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Fuzzy PID ControlThe 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.

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Fuzzy PID ControlTo 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:

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Fuzzy PID ControlIn 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,

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Example

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Example

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Example

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Example

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Example

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

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.

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Supervisory Control Systems

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

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

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Supervisory Control SystemsFor 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.

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Supervisory Control SystemsConceptually, 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.

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Supervisory Control Systemsthe 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.

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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.

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Supervisory Fuzzy Control

There are four types of Fuzzy supervisory control:1. Fuzzy replaces PID2. Fuzzy replaces operator3. Fuzzy adjusts PID parameters4. Fuzzy adds to PID control

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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.

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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.

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Fuzzy replaces operator

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Fuzzy adjusts PID parametersIn 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.

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Fuzzy adjusts PID parameters

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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).

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Fuzzy adds to PID control

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Homework

13.2, 13.4, 13.5

Due 20/11/2011

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