lect-6-supervisory-fuzzy.pptx

7/29/2019 Lect-6-Supervisory-Fuzzy.pptx

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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

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PID

PID: Proportional Integral Derivative

More than 90% of controllers used in

industries are PID or PID type controllers (therest are PLC)

PID controllers are simple, reliable, effective

For lower order linear system PID controllershave remarkable set-point trackingperformance 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 Controller

There are methods for tuning PID controllers, for

example:

hand-tuning,

ZieglerNichols tuning,

optimal design,

pole placement design, and

auto-tuning (A strom and Hagglund 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 unableto compensate for disturbances.

We will use Fuzzy Logic controllers to improve thePID 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 -

Slide 13

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

Fuzzification Inference Defuzzification

IF temp=low

AND P=high

THEN A=med

IF ...

Variables

Measured Variables

Plant

Command

Fuzzy Rules Output

Absolute Values !


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- PID Adaptation -

Slide 14

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


IF temp=low

AND P=high

THEN A=med

IF ...

P

Measured Variable

PlantPID

I

D

Set Point Variable

Command Variable

The Fuzzy Logic System

Analyzes the Performance of the

PID Controller and Optimizes It !


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- Fuzzy Intervention -

Slide 15

Fuzzy Logic Controller and PID Controller in Parallel:


IF temp=low

AND P=high

THEN A=med

IF ...

Measured Variable

PlantPID

Set Point Variable

Command Variable

Intervention of the Fuzzy Logic

Controller into Large Disturbances !


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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 knowledgeavailable 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 PIDcontrollers. 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 tuninggains, 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, ore for short.Basil Hamed 18


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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.

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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 errore,

its integral and its derivative. The parameter Kp is the

proportional gain, Ti is the integral time, and Td thederivative time.

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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 beused:

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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

Tdin order to achieve a good closed-loop performance.

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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


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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 complicatedplants using their experience and training, and thus

fuzzy control is a relevant method within supervisory

control.

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Supervisory control is a multilayer (hierarchical) controller

with the supervisor at the highest level, as shown in

Figure


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The supervisor can use any available data from the controlsystem to characterize the systems 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 otherinformation 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 systemand modify the controller to improve the performance

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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 caror more like

a sluggish family car. The other subsystem information that a

supervisor could incorporate for supervisory control for anautomotive 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 ora performance that is more to the liking of the driver.

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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.

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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 thiscontroller should be tuned under various operating

conditions.

2. Information gathered by a control engineer who knows

that under different operating conditions controllerparameters 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-levelcontrol 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 supervisorycontrol:

1. Fuzzy replaces PID2. Fuzzy replaces operator

3. Fuzzy adjusts PID parameters

4. 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 thecontroller 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, maycreate conflicts.

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Fuzzy replaces operator

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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 narrowoperational 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 PIDcontrol

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 theprocess 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 PIDcontrol

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Homework

13.2, 13.4, 13.5

Due 20/11/2011

lect-6-supervisory-fuzzy.pptx

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