feedback control systems chapt

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Abdel Aitouche, Feedback Control Systems, 2007-2008 1/23

CHAPTER 7

Process Identification

FEEDBACK CONTROL SYSTEMS


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Process Identification

yIntroduction :

The objective of the process identification is to obtain amodel of process given in transfer function . Theobjective of different identification methods is to give amodel close to the output response of the process.

To reach this, two experiences can be realized :

Open loop identification

Closed loop identification


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Open Loop Process Identification

yIntroduction :

Process identification contains 4 steps: :

Application of test signal in view to obtain theresponse of actual system. Choice of model which

approximate the actual system,Computation of parameters of the model, function ofthe obtained response.

Comparison of the outputs of actual system andmodel in view to validate the model.


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{

Empirical dynamic models :This methods are based on stepresponse of the output of actualsystem. Two cases can be :

z The system contains an integration, theresponse is time invariant. The systemis unstable.

z The system is stable and the responseis constant at operating point.


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{ Empirical Models :

Is the output periodical ?

YES YES

Second Order System

OvershootPseudo-period

Slope at origin

NO

First Order

YES

Order > 1

Strejc Broda

Ziegler-Nichols

ParticularPoints

Othermethods


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{ Identification of stable systemsz First order system :

Model :

pT

K

pG +=1)(

We determine :- Gain K = sf / E0

- time constant T since 63,2% of sf


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Open Loop Process Identificationz First Order System :

Once the values of k and T deduced, we plot the

model and we compare it to the step responseof actual system

Example :


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z First order system :

Model :

pbp

KpG

++

=11

)(

We determine b, and we

deduce and .


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z First order system with delay :

Model of BROIDA

Model :

pT

eKpG

p

+=

1)(


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z First order system with delay : Model of BROIDA

T = 5.5 (t2 t1) = 2.8 t

1 1.8 t

2


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System with delay : Model of STREJ C

Model :

The model is possible if the actual output response is periodicalwith horizontal asymptote and have only one inflexion point.

THIS METHOD DEPENDS ON THE PLOT OF INFLEXION

POINT

n

p

pT

eKpG

)1()(

+=


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Method :

1 Determine he steadystate gain K

2 Find the inflexion Yq

3 Plot the slope anddetermine Tu and Ta

4 Compute Tu / Ta


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5 From Tu / Ta of thetable, deduce the order of

the system. The weak orderis chosen

6 From table, deduce the

time constant T.

7- The time delay is givenby:

Exercise : K = 5, Tu = 3 s and Ta = 11 sGive the model of Stejc

00 =

feedback control systems chapt

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