Integral_Control.odp

8/10/2019 Integral_Control.odp

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Integral Control System

LORABSCHE-5A


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Often control systems are

designed using Integral Control. Intis control metod! te controlsystem acts in a "ay tat

te control e#ort is $ro$ortional tote integral of te error.


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%e $ro$ortional controller am$li&este error and a$$lies a control e#ort tote system tat is $ro$ortional to te

error. In integral control! te controe#ort is $ro$ortional to te integral sote controller no" needs to 'e anintegrator! and it "ill a(e a transfe

function of )i*s - not +ust a gain! )$.


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Integral control is "at you a(e "ente signal dri(ing te controlledsystem is deri(ed 'y integrating te

error in te system.


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An integral is te area under a cur(eAssuming tat te inde$enden(aria'le is time! t. %en as time goes

on te area accumulates. Integrationis te limit of a $rocess of ta,ing smalincremental areas and letting teinter(al! %! srin, to ero.


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If te integral starts at ero! ten teintegral is +ust te area under te cur(e.

Implications: If the input goes to zero, then the integra

stops changing and just has whatever valueit had just before the input became zero. The integral can change in either direction as

the signal goes positive and negative.Negative area can subtract from positive

area, lowering the value of an integral.


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sing Integral Control


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te out$ut le(el is te desired le(el! tis is adesira'le steady state.

Re(ie" on te situation/

If output level matches the desired level, the error iszero.

Because the error is zero, the integrator output doesnot change.

Because the integrator output doesnt change, if the

rest of the s!stem is at stead! state nothing elsechanges. The s!stem has to reach stead! state. "oull need to

learn something about s!stem d!namics to ensurestabilit!. If the s!stem starts to oscillate wildl!then it ma! not reach a stead! state, so the zerostate state behavior is never reall! seen.

#lthough the error goes to zero, no guaranteesabout speed of response are given.


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0isad(antages of IntegralControl

#n integral controller is not particularl! di$cult toimplement. In an analog s!stem, an integral control s!stem

integrates the error signal to generate thecontrol signal. If the error signal is a voltage, andthe control signal is also a voltage, then a

proportional controller is just an analogintegrator.

In a digital control s!stem, an integral contros!stem computes the error from measuredoutput and user input to a program, and

integrates the error using some standardintegration algorithm, then generates anoutput%control signal from that integration.


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Integral Controller

1i(en a system in "ic you "antto use integral control!

#& Be able to predict the e'ect of

integral control on (().B& Be able to predict the e'ect ofintegral control on stabilit!.*& Be able to predict the e'ect of

integral control on speed of response.


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2ro$erties Of IntegralControllers

%e controller integrates te error asso"n in te 'loc, diagram of ane3am$le system 'elo".

%e integral controller as a transferfunction of )i*s

So! te actuating signal 4te in$ut to tesystem 'eing controlled is $ro$ortiona

to te integral of te error.


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In an integral controller! steady state

error sould 'e ero. The s!stem would have to have a zero

at the origin to ma+e this claim false.

f course, the closed loop s!stem has to

be stable.

Integral control as a tendency to ma,ea system slo"er.


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