现代控制工程-第十五章

Chapter8TheDesign

ofFeedbackControlSystem8-1ReviewonthePerformanceIndicesandtheirRegulation8-2ConceptofCompensation8-3CompensationNetworks

A.dynamicperformanceindices(fortransientresponseofunderdampedsystems)

risetimepeaktimesettlingtimeP.O.8-1ThePerformanceIndicesandtheirRegulations

Note:P.O.dependsonlyon!1.dynamicindicesinthetimedomainandtheirregulationsTimetrRisePeaktimetpABP.O.σ%=AB100%SettlingtimetsDynamicperformanceindices

timeconstantattenuationfactordampedfrequencyphaseangle

dampingrationaturefrequencyB.moreindicesandparametersj0

↓

(polesmovingleft,morestable)

Note:anddependonlyon!↓

(moresteady)↑

(faster)，↓

(faster,notsynchronouslywithand)

then:，↑

(respondsslower)

iffixed,and↑(moredamped)C.Theregulationofperformanceindices↓

(moresteady)

Principles:determiningaccordingtothespecificationoffirst,andthendeterminingaccordingtootherrequirements!↑

(faster)，↓

(faster,synchronouslywithand)

then:，

↓

(faster)

iffixed,and↑(lesssteady)C.Theregulationofperformanceindices↑

(lesssteady)

peakmagnitude(attainedatresonantfrequency)

↑→↑(lesssteady)

resonantfrequency(when)

↑

→，↓

(faster)

phasemargin：

，(proportionalto)

bandwidth

↑

→，↓(faster)D.Theregulationoffrequencydomainspecifications(1)AttachingextraCLzerosthatcannotbeneglected,resultstheeffectofdecreasingofthedampingratioandothercorrespondingeffects.Thenearerthezerosapproachtheorigin,themoreremarkabletheeffectsare.E.othermeasuresregulatingperformanceindicesY(s)R(s)Gu(s)+-H(s)KGc(s)(2)AttachingextraCLpolesthatcannotbeneglected,resultstheeffectofincreasingofthedampingratioandothercorrespondingeffects.Thenearerthezerosapproachtheorigin,themoreremarkabletheeffectsare.Y(s)R(s)Gu(s)+-H(s)KGc(s)

(3)AttachingextraOLzeroswillmovetheCLrootlocustotheleft.Thisisfavorabletotheincreasingofphasemargin,thesystemstability,etc.Y(s)R(s)Gu(s)+-H(s)KGc(s)

(4)AttachingextraOLpoleswillmovetheCLrootlocustotheright.Thisisunfavorabletothesystemstability.Itisnotusedingeneral.Thesemeasureswillbestudiedindetailinthecominglectures.

Y(s)R(s)Gu(s)+-H(s)KGc(s)

(5)Themovingmodesofhigherordersystemsaredeterminedbythepoles.Thefartheronepoleisfromtheimaginaryaxis,thelessitsimpactonthetransientdynamicbehavior.(6)Thetransientbehaviorofahigherordersystemismainlydeterminedbythedominantpoles.Thenearertheyareapproachingtheimaginaryaxis,themoredominanttheyare,andtherefore,thebetterthelower-orderapproximatemodelis.Let’sgotothereviewonthesteady-stateperformance.

2.Steady-stateperformanceindicesandtheirregulationA.Steady-stateperformanceindices

Errorconstants.Theyaredefinedfordifferenttestinputsignals,namely:positionerrorconstantvelocityerrorconstantaccelerationerrorconstantThebiggertheerrorconstantsare,thebetterthesteady-stateperformanceis.

Ⅰ0ⅡA·1(t)

A1+kA

kA

kA·t000∞∞∞At2/2A·1(t)A·tAt2/2kkk000∞∞∞?123Kp=?Kv=?Ka=?νErrorConstantsSteady-stateError

B.Regulatingthesteady-stateperformance

1.TypenumberV(attachingOLpolesatorigin)V

↑→trackingability↑stability↓2.OLgainK(mostwidelyused)K↑→Steady-stateerror↓

affectstabilityandtransientperformance3.disturbancecompensation4.choosinghighqualitydevices

C、inthefrequencydomain:directlyrepresentedbythephasemarginandmagnitudemargin

,↑→stability↑

3.Regulatingonthestability(relative)A.intheSplane:directlyrepresentedbytheattenuationfactorδ

δ↑→stability↑

B.OLgainKtheimpactofKonthestabilitycanbejudgedbyusingtherootlocus.

D.AttachingextraOLzerosisfavorabletothesystemstability,etc.

4.FromOLtoCLSomeindicesandparametersaredefined,andsomemethodsaredevelopedfromOLtransferfunction,butusedfortheCLanalysisanddesign.Theyare:

PhasemarginMagnitudemarginBreakfrequencyTypenumberVOLgainKRootlocusmethod

Nyquistcriterion

Nicolisplot8-2Conceptofcompensation1.Whydoweneedcompensation?Allwehavelearntaboutthesystemmodeling,systemanalysis,andetc.arepreparationsforthefinalobject:

Designandimplementsatisfactorycontrolsystems!Letsrestudyanexamplefirst.

Example4.4(Proportionalregulation):GiventheOLtransferfunctionofanunitnegativefeedbacksystemas:

lettheinputtobeunitstepsignal,calculatethetransientperformanceindicesofthesystemwhenthegainis

KA=200.InvestigatethechangeoftheperformancewhenKAisincreasedto1500,ordecreasedto13.5?

WecannotdeceasethesettlingtimeandP.O.atthesametimeonlybyadjustingK.Theyarechangingcontradictorily,orthedesignrequirementsareconflictwitheachother.

Firstchoiceincontrolsystemdesign:tryourbesttooptimizetheprocessitselfbyselectinggooddevices,carefullyadjustingitsparameters,etc..

But,therearelimitationsontheregulationabilityandpossibilityof

theadjustmentofparameters.

Wehavetoconsiderthechangeofthestructureofthesystemandredesignitinordertoobtaindesiredperformance.Thatiswhyweneedcompensations.

8-2

ConceptofCompensation

1.Definition&Types

Definition

Redesigningoradjustingthesystemstructuretoalterthesystemresponse,inordertomakeupfordeficienciesorinadequacies,byinsertingadditionalcomponentsordeviceswithinthestructureofthefeedbackcontrolsystem.Theadditionalcomponentsarecalledcompensators.

Compensationtypes（1）Cascade（2）Feedback（3）Prefilter

（4）NoiseCascadeCompensation

ProcessFeedbackCompensation——RY—PrefilterCompensation

ProcessRY—ControllerProcess

NoiseCompensationRYN

2.ChoosetheTypeofCompensation

Oftenused:CascadeCompensation&FeedbackCompensation.

Thechoicedependsonmanyfactors,itiseasiertodesignCascadeCompensation,soitismostlypreferred,especiallyinclass.Inthecaseofhighstandardsystem,CascadeCompensationandFeedbackCompensationwillbeusedatthesametime.

3.ApproachestoSystemDesignTheperformancerequirementsareofgreatimportancetocontrolsystemdesign.Itcanbedescribedintermsofthetime-domainorfrequency-domainindices,thus,approachestocontrolsystemdesignareusuallydeterminedbytheformofthegivenorrequiredspecifications.Iftheperformancerequirementsaregivenintime-domain,weadopttherootlocusmethodtodesignthecompensatortobeadded.

Iftheperformancerequirementsaregiveninfrequency-domain,wedesignthecompensatortobeaddedusingBodediagram.Often,weneedtransferthesetoftime-domainrequirementstofrequency-domainrequirements,orreverse.8-3CompensationNetworks1.Phase-leadnetwork（differentiator-type）TransferfunctionisR2R1V2V1Thus:Where:CThephase-leadcompensationincascadewillresults:1.Theopen-loopgainofthesystemwillbeattenuatedby1/a,thus,foranacceptablefinaldesign,raisethegainoftheamplifierinordertoaccountfortheattenuation.2.Theclosed-looprootlocuswillbereshapedleftward,thiswillbeinfavorofthesystemstability.j0Pole-zerodiagramo