一种自校正PID控制器设计与仿真研究-闫秀英

182©Vol.18Suppl.220068JournalofSystemSimulationAug.,2006·753·PID1,21,231.,710055;2.,710055;3.,710049Ziegler-NicholsPIDARXPIDZiegler-NicholsMATLABPIDPIDZiegler-NicholsMATLABTP273.2A1004-731X(2006)S2-0753-04DesignandSimulationforSelf-tuningPIDControllerYANXiu-ying1,2,RENQing-chang1,2,MENGQing-long3(1.DepartmentofInformation&ControlEngineering,Xi’anUniversityofArchitecture&Technology,Xi’an710055,China;2.SchoolofEnvironmental&MunicipalEngineering,Xi’anUniversityofArchitecture&Technology,Xi’an710055,China;3.SchoolofEnergy&PowerEngineering,Xi’anJiaotongUniversity,Xi’an710049,China)Abstract:Aself-tuningPID(Proportional-Integral-Derivative)controllerbasedonmodifiedZiegler-Nicholscriterionwasintroduced.Firstly,systemARXmodel,recursiveleastsquaresmethodwithforgettingfactorandtheincrementPIDcontrolalgorithmwerepresent.Secondly,modifiedZNmethodwasintroduced,andultimategainandultimateperiodofrelationwithsystemparameterswereformulated.Finally,modelsoftransducermotor-ductstaticpressurecontrolloopinvariableairvolume(VAV)systemwereappliedinMATLABsimulation.Resultsshowthatself-tuningPIDcontrolsystemproposedcanreal-timeestimatesystemparameters,tunecontrollerparametersandadaptaccordingtovariationofcontrolledprocess,thereforeittakesonpowerfulperformanceofreal-timesystemparametersestimationandcontrollerparametersauto-tuning.Keywords:self-tuningPIDcontrol;parameterestimation;Ziegler-Nicholstuning;MATLAB;VAV1PID[1]PIDPID/[2]PIDPID[3]Ziegler-Nichols2006-04-052006-6-8(2003F36)(1980-),,,,,;(1945-),,,,,;(1979-),,,,PIDMATLABMATLAB\SIMULINKZiegler-Nichols1PIDSTR[4]PIDPID11PID182Vol.18Suppl.220068Aug.,2006·754·u(t)y(t)[5]θZiegler-Nichols[6]PIDPIDu(t)[7]2PID2.1(SISO)ARX[8]-1-1()()()(-)()AqytBqutdet=+(1)-11212()1aannAqaqaqaq−−−=++++L-11212()bbnnBqbqbqbq−−−=+++L{u(t)}{y(t)}{e(t)},1()(1)qytyt−=−d2.2[9]](1)-1-1()()()()()ytGqutHqet=+(2)-1-1-1()()/()GqBqAq=-1-1H(q)=1/A(q)()()()Tyttetϕθ=+(3)θ,1212[,,,,,,]abTnnaaabbbθ=LL(4)()[(1),(2),,(),(1),(2),,()]Tabtytytytnutdutdutdnϕ=−−−−−−−−−−−−LL(5){u(t),y(t)},21()[()()]TitJyiiθϕθ=∑=−(6)θ[10]RFFLS[9]1()(1)()[()()(1)]()(1)()[()(1)()]1()[()()](1)TTTttKtytttKtPtttPttPtIKttPtϕθθθϕλϕϕϕλ∧∧∧−=−+−−=−+−=−−(7)2.3PIDPID[11]1121[(2)]sDkpkkkkkkkIsTTuKeeeeeeuTT−−−−=−++−++(8)kkkery=−ukKpTITDTS011221kkkkkuqeqeqeu−−−=+++(9)012[1][12]sDDDpppIsssTTTTqKqKqKTTTT=++=−+=(10)3Ziegler-NicholsZiegler-Nichols[6,12-13]KpTITDKuTuKp=0.6KuTI=0.5TuTD=0.125Tu(11)KuTuZiegler-Nichols[14]-1-1-1()()/()GqBqAq=(12)Ziegler-NicholsPID1-1-11-1-1()()()1()()()ppcppKGqKBqGqKGqAqKBq−−==++(13)11()()pAqKBq−−+=0z(1)z=α=1-11()(1)jDqq=+(2)1zjαβ=+2zjαβ=−221αβ+=2212()()()21Dqqqqqqqα=−−=−+Z22Z182Vol.18Suppl.220068,PIDAug.,2006·755·(1)1111[()()]()aaunnjqAqKBqDqEq−−−−+=(14)11()1anjiiiEqeq−−−==+∑eiKu(14)qKu(2)22111[()()]()aannuqAqKBqDqFq−−−−+=(15)211()1aniiiFqfq−−−==+∑(15)Kuα(1)(α=1)(2)Tucos()1/arccos2/SuuSuuTTTωαωαπω===(16)KuTuKuTuPID4PID(1)^θPλTs(2)y(t),u(t)((7))(3)(14)(16)(15)(16)KuTu(11)PID(4)(9)(10)u(t)(2)-(4)55.1(VAV)VAVVAVVAVMATLAB12()0.81.3()()1.20.5yssGsusss−+==++(17)22()0.9681.524()()1.3560.6206yssGsusss−+==++(18)11211121212()0.0060.72011()()11.0220.301212112yqqqGquqqqbqbqaqaq−−−−−−−−−−+−==−++=++(19)112121121212()0.0070.7862()()10.93470.257712112yqqqGquqqqbqbqaqaq−−−−−−−−−−−+==−++=++(20)a1=-1.022(-0.9347)a2=0.3012(0.2577)b1=0.006(0.007)b2=0.7201(0.7862)TSTS1s5.2PIDPIDMatlab\Simulink[14-16]3StepadaptivecontrollerPIDSaturationControlledprocess/1Band-LimitedWhiteNoise/1Noisetransfer/1ClockSwitchu_in(k)r(k)y(k)u_out(k)SYSIDparamsadaptivecontrollerSwitchStepSaturationOutputResult0.01s+1.2s+0.52Noisetransfer10.01s+1.356s+0.62062NoisetransferIDparameters-0.8s+1.3s+1.2s+0.52Controlledprocess1-0.9686s+1.524s+1.356s+0.62062ControlledprocessClockBand-LimitedWhiteNoise2Band-LimitedWhiteNoise13PID182Vol.18Suppl.220068Aug.,2006·756·050100150200250300-1.0-0.8-0.6-0.4-0.20.00.20.40.60.8b2a2b1SYSID_ParamsTime/sa1OutputResulty(t)r(t)u(t)IDparameters5.3Ts=1s0()1ut≤≤^(0)θ=[0.1,0.2,0.3,0.4]P(0)=8410Iλ=0.984r(t)y(t)u(t)150s0501001502002503000.00.20.40.60.81.01.21.41.61.82.02.2u(t)y(t)r(t)_y(t)_u(t)Time/sr(t)45150sPID56PIDPIDPID[18-19][1]YunLi,KiamHeongAng,ChongG.C.Y.PIDControlSystemAnalysisandDesign[J].ControlSystemsMagazine,IEEE(S0272-1708),2006,26:32-41.[2],,.PID-I[J].(),1994,(5):523-529.[3]K.S.Narendra.TheChangingFaceofAdaptiveControl[C]//The4thAsianControlConference,Singapore,2002.[4]K.J.,B..[M].,.:,1992.[5]C.J.,S.A..[M].:,1986.[6]WilliamY.Svrcek,DonaldP.Mahoney,BrentR.Young.AReal-TimeApproachtoProcessControl[M].NewYork:Chichester.JohnWiley&Sons,2000.[7],.[M].:,2002.[8]LennartLjung.Black-boxModelsfromInput-outputMeasurements[C]//IEEEInstrumentationandMeasurementTechnologyConference.Budapest,Hungary,2001.[9]LennartLjung.SystemIdentificationTheoryfortheUserSecondEdition[M].:,2002.[10],.[M].:,2001.[11].PID[M].:,2002.[12]Hang,C.C.,Sin,K.K..AComparativePerformanceStudyofPIDAuto-Tuners[J].ControlSystemsMagazine,IEEE(S0272-1708),1991,11:41-47.[13]K.J.Astrom.AdaptiveControl[M].:,2003.[14]Bobal.V,Bohm.J,Fessl.J,Machacek,J..DigitalSelf-tuningControllersAlgorithms,Implementationan