模型预测控制ppt课件

.1第七章模型预测控制算法之一~5杨根科上海交通大学自动化系2005年9月.2内容提要概述动态矩阵控制动态矩阵控制的进一步讨论模型算法控制应用.3思想Z域设计（直接设计）时域设计现代控制理论（基于状态空间）：如最优控制、极点配置等应用航空航天（理想环境）工业过程控制（基于模型预测）：预测控制！石油、化工、发电等先进控制算法.4工业过程特点数学模型的非精确性不确定性、随机性、参数时变性material,energybalancesflowdynamicsphysicalproperties(oftenunknown)thermodynamics多变量系统控制算法的可实施性历史，。。。脉冲响应与阶跃响应；滚动.5模型预测控制,动态复杂性Figure:Twoprocessesexhibitingunusualdynamicbehavior.(a)changeinbaselevelduetoastepchangeinfeedratetoadistillationcolumn(分裂蒸馏塔).(b)steamtemperaturechangeduetoswitchingonsootblower(吹灰器)inaboiler..6模型预测控制,方法ModelPredictiveControl(MPC)–regulatorycontrolsthatuseanexplicitdynamicmodeloftheresponseofprocessvariablestochangesinmanipulatedvariablestocalculatecontrol“moves”.Controlmovesareintendedtoforcetheprocessvariablestofollowapre-specifiedtrajectoryfromthecurrentoperatingpointtothetarget.Basecontrolactiononcurrentmeasurementsandfuture.7模型预测控制,优点OptimalcontrollerisbasedonminimizingerrorfromsetpointBasicversionuseslinearmodel,buttherearemanypossiblemodelsCorrectionsforunmeasureddisturbances,modelerrorsareincludedSinglestepandmulti-stepversions•Treatsmultivariablecontrol,feedforwardcontrol.8模型预测控制,优点/特点ProcessesaredifficulttocontrolwithstandardPIDalgorithm–longtimeconstants,substantialtimedelays,inverseresponse,etc.Thereissubstantialdynamicinteractionamongcontrols,i.e.,morethanonemanipulatedvariablehasasignificanteffectonanimportantprocessvariable.Constraints(limits)onprocessvariablesandmanipulatedvariablesareimportantfornormalcontrol..9模型预测控制Techniquesdevelopedbyindustry:1.DynamicMatrixControl(DMC)-ShellDevelopmentCo.,CutlerandRamaker(1980),-CutlerlaterformedDMC,Inc.-DMCacquiredbyAspentechin1997.2.ModelAlgorithmicControl(MAC)•ADERSA/GERBIOS,Richaletetal(1978)•Over4000applicationsofMPCsince1980(QinandBadgwell,1998and2003)..10模型预测控制,优点/特点Time-delaycompensationtechniquespredictprocessoutputonetimedelayahead.Hereweareconcernedwithpredictivecontroltechniquesthatpredicttheprocessoutputoveralongertimehorizon.(e.g.,open-loopresponsetime)..11模型预测控制,ideaBasicconceptforModelPredictiveControl.12模型预测控制,优点/特点GeneralCharacteristics•Targets(setpoints)selectedbyreal-timeoptimizationsoftwarebasedoncurrentoperatingandeconomicconditions•Minimizesquareofdeviationsbetweenpredictedfutureoutputsandspecificreferencetrajectorytonewtargets•Discretestepresponsemodel•Frameworkhandlesmultipleinput,multipleoutput(MIMO)controlproblems..13模型预测控制,优点/特点Canincludeequalityandinequalityconstraintsoncontrolledandmanipulatedvariables•Solvesaquadraticprogrammingproblemateachsamplinginstant•Disturbanceisestimatedbycomparingtheactualcontrolledvariablewiththemodelprediction•UsuallyimplementsthefirstmoveoutofMcalculatedmoves.141动态矩阵控制(2)动态矩阵控制原理与算法控制结构组成优化策略反馈校正算法设计参数选择采样周期优化时域长度控制时域程度权矩阵误差校正向量.151动态矩阵控制()DMC依靠对象的阶跃响应控制结构组成预测模型a2a1123N-1Na3aN-1aN模型截断离散的阶跃响应.161动态矩阵控制()StepResponseModelsStepresponsemodelsarebasedonthefollowingidea.Assumethatthesystemisatrest.Foralineartime-invariantsingle-inputsingle-output(SISO)systemlettheoutputchangeforaunitinputchangebegivenby{0,a1,a2,...,aN,aN,...}HereweassumethatthesystemsettlesexactlyafterNsteps.Thestepresponse{a1,a2,...,aN}constitutesacompletemodelofthesystem,whichallowsustocomputethesystemoutputforanyinputsequence:可加性)1()()(1NkuaikuakyNNii.171动态矩阵控制()预测模型对象的动态特性通过动态系数{a1,a2,…,aN}来描述{a1,a2,…,aN}是阶跃响应在采样时刻t=T,2T,…,NT的值(aistepresponsecoefficients)(ai+1-aiimpulseresponsecoefficients)N的选择应该使ai~as,(jN),as是阶跃响应终止值.181动态矩阵控制()Forexampleifthediscretesystemdescription(samplingtimeT=0.1)isy(k)=–0.5y(k–1)+u(k–3)thenthetransferfunctionis.191动态矩阵控制()Thefollowingcommandsgeneratethestepresponsemodelforthissystemandplotit:num=[01];den=[10.5];delt1=0.1;delay=2;%whydon’twechoose3?g=poly2tfd(num,den,delt1,delay);%Setupthemodelintfformattfinal=1.6;delt2=delt1;nout=1;plant=tfd2step(tfinal,delt2,nout,g);%Calculatethestepresponseplotstep(plant)%Plotthestepresponse.201动态矩阵控制().211动态矩阵控制()plant=0---a10---a21.0000---a30.50000.75000.62500.68750.65630.67190.66410.66800.66600.66700.66650.66670.6666---a161.0000---nout(i)=1ifoutputiisstable.1.0000---ny0.1000---delt2.221动态矩阵控制()预测模型线性系统的可加性，可以由a=[a1,a2,…,aN]T描述假设t=kT有一个控制增量Δu(k),后面控制量不变在采样时刻t=(k+1)T,(k+2)T,…,(k+N)T的值)|(~)|2(~)|1(~)(~0000kNkykkykkykyN)|(~)|2(~)|1(~)(~1111kNkykkykkykyN)()(~)(~01kuakykyNN.231动态矩阵控制()1预测模型假设t=kT,(k+1)T,…,(k+M-1)T有控制增量Δu(k),Δu(k+1),…,Δu(k-M+1);后面控制量不变在采样时刻t=(k+1)T,(k+2)T,…,(k+P)T的值(滚动))|(~)|2(~)|1(~)(~0000kPkykkykkykyP)|(~)|2(~)|1(~)(~kPkykkykkykyMMMPM)()(~)(~0kuAkykyMPPM1112100000;)1()()(MPPPMaaaaaaAMkukuku.241动态矩阵控制()2优化策略权矩阵：期望轨迹：优化控制变量:ΔuM(k)期望指标(无约束问题)：误差小，控制量小，即MPrrrRqqqQ,...,,;,...,,2121)(),...,1()(PkWkWkWP221212)()(~)()(min)1())|(~)(()(minRMQPMPMiiPiMikukykWkJorikurkikyikWqkJ.251动态矩阵控制()优化策略优化控制量:ΔuM(k)TPoPTTMMMPoPTMMMMMPoPTMPoPMiiPiMiMiiPiMiAAxxthatNotekykWQARQAAkukuRkuAkykWQAkukJkukJkuRkukuAkykWQku