利用S-Function实现传递函数

1、Byali2016-5-3利用S-Function实现传递函数利用S-Function实现传递函数1.引言1.1、MATLAB函数命令介绍2.1.1 MATLABtf函数命令：2.1.2 MATLABss函数命令：2.1.3 MATLABtf2ss函数命令：2.2、实例仿真3.2.1 假设工业过程某传递函数：3.2.2 修改S-Function模板参数：4.2.3 仿真结果1.0引言自然界大多数的过程都可以看做是一个系统，一般来说系统都会有输入和输出，而传递函数就是输入到输出的一个转换方式，比如，对于一个罐体来说，流量是输入，液位是输出，则从流量转换到Byali2016-5-3液位的过程就是传

2、递函数的本质，可以通过求解方程式，来确定传递函数的数学形式，也可以通过实验法来辨识这个数学模型。S-Function的功能就不多说了，总之，其功能之强大，属MATLAB/Simulink开发者必学之内容。这篇短文讲述的就是如何利用S-Function实现传递函数：我们知道S-Function有自己的模板，而我们要做的就是更改模板代码中的某些参数就行了，考虑到这些参数和状态方程的关系密切，因此，本文的思路就是首先将传递函数转为系统状态方程，然后再对参数进行修改。1、MATLAB函数命令介绍1.1 MATLABtf函数命令：建立传递函数：例1：s=tf('s');H=s/(sA2+

3、2*s+10);例2:h=tf(10,1210);1.2 MATLABss函数命令:建立状态空间模型连续模型：sys=ss(a,b,c,d)createsastate-spacemodelobjectrepresentingthecontinuous-timestate-spacemodelx=Ax+Bhj=Cx+ForamodelwithNxstates,Nyoutputs,andNuinputs:aisanNx-by-Nxreal-orcomplex-valuedmatrix.bisanNx-by-Nureal-orcomplex-valuedmatrix.cisanNy-by-Nxrea

4、l-orcomplex-valuedmatrix.disanNy-by-Nureal-orcomplex-valuedmatrix.TosetD=0,setdtothescalar0(zero),regardlessofthedimension.离散模型：sys=ss(a,b,c,d,Ts)createsthediscrete-timemodel+1|=Ax凡+Bun+-ZhinwithsampletimeTs(inseconds).SetTs=-1orTs=toleavethesampletimeunspecified.1.3 MATLABtf2ss函数命令:将传递函数模型转化为状态空间模型

5、，单输入单输出系统转换如下：-誓-生:七&Cisf-D4因的产一+次的Ht0怙利用该命令不仅可以转换SISO系统也可以转换MIMO系统,如下MISO系统也可以：2s+J+2sJ+0.45+1Byali2016-5-3den=023;121;num=10.41;A,B,C,D=tf2ss(den,num)结果：A=-0.4000-1.00001.00000B=10C=2.00003.00001.60000D=012、实例仿真2.1假设工业过程某传递函数：L5s2+5S+1den=1.5;num=151;A,B,C,D=tf2ss(den,num)结果：a=x1x2x1-5-1x210b=

6、u1x11x20c=x1x2y101.5u1%0SIZES,X0,STR,TSInitialization,returnsystemsizesinSYS,%initialstateinX0,stateorderingstrings%inSTR,andsampletimesinTS.%1DXReturncontinuousstatederivativesinSYS.%2DSUpdatediscretestatesSYS=X(n+1)%3YReturnoutputsinSYS.%4TNEXTReturnnexttimehitforvariablestepsample%timeinSYS.%5Res

7、ervedforfuture(rootfinding).%9Termination,performanycleanupSYS=.y10所以有：2.2修改S-Function模板参数:从结果可以看出，系统有两个状态，没有离散状态，输入1个，输出1种采用时间，打开模板，复制代码。functionsys,x0,str,ts,simStateCompliance=sfuntmpl(t,x,u,flag)函数名：sfuntmpl】%SFUNTMPLGeneralMATLABS-FunctionTemplate%WithMATLABS-functions,youcandefineyouownordinar

8、ydifferential%equations(ODEs),discretesystemequations,and/orjustabout%anytypeofalgorithmtobeusedwithinaSimulinkblockdiagram.%ThegeneralformofanMATLABS-functionsyntaxis:%SYS,X0,STR,TS,SIMSTATECOMPLIANCE=SFUNC(T,X,U,FLAG,P1,，Pn)%WhatisreturnedbySFUNCatagivenpointintime,T,dependsonthe%valueoftheFLAG,th

9、ecurrentstatevector,X,andthecurrent%inputvector,U.%FLAGRESULTDESCRIPTIONByali2016-5-3个，无直通反馈，-【一个主函数，需修改原%Thestatevectors,XandX0consistsofcontinuousstatesfollowed%bydiscretestates.%Optionalparameters,P1,PncanbeprovidedtotheS-functionand%usedduringanyFLAGoperation.%WhenSFUNCiscalledwithFLAG=0,thefoll

10、owinginformationByali2016-5-3%shouldbereturned:%SYS(1)=Numberofcontinuousstates.%SYS(2)=Numberofdiscretestates.%SYS(3)=Numberofoutputs.%SYS(4)=Numberofinputs.%AnyofthefirstfourelementsinSYScanbespecified%as-1indicatingthattheyaredynamicallysized.The%actuallengthforallotherflagswillbeequaltothe%lengt

11、hoftheinput,U.%SYS(5)=Reservedforrootfinding.Mustbezero.%SYS(6)=Directfeedthroughflag(1=yes,0=no).Thes-function%hasdirectfeedthroughifUisusedduringtheFLAG=3%call.Settingthisto0isakintomakingapromisethat%UwillnotbeusedduringFLAG=3.Ifyoubreakthepromise%thenunpredictableresultswilloccur.%SYS(7)=Numbero

12、fsampletimes.ThisisthenumberofrowsinTS.%X0=Initialstateconditionsorifnostates.%STR=Stateorderingstringswhichisgenerallyspecifiedas.%TS=Anm-by-2matrixcontainingthesampletime%(period,offset)information.Wherem=numberofsample%times.Theorderingofthesampletimesmustbe:%TS=00,:Continuoussampletime.%01,:Cont

13、inuous,butfixedinminorstep%sampletime.%PERIODOFFSET,:Discretesampletimewhere%PERIOD>0&OFFSET<PERIOD.%-20;:Variablestepdiscretesampletime%whereFLAG=4isusedtogettimeof%nexthit.%Therecanbemorethanonesampletimeproviding%theyareorderedsuchthattheyaremonotonically%increasing.Onlytheneededsamplet

14、imesshouldbe%specifiedinTS.Whenspecifyingmorethanone%sampletime,youmustcheckforsamplehitsexplicitlyby%seeingif%abs(round(T-OFFSET)/PERIOD)-(T-OFFSET)/PERIOD)%iswithinaspecifiedtolerance,generally1e-8.This%toleranceisdependentuponyourmodel'ssamplingtimesByali2016-5-3%andsimulationtime.%Youcanalso

15、specifythatthesampletimeoftheS-function%isinheritedfromthedrivingblock.Forfunctionswhich%changeduringminorsteps,thisisdoneby%specifyingSYS=1andTS=-10.Forfunctionswhich%areheldduringminorsteps,thisisdonebyspecifying%SYS(7)=1andTS=-11.%SIMSTATECOMPLIANCE=Specificeshowtohandlethisblockwhensavingand%res

16、toringthecompletesimulationstateofthe%model.Theallowedvaluesare:'DefaultSimState',%'HasNoSimState'or'DisallowSimState'.Ifthisvalue%isnotspeficified,thentheblock'scompliancewith%simStatefeatureissetto'UknownSimState'.%Copyright1990-2010TheMathWorks,Inc.%$Revision:1

17、.18.2.5$%ThefollowingoutlinesthegeneralstructureofanS-function.%switchflag,%Initialization%case0,sys,x0,str,ts,simStateCompliance=mdlInitializeSizes;%Derivatives%case 1,sys=mdlDerivatives(t,x,u);%Update%case 2, sys=mdlUpdate(t,x,u);%Outputs%Byali2016-5-3%case 3, sys=mdlOutputs(t,x,u);%GetTimeOfNextV

18、arHit%case 4,sys=mdlGetTimeOfNextVarHit(t,x,u);%Terminate%case9,sys=mdlTerminate(t,x,u);%Unexpectedflags%otherwiseDAStudio.error('Simulink:blocks:unhandledFlag',num2str(flag);end%endsfuntmpl%=%mdllnitializeSizes%Returnthesizes,initialconditions,andsampletimesfortheS-function.%=%functionsys,x

19、0,str,ts,simStateCompliance=mdlInitializeSizes%callsimsizesforasizesstructure,f川itinandconvertittoa%sizesarray.%Notethatinthisexample,thevaluesarehardcoded.Thisisnota%recommendedpracticeasthecharacteristicsoftheblockaretypically%definedbytheS-functionparameters.%sizes=simsizes;【不要更改】sizes.NumContSta

20、tes=2;【包括x1和x2两个连续状态】Byali2016-5-3sizes.NumDiscStates=0;sizes.NumOutputs=1;sizes.NumInputs=1;sizes.DirFeedthrough=0;sizes.NumSampleTimes=1;多个】【一个采用周期时间，可有【无离散状态】【一个输入u】y】【y和u无关】%atleastonesampletimeisneededsys=simsizes(sizes);【不要更改】%initializetheinitialconditions%x0=0;0;【初始状态均为0】%strisalwaysanemptym

21、atrix%str=;系统预留参数，不要更改】%initializethearrayofsampletimes%ts=00;【采样时间和偏移量，都为0说明为连续无偏移】%SpecifytheblocksimStateCompliance.Theallowedvaluesare:%'UnknownSimState',<Thedefaultsetting;warnandassumeDefaultSimState%'DefaultSimState',<Samesimstateasabuilt-inblock%'HasNoSimState',

22、<Nosimstate%'DisallowSimState'<ErroroutwhensavingorrestoringthemodelsimstatesimStateCompliance='UnknownSimState'%endmdlInitializeSizes%=%mdlDerivatives%Returnthederivativesforthecontinuousstates.%=%functionsys=mdlDerivatives(t,x,u)【求导，输出为状态x的导数】sys=-5-1;10*x+1;0*u;%endmdlDerivativesByali2016-5-3%=%mdlUpdate%Handlediscretestateupdates,sampletimehits,andmajortimestep%requirements.%=%functionsys=mdlUpdate(t,x,u)【离散情况下的x(n+1)】sys二口；%endmdlUpdate%=%mdlOutputs%Returntheblockoutput