《过程控制技术》课件-PID控制规律

PIDcontrollawsPID控制规律PID控制规律PIDcontrollaws谢聪XieCong主讲教师TeacherPID控制规律PIDcontrollawsPID控制规律PIDcontrollawsPID控制PIDcontrol工业控制Industrialcontrol自动化系统AutomationsystemsCaseImport案例导入小到家里的恒温热水器，大到工厂里的生产线、航天器的姿态调整，PID控制就像一位精准的“调节器”，默默维持着系统的稳定运行。Fromtheconstant-temperaturewaterheaterathometotheproductionlineinafactoryandtheattitudeadjustmentofaspacecraft,thePIDcontrolleractslikeaprecise"regulator",silentlymaintainingthestableoperationofthesystem.CaseImport案例导入如何实现这种“稳、准、快”的控制效果？Howisthis"stable,accurateandfast"controleffectachieved?比例、积分、微分这三个看似抽象的环节，又各自扮演着怎样的角色？Whatrolesdothethreeseeminglyabstractproportional,integralandderivativecontrollinksplayrespectively?Proportional(P)control比例（P）控制Proportional(P)control比例（P）控制控制器输出MV(t)和偏差信号e(t)成比例关系ThecontrolleroutputMV(t)isproportionaltothedeviationsignale(t)MV(t)=Kpe(t)+-Kpe被控参数Controlledparameter测量值PVMeasuredvaluePV被控参数Controlledparameter给定值SVSetvalueSV控制器输出值MVControlleroutputvalueMV控制器ControllerKp—比例增益Kp-proportionalgainKpProportional(P)control比例（P）控制控制器输出MV(t)和偏差信号e(t)成比例关系ThecontrolleroutputMV(t)isproportionaltothedeviationsignale(t)MV(t)=Kpe(t)+-Kpe被控参数Controlledparameter测量值PVMeasuredvaluePV被控参数Controlledparameter给定值SVSetvalueSV控制器Controller传递函数为ThetransferfunctionisKp—比例增益Kp-proportionalgain控制器输出值MVControlleroutputvalueMVProportional(P)control比例（P）控制例：自力杠杆式液位比例控制系统Example:Self-containedlever-typeliquidlevelproportionalcontrolsystem浮球为水位传感器，杠杆为控制器，活塞阀为执行器。如果某时刻Q2加大，造成水位下降，则浮球带动活塞提高，使Q1加大，才能阻止水位下降。Thefloatballservesasthewaterlevelsensor,theleverservesasthecontroller,andthepistonvalveservesastheactuator.IfQ2increasesatacertainmoment,causingthewaterleveltodrop,thefloatballwilldrivethepistontorise,increasingQ1topreventthewaterlevelfromdropping.Proportional(P)control比例（P）控制例：自力杠杆式液位比例控制系统Example:Self-containedlever-typeliquidlevelproportionalcontrolsystem

如果

e

=0，则活塞阀关闭，Q1=0。Ife=0,thepistonvalveisclosed,andQ1=0.浮球为水位传感器，杠杆为控制器，活塞阀为执行器。如果某时刻Q2加大，造成水位下降，则浮球带动活塞提高，使Q1加大，才能阻止水位下降。Thefloatballservesasthewaterlevelsensor,theleverservesasthecontroller,andthepistonvalveservesastheactuator.IfQ2increasesatacertainmoment,causingthewaterleveltodrop,thefloatballwilldrivethepistontorise,increasingQ1topreventthewaterlevelfromdropping.比例度（比例带）的概念Theconceptofproportionalband(proportionalityzone)Theconceptofproportionalband(proportionalityzone)比例度（比例带）的概念比例度P是纯比例控制器输入偏差的相对变化值与相应输出相对变化值之比的百分数。TheproportionalbandPisthepercentageratiooftherelativechangeintheinputdeviationofapureproportionalcontrollertothecorrespondingrelativechangeintheoutput.输入偏差(变化)值Inputdeviation(change)value控制器输出(变化)量Controlleroutput(change)测量输入的最大变化量Maximumchangeinthemeasuredinput（控制器的输入量程）(Inputrangeofthecontroller)输出的最大变化量Maximumchangeintheoutput（控制器的输出量程）(Outputrangeofthecontroller)比例度P比比例增益Kp更常用，用于表示比例控制作用的强弱。TheproportionalbandPismorecommonlyusedthantheproportionalgainKptoindicatethestrengthoftheproportionalcontrol.比例度P的工程意义EngineeringsignificanceoftheproportionalbandPEngineeringsignificanceoftheproportionalbandP比例度P的工程意义在纯比例控制下，使控制器输出变化100%时，所对应偏差e的相对量变化。Underpureproportionalcontrol,itrepresentstherelativechangeinthedeviationewhenthecontrolleroutputischangedby100%.MVSV0%(4mA)100%(20mA)50%PVmaxPVminP=50%P=100%PV/SV例如P=50%，则表明输入偏差变化满量程的50%时，就可使控制器输出变化100%。Forexample,ifP=50%,itmeansthatwhentheinputdeviationischangedby50%ofthefullrange,thecontrolleroutputcanbechangedby100%.若输入偏差变化超过此范围(50%)，则控制器输出进入饱和状态，不再符合比例关系。Iftheinputdeviationischangedbeyondthisrange(50%),thecontrolleroutputentersasaturatedstateandnolongerfollowstheproportionalrelationship.EngineeringsignificanceoftheproportionalbandP比例度P的工程意义例：某比例控制器，温度控制范围为400～800℃，输出信号范围是4～20mA。当测量指示值指针从600℃变到700℃时，控制器相应的输出从8mA变为16mA。求控制器的比例度。Example:Foracertainproportionalcontroller,thetemperaturecontrolrangeis400-800℃,andtheoutputsignalrangeis4-20mA.Whenthepointerofthemeasuredindicationvalueischangedfrom600℃to700°C,thecorrespondingcontrolleroutputischangedfrom

8mA

to

16mA.Calculatetheproportionalbandofthecontroller.MV/mAPV/℃Δe420800400P=50%ΔMVΔe=700−600=100℃ΔPVmax=800−400=400℃ΔMV=16−8=8mAΔMVmax=20−4=16mAEngineeringsignificanceoftheproportionalbandP比例度P的工程意义MV/mAPV/℃Δe420800400P=50%ΔMV解:Solution:例：某比例控制器，温度控制范围为400～800℃，输出信号范围是4～20mA。当测量指示值指针从600℃变到700℃时，控制器相应的输出从8mA变为16mA。求控制器的比例度。Example:Foracertainproportionalcontroller,thetemperaturecontrolrangeis400-800℃,andtheoutputsignalrangeis4-20mA.Whenthepointerofthemeasuredindicationvalueischangedfrom600℃to700°C,thecorrespondingcontrolleroutputischangedfrom

8mA

to

16mA.Calculatetheproportionalbandofthecontroller.EngineeringsignificanceoftheproportionalbandP比例度P的工程意义MV/mAPV/℃Δe420800400P=50%ΔMV解:Solution:答:Solution:比例度为50%，即温度的偏差在输入量程的50％区间。Theproportionalbandis50%,whichmeansthatwhenthetemperaturedeviationiswithin50%oftheinputrange（即200℃）内时，e

和

MV（满量程相对值）是2倍的关系。(i.e.,200°C),eandMV

(relativevaluesofthefullrange)havea2-foldrelationship.EngineeringsignificanceoftheproportionalbandP比例度P的工程意义当要求定值控制系统被控参数无余差时，就需要在比例控制的基础上，增加积分控制。Whenasetvaluecontrolsystemrequiresthecontrolledparametertohavenooffset,integralcontrolneedstobeaddedonthebasisofproportionalcontrol.比例积分控制（PI）Proportional-integralcontrol(PI)积分（I）控制Integral(I)control输出变值MV与输入偏差e的积分成正比TheoutputchangeMVisproportionaltotheintegraloftheinputdeviatione当e是幅值为E的阶跃值时WheneisastepvaluewithanamplitudeofETI—积分时间integraltimeeEt0tMVMV0EngineeringsignificanceoftheproportionalbandP比例度P的工程意义对于惯性较大的对象，常常希望能加快控制速度，此时可增加微分控制。Forobjectswithlargeinertia,itisoftendesiredtospeedupthecontrol.Inthiscase,derivativecontrolcanbeadded.比例微分控制（PD）Proportional-derivativecontrol(PD)微分（D）控制Derivative(D)control理想微分控制IdealderivativecontroleEttMVTD

—微分时间derivativetime—偏差变化速度RateofdeviationchangeEngineeringsignificanceoftheproportionalbandP比例度P的工程意义理想的比例微分控制Idealproportional-derivativecontroletE/PtMV

理想比例微分控制

Idealproportional-derivativecontroltMV实际的比例微分控制Actualproportional-derivativecontrolE/P理想微分控制（对阶跃扰动）持续时间太短，执行器（如调节阀）来不及响应（右中图所示）。Thedurationofidealderivativecontrol(forastepdisturbance)istooshort,andtheactuator(suchasacontrolvalve)hasnotimetorespond(asshowninthemiddle-rightfigure).工程中一般采用实际微分控制（右下图所示）。Inengineering,actualderivativecontrolisgenerallyused(asshowninthebottom-rightfigure).PID控制原理：P、I、D作用解析与参数整定PIDControlPrinciple:AnalysisofP,I,DActionsandParameterTuningPIDControlPrinciple:AnalysisofP,I,DActionsandParameterTuningPID控制原理：P、I、D作用解析与参数整定将比例、积分、微分三种控制结合在一起，只要三项控制作用配合适当，即可得即能快速控制，又能消除余差的满意控制效果。Bycombiningproportional,integralandderivativecontrols,aslongasthethreecontrolactionsareproperlycoordinated,asatisfactorycontroleffectcanbeachieved,whichcanprovidefastcontrolandeliminateoffset.比例+积分+微分（PID）控制Proportional+integral+derivative(PID)controlP是比例度PistheproportionalbandTI是积分时间TIistheintegraltimeTD是微分时间TDisthederivativetimeMVe0t0t积分控制部分Integralcontrolpart比例控制部分Proportionalcontrolpart微分控制部分DerivativecontrolpartPID控制作用PIDcontrolactionE比例（P）控制是基础，为系统提供基本的控制作用；Proportional(P)controlisthefoundation,providingthebasiccontrolactionforthesystem;微分（D）控制用于抑制偏差（增加）变化，加快系统控制速度；Derivative(D)controlisusedtosuppresstheincreaseindeviationandspeedupthesystemcontrol;积分（I）控制用于在偏差e=0时，保持控制器输出MV，消除静差。Integral(I)controlisusedtomaintainthecontrolleroutputMVwhenthedeviation

e=0toeliminatethestaticerror.PIDControlPrinciple:AnalysisofP,I,DActionsandParameterTuningPID控制原理：P、I、D作用解析与参数整定PIDControlPrinciple:AnalysisofP,I,DActionsandParameterTuningPID控制原理：P、I、D作用解析与参数整定比例、积分、微分特点Characteristicsofproportional,integralandderivativecontrols控制类型Controltype核心作用Corefunction主要优点Mainadvantages主要缺点Maindisadvantages比例（P）Proportional(P)直接按误差比例调节Adjustdirectlyinproportiontotheerror响应快速、结构简单Fastresponse,simplestructure易超调、可能存在静态误差Pronetoovershoot,mayhavestaticerror积分（I）Integral(I)消除累计误差（静态误差）Eliminatecumulativeerror(staticerror)无静差调节Zerostaticerrorregulation响应滞后、可能积分饱和Responselag,maycauseintegralsaturation微分（D）Derivative(D)预测误差变化趋势（斜率）Predictthetrendoferrorchange(slope)抑制超调、改善稳定性Suppressovershoot,improvestability对噪声敏感、易放大高频干扰Sensitivetonoise,mayamplifyhigh-frequencyinterferenceP

是基础：必须存在，否则系统无调节力（纯I/D无法单独工作）；Pisthefoundation:itmustexist;otherwise,thesystemhasnoregulatingability(pureI/Dcannotworkalone);PIDControlPrinciple:AnalysisofP,I,DActionsandParameterTuningPID控制原理：P、I、D作用解析与参数整定比例、积分、微分特点Characteristicsofproportional,integralandderivativecontrols控制类型Controltype核心作用Corefunction主要优点Mainadvantages主要缺点Maindisadvantages比例（P）Proportional(P)直接按误差比例调节Adjustdirectlyinproportiontotheerror响应快速、结构简单Fastresponse,simplestructure易超调、可能存在静态误差Pronetoovershoot,mayhavestaticerror积分（I）Integral(I)消除累计误差（静态误差）Eliminatecumulativeerror(staticerror)无静差调节Zerostaticerrorregulation响应滞后、可能积分饱和Responselag,maycauseintegralsaturation微分（D）Derivative(D)预测误差变化趋势（斜率）Predictthetrendoferrorchange(slope)抑制超调、改善稳定性Suppressovershoot,improvestability对噪声敏感、易放大高频干扰Sensitivetonoise,mayamplifyhigh-frequencyinterferenceI用于除静差：仅在需要高精度稳态时加入（避免积分饱和导致响应滞后）；Iisusedtoeliminatestaticerror:itisaddedonlywhenhigh-precisionsteady-stateisrequired(toavoidresponselagcausedbyintegralsaturation);PIDControlPrinciple:AnalysisofP,I,DActionsandParameterTuningPID控制原理：P、I、D作用解析与参数整定比例、积分、微分特点Characteristicsofproportional,integralandderivativecontrols控制类型Controltype核心作用Corefunction主要优点Mainadvantages主要缺点Maindisadvantages比例（P）Proportional(P)直接按误差比例调节Adjustdirectlyinproportiontotheerror响应快速、结构简单Fastresponse,simplestructure易超调、可能存在静态误差Pronetoovershoot,mayhavestaticerror积分（I）Integral(I)消除累计误差（静态误差）Eliminatecumulativeerror(staticerror)无静差调节Zerostaticerrorregulation响应滞后、可能积分饱和Responselag,maycauseintegralsaturation微分（D）Derivative(D)预测误差变化趋势（斜率）Predictthetrendoferrorchange(slope)抑制超调、改善稳定性Suppressovershoot,improvestability对噪声敏感、易放大高频干扰Sensitivetonoise,mayamplifyhigh-frequencyinterferenceD

用于抗超调：仅在系统惯性大、易超调时加入（噪声环境慎用，需加滤波）；Disusedtoresistovershoot:itisaddedonlywhenthesystemhaslargeinertiaandispronetoovershoot(usewithcautioninnoisyenvironmentsandaddfiltering);PIDControlPrinciple:AnalysisofP,I,DActionsandParameterTun