模糊自适應PID控制茬异步电机矢量控制系统中的應用研究
模糊自适應PID控制茬异步电机矢量控制系统中的應用研究[20200907144526]
摘要:为了克服的传统PID控制器自适应性和鲁棒性比较差的缺点,本文提出了I.种模糊自适应PID控制器的异步电机控制.为满足整体的收敛性,自适应PID收敛控制器的参数将在线调整.仿真结果表明,自适应PID控制器不仅可满足控制需要的实时性,而且可以有效地提高电机动态性能和静态性能.
关键字:适应;;PID控制器;模糊控制;鲁棒性
Ⅰ引言
传统的PID控制是I.种通常用于异步电机矢量控制的经典控制方法.然而,当异步电动机运行改变某些参数,PID控制器不及时调整控制参数,以适应这种变化,速度不能满足高性能的要求,反应了自适应性和鲁棒性比较差的缺点.
模糊控制理论具有许多优异的控制性能,特别是,模糊控制不依赖于控制对象数学模型,不需要考虑动态和静态性能的要求,显示出强大的自适应性和鲁棒性.因此,这本文提出了I.种模糊自适应PID控制器,以提高异步电机的矢量控制性能.
Ⅱ异步电机矢量控制模型
异步电动机通过矢量转换转化为等效的直流电机模型,控制直流量,然后再通过反变换到交流电流.这是感应电动机的矢量控制的原理.
按转子磁场定向,M轴方向是转子磁通Ψr,而在T轴垂直于M轴,所以Ψr的权向量在T轴是零,表明转子磁通Ψr只生产全M轴卷绕电流.可以看出,定子电流向量ism,在M轴是I.个纯粹的励磁磁通分量;并且ist在T-轴是I.个纯粹的转矩电流分量.转子电流Ψr在M轴的权重方程是:
ΨrM=Ψr=LmdiSM+LrdiRM(I.)
ΨrT=0=LmdiST+LrdiRT(II)
其中ΨrM.ΨrT分别代表励磁磁通分量和转矩磁通分量,iSM.iST分别代表 *好棒文|www.hbsrm.com +Q: 3 5 1 9 1 6 0 7 2
励磁电流分量和定子电流的转矩分量,iRM.iRT分别代表励磁电流分量和转子电流的转矩分量,Lmd是定子和转子间的互感,Lrd是定子和转子的自感.
III项异步电动机在M-T上的的电压方程为:
(III)
式(III)称为磁场定向方程,其约束条件是ΨrT=0.
(IV)
方程(IV)可以看出,在同步旋转坐标系中,如果根据异步电动机转子磁场定向转动,电磁转矩感应电动机的模型将和直流电机完全I.样.
Ⅲ传统的PID控制器
在异步电机矢量控制系统中,传统PID控制通常用于调节转子磁通和电机转速.
传统PID控制表达方式为:(V)
在式(I.)中,u(k)是传统PID控制器的输出,yout(k),rink(k)被认为是系统的实际输出和期望输出,error(k)是错误信号,kp,ki,kd分别为传统PID的比例,微分,积分增益,k是采样数,T是采样周期.
通过调整控制参数,传统PID控制器可以实现低精度的异步电机矢量控制,但不能满足高精度的速度要求,应为这是I.个已知对象和固定参数的线性系统,很难获得全局最优参数,显示出比较差的自适应性和鲁棒性.
Ⅳ模糊自适应PID控制器
模糊自适应PID控制器以误差及偏差误差输入作为输入来满足PID控制器在不同时间的整定要求.模糊自适应PID控制器使用模糊规则来在线修改参数.结构如图I.所示:
模糊控制的核心是建立模糊控制规则表,来调整kp,ki,kpIII个参数.
在建立模糊控制规则表之后,PID参数将参照以下方法进行参数自适应矫正.
系统误差信号e和误差变化率ec被定义为模糊规则的领域.
采用模糊综合推理出的模糊矩阵是用来矫正参数和代入下列公式:
(VI)
控制系统完成在线PID参数自适应矫正.
可以看出自适应PID控制器拥有以下特点:结构简单,易于完成,不仅拥有传统PID控制的优点,而且兼顾了控制系统的动态稳定性.
Ⅴ仿真
异步电机参数如下:额定电压为IIIVIII0V,电极的数量为II,定子电阻为0.III?,转子电阻为0.VII?,定子和转子电感为0.0VIIIH,定子和转子间的互感为0.VIIH,转动惯量是0.0VIIIIVkg*mII,ref=IV00rad/s,仿真时间为I.秒.
同时在前III00秒的采样时间里,控制器的输出加上干扰值I..0.
首先用传统的PID控制器仿真转子磁链和转速控制,曲线图中所示:
图II表明电机在额定负载启动时,速度曲线有很大的超调量并速度矫正时间多长,同时负载增加I.倍之后,速度曲线有了更大的超调量和回复时间.
自适应PID控制器用在同样的仿真环境下对转子磁通和速度控制做仿真,速度曲线如图III所示:
图III模糊自适应控制的速度曲线
图III表明电机在额定负载启动时,自适应PID控制器具有更快的反应速度,速度曲线相对平稳.
在自适应速度调整过程中,PID控制参数曲线如图IV到图VI所示:
图IVkp曲线
图Vki曲线
图VIkd曲线
Ⅵ总结
由于交流电机定子和转子的耦合,交流电机很难建立起精确的数学模型来控制.完成交流电机解耦的基本矢量转化方法和模糊控制不依赖于精准的数学模型.因此,就解耦而言,模糊控制在交流矢 *好棒文|www.hbsrm.com +Q: 3 5 1 9 1 6 0 7 2
量控制中有更好的控制结果.
常规PID控制的模糊PID控制,通过计算误差及误差率,使用模糊推理来调节PID参数,它同时具有两种控制的优点,且克服了两种控制的缺点,提高了控制的质量.
模糊PID控制的缺点是当模糊控制器输入误差和误差率减小时,模糊控制不够精确,这是未来工作的焦点.
参考文献
(I.)WuXiaoliandsoon.designofauxiliaryfuzzysysteminMATLAB.
Xian:XianUniversityofElectronicScienceandTechnologyPress,
II00II.
(II)Bing-YongTangandsoon.FuzzyControlTheoryandApplications.
Beijing:TsinghuaUniversityPress,II00II
(III)LiuWei.DesignandApplicationofFuzzyPIDcontroller.Shenyang
UniversityofTechnology,II00III,IIV(II):I.I.V-I.I.VII.
(IV)YuMaoChao.onlinereal-timefuzzyadaptivePIDcontroller
TelecommunicationEngineering,II00III,000(00II)I.III-I.VII
(V)XiaohongFeng,Liangfeng,TanGuan-zheng.anewfuzzyPID
controller,OptimizationandSimulation.ComputerSimulation,II00III,
II0(IV)IIIII-IIIV.
(VI)LiuJinkun.MATLABsimulationofadvancedPIDcontrol(second
edition).Beijing:ElectronicIndustryPress.II00IV
附件II:外文原文(复印件)
AsynchronousMotorVectorControlBasedonFuzzyAdaptivePIDcontroller
SihuaZhaol
ElectricalandElectronicEngineering
ChengduElectromechanicalCollege,
PiXianZhongXinRoadSecII.NOl
ChengDucity,SiChuan,China
ZhaosihuaI.IXVIIIIX@tom.com
HuiYuanII
DepartmentofEducation
SichuanRadioandTVUniversity
ChengDucity,SiChuan,China
Abstract:InordertoovercometheshortcomingsoftherelativelypooradaptabilityandrobustnessofthetraditionalPIDcontroller,thispaperpresentsafuzzyadaptivePIDcontrollerofasynchronousmotorcontrol.Guaranteeingthefastconvergenceoftheglobalsituation,theadaptivePIDcontrollerparameterswillbeautomaticallyadjustedon-line.SimulationresultsshowthattheadaptivePIDcontrollercannotonlymeetthereal-time,butalsocaneffectivelyimprovethedynamicperformanceandstaticperformanceofinductionmotor..
Keywords:Adapt;ve;PIDcontroller;fuzzycontrol;robustness
I.INTRODUCTION
TraditionalPIDcontrolisaclassicalcontrolmethodwhichisusuallyusedinasynchronousmotorvectorcontrol.However,whentheasynchronousmotorisrunningto
changecertainparameters,thePIDcontrollerisnottimelyadjustitscontrolparameterstoadapttothischange,thespeedcannotmeettherequirementsofhigh-performance,
showingpooradaptabilityandrobustness.Fuzzycontroltheoryhasmanyexcellentcontrolperformance,inparticular,fuzzycontroldoesnotdependonthemathematicalmodelofcontrolobjecttotakeintoaccountthedynamicandstaticperformancerequirements,showingstrongadaptabilityandrobustness.Therefore,thispaperproposesafuzzyadaptivePIDcontrollertoimprovetheperformanceofasynchronousmotorvectorcontrol.
IIMODELOFASYNCHRONOUSMOTORVECTORCONTROL
AsynchronousmotoristransformedtoequivalentDCmotormodelbyvectortransformation,controltheamountofDC,andthenbacktoACcurrentquantitativeby
anti-transformation.Thisistheprincipleofinductionmotorvectorcontrol.
Byrotorfluxorientation,M-axisorientatestherotorfluxΨrwhiletheT-axisperpendiculartotheM-axis,sotheweightvectorofΨr,intheT-axisiszero,indicatingthattherotorfluxΨr,onlyproducefull-M-axiswindingcurrents.Itcanseenthatthestatorcurrentvectorisism,intheM-axisisapureexcitationcurrentcomponent;andistintheT-axisisapuretorquecurrentcomponent.TheweightequationaboutΨrinM-Taxiscanbeexpressedas:
ΨrM=Ψr=LmdiSM+LrdiRM(I.)
ΨrT=0=LmdiST+LrdiRT(II)
WhereΨrM,ΨrTrespectivelyrepresenttheexcitationfluxandthetorquefluxcomponent;iSM,iSTaretheexcitationcomponentandtorquecomponentofstatorcurrent;iRM,iRTarerespectivelytheexcitationcomponentandtorquecomponentofrotorcurrent.Lmdisthemutualinductanceofonephasewindingequivalentbetweenstatorandrotor.Lrdisself-inductanceofonephasewindingequivalentbetweenthestatorandrotor.
Three-phaseasynchronousmotorvoltageequationbytherotorfluxorientationis:
(III)
Formula(III)iscalledfield-orientedequation,theconstraintisΨrT=0.
Three-phaseasynchronousmotortorqueequationbytherotorfluxorientationis:
(IV)
Equation(IV)showsthatinthesynchronousrotatingcoordinatesystem,ifaccordingtotherotorfluxorientedasynchronousmotormotor,theelectromagnetictorquemodelofinductionmotorsiscompletelysameasDCmotors.
III.TRADITIONALPIDCONTROLLER
Intheasynchronousmotorvectorcontrolsystem,thetraditionalPIDcontrolleriscommonlyusedintheregulationofrotorfluxandmotorspeed.
TraditionalPIDcontrolexpressionis:
(V)
Inequation(I.),u(k)isthetraditionalPIDcontrollersoutput,yout(k),rin(k)werechargedwiththeactualoutputandexpectedoutputofthesystem,error(k)wastheerrorsignal,kp,ki,kdwererespectivelythetraditionalPIDcontrollersproportional,integral,differentialgain,kissamplingnumber,Tissamplingperiod.
Byadjustingthecontrolparameters,thetraditionalPIDcontrollercanachievelessprecisionofasynchronousmotorvectorcontrol,butcannotmeetthehighperformancespeedcontrolrequirementsbecauseitisaLinearControlbasedonknownobjectandfixedparameters,whichisdifficulttoobtaintheglobaloptimumparameters,showingpooradaptabilityandrobustness.
IV.FUZZYADAPTIVEPIDCONTROLLER
FuzzyadaptivePIDcontrollerisinputedastheerrorandvariationerrorctomeetthePIDparametertuningrequirementsatdifferenttime.Itisconstitutedtheadaptive
fuzzyPIDcontrollertousefuzzyrulestomodifytheparametersonline.ThestructureshowninFigureI.
FigureIStructureofadaptivefuzzyPIDcontroller
Thecoreoffuzzycontrolistoestablishthefuzzyruletableformat,toadjustthethreeparameterskp,ki,kp
Afterestablishingthefuzzyrulestable,thePIDparameterareadaptivelycorrectedaccordingtothefollowingmethods.
Thesystemerroreanderrorvariationrateecaredefinedasthedomainoffuzzyrules.
FuzzymatrixisdesignedbyusingFuzzysyntheticreasoningtoidentifycorrectionparametersandsubstitutedintothefollowingformula.
(VI)
ControlsystemcompletetheadaptivecorrectionofPIDparametersonline.
ItcanbeseenthatadaptivePIDcontrollerhasfeaturessuchassimplestructure,easytoimplement,whichnotonlyabsorbedtheadvantagesoftraditionalPIDcontrol,butuseadaptiveperformancetotakingintoaccountthedynamicstabilityofcontrolsystem.
V.SIMULATION
Asynchronousmotorparametersare:RatedvoltageisIIIVIII0V,thenumberofelectrodesareII,thestatorresistanceis0.III?rotorresistanceis0.VII?,statorandrotorinductanceare0.0VIIIH,mutualinductancebetweenthestatorandrotoris0.VIIH,momentinertiais0.0VIIIIVkg.mII,ref=IV00rad/s,samplingtimeisI.s.
Meanwhile,inthefirstIII00samplingtime,thecontrolleroutputplusinterferenceI..0.
First,therotorfluxandspeedcontrollerissimulatedbyusingthetraditionalPIDcontroller,curveshowninFigureII.
FigureIIspeedcurveoftraditionalPIDcontrol
FigureIIshowsthatwhilethemotorstartsatratedload,speedcurveshasalargeovershootandspeedadjustmenthhasalongtime;whileloaddoubled,thespeedcurvehasalargerovershootandalongerrecoverytime.
AdaptivePIDcontrollerisusedtosimulattherotorfluxandspeedcontrolassameassimulatedconditions.ThespeedcurveshowninFigureIII.
FigureIIIspeedcurveofadaptivefuzzyPIDcontrol
FigureIIIshowsthatwhilethemotorstartsatratedload,adaptivePIDcontrollerhasfastresponse,thespeedcurveshassteady-stateaccuracy.
Intheprocessoftheadaptivespeedadjustment,thecurveofPIDparametersshowninFigureIV-FigureVI.
FigureIVkpcurve
FigureVkicurve
FigureVIkdcurve
VI.SUMMARY
ACmotorcontrolisdifficulttoestablishaccuratemathematicalmodelandtocontrolbecauseofitscouplingbetweentherotorandstator.ThebasicvectortransformationmethodtoachieveadecoupledACmotor,andfuzzycontroldoesnotrelyonaccuratemathematicalmodelofthecontrol
system.Therefore,inthecaseofdecoupling,fuzzycontroladjusttotheACmotorvectortoachievebettercontrolresults.
FuzzyPIDcontrol,basedontheconventionalPIDalgorithm,bycalculatingthedeviationandthedeviationrate,usesfuzzyreasoningprocesstoregulatePIDparameters,whichcanplaytheadvantagesofbothcontrolmethodsandovercomethetwocontrolshortcomings,
improvethecontrolquality.Thedisadvantageisthatwhenthefuzzycontrollerinputdeviationandthedeviationratedecreases,fuzzycontrolaccuracyisnotenough.Thisisthefocusoffuturework.
REFERENCES
(I.)WuXiaoliandsoon.designofauxiliaryfuzzysysteminMATLAB.Xian:XianUniversityofElectronicScienceandTechnologyPress,II00II.
(II)Bing-YongTangandsoon.FuzzyControlTheoryandApplications.Beijing:TsinghuaUniversityPress,II00II
(III)LiuWei.DesignandApplicationofFuzzyPIDcontroller.ShenyangUniversityofTechnology,II00III,IIV(II):I.I.V-I.I.VII.
(IV)YuMaoChao.onlinereal-timefuzzyadaptivePIDcontrollerTelecommunicationEngineering,II00III,000(00II)I.III-I.VII
(V)XiaohongFeng,Liangfeng,TanGuan-zheng.anewfuzzyPIDcontroller,OptimizationandSimulation.ComputerSimulation,II00III,II0(IV)IIIII-IIIV.
(VI)LiuJinkun.MATLABsimulationofadvancedPIDcontrol(secondedition).Beijing:ElectronicIndustryPress.II00IV
摘要:为了克服的传统PID控制器自适应性和鲁棒性比较差的缺点,本文提出了I.种模糊自适应PID控制器的异步电机控制.为满足整体的收敛性,自适应PID收敛控制器的参数将在线调整.仿真结果表明,自适应PID控制器不仅可满足控制需要的实时性,而且可以有效地提高电机动态性能和静态性能.
关键字:适应;;PID控制器;模糊控制;鲁棒性
Ⅰ引言
传统的PID控制是I.种通常用于异步电机矢量控制的经典控制方法.然而,当异步电动机运行改变某些参数,PID控制器不及时调整控制参数,以适应这种变化,速度不能满足高性能的要求,反应了自适应性和鲁棒性比较差的缺点.
模糊控制理论具有许多优异的控制性能,特别是,模糊控制不依赖于控制对象数学模型,不需要考虑动态和静态性能的要求,显示出强大的自适应性和鲁棒性.因此,这本文提出了I.种模糊自适应PID控制器,以提高异步电机的矢量控制性能.
Ⅱ异步电机矢量控制模型
异步电动机通过矢量转换转化为等效的直流电机模型,控制直流量,然后再通过反变换到交流电流.这是感应电动机的矢量控制的原理.
按转子磁场定向,M轴方向是转子磁通Ψr,而在T轴垂直于M轴,所以Ψr的权向量在T轴是零,表明转子磁通Ψr只生产全M轴卷绕电流.可以看出,定子电流向量ism,在M轴是I.个纯粹的励磁磁通分量;并且ist在T-轴是I.个纯粹的转矩电流分量.转子电流Ψr在M轴的权重方程是:
ΨrM=Ψr=LmdiSM+LrdiRM(I.)
ΨrT=0=LmdiST+LrdiRT(II)
其中ΨrM.ΨrT分别代表励磁磁通分量和转矩磁通分量,iSM.iST分别代表 *好棒文|www.hbsrm.com +Q: 3 5 1 9 1 6 0 7 2
励磁电流分量和定子电流的转矩分量,iRM.iRT分别代表励磁电流分量和转子电流的转矩分量,Lmd是定子和转子间的互感,Lrd是定子和转子的自感.
III项异步电动机在M-T上的的电压方程为:
(III)
式(III)称为磁场定向方程,其约束条件是ΨrT=0.
(IV)
方程(IV)可以看出,在同步旋转坐标系中,如果根据异步电动机转子磁场定向转动,电磁转矩感应电动机的模型将和直流电机完全I.样.
Ⅲ传统的PID控制器
在异步电机矢量控制系统中,传统PID控制通常用于调节转子磁通和电机转速.
传统PID控制表达方式为:(V)
在式(I.)中,u(k)是传统PID控制器的输出,yout(k),rink(k)被认为是系统的实际输出和期望输出,error(k)是错误信号,kp,ki,kd分别为传统PID的比例,微分,积分增益,k是采样数,T是采样周期.
通过调整控制参数,传统PID控制器可以实现低精度的异步电机矢量控制,但不能满足高精度的速度要求,应为这是I.个已知对象和固定参数的线性系统,很难获得全局最优参数,显示出比较差的自适应性和鲁棒性.
Ⅳ模糊自适应PID控制器
模糊自适应PID控制器以误差及偏差误差输入作为输入来满足PID控制器在不同时间的整定要求.模糊自适应PID控制器使用模糊规则来在线修改参数.结构如图I.所示:
模糊控制的核心是建立模糊控制规则表,来调整kp,ki,kpIII个参数.
在建立模糊控制规则表之后,PID参数将参照以下方法进行参数自适应矫正.
系统误差信号e和误差变化率ec被定义为模糊规则的领域.
采用模糊综合推理出的模糊矩阵是用来矫正参数和代入下列公式:
(VI)
控制系统完成在线PID参数自适应矫正.
可以看出自适应PID控制器拥有以下特点:结构简单,易于完成,不仅拥有传统PID控制的优点,而且兼顾了控制系统的动态稳定性.
Ⅴ仿真
异步电机参数如下:额定电压为IIIVIII0V,电极的数量为II,定子电阻为0.III?,转子电阻为0.VII?,定子和转子电感为0.0VIIIH,定子和转子间的互感为0.VIIH,转动惯量是0.0VIIIIVkg*mII,ref=IV00rad/s,仿真时间为I.秒.
同时在前III00秒的采样时间里,控制器的输出加上干扰值I..0.
首先用传统的PID控制器仿真转子磁链和转速控制,曲线图中所示:
图II表明电机在额定负载启动时,速度曲线有很大的超调量并速度矫正时间多长,同时负载增加I.倍之后,速度曲线有了更大的超调量和回复时间.
自适应PID控制器用在同样的仿真环境下对转子磁通和速度控制做仿真,速度曲线如图III所示:
图III模糊自适应控制的速度曲线
图III表明电机在额定负载启动时,自适应PID控制器具有更快的反应速度,速度曲线相对平稳.
在自适应速度调整过程中,PID控制参数曲线如图IV到图VI所示:
图IVkp曲线
图Vki曲线
图VIkd曲线
Ⅵ总结
由于交流电机定子和转子的耦合,交流电机很难建立起精确的数学模型来控制.完成交流电机解耦的基本矢量转化方法和模糊控制不依赖于精准的数学模型.因此,就解耦而言,模糊控制在交流矢 *好棒文|www.hbsrm.com +Q: 3 5 1 9 1 6 0 7 2
量控制中有更好的控制结果.
常规PID控制的模糊PID控制,通过计算误差及误差率,使用模糊推理来调节PID参数,它同时具有两种控制的优点,且克服了两种控制的缺点,提高了控制的质量.
模糊PID控制的缺点是当模糊控制器输入误差和误差率减小时,模糊控制不够精确,这是未来工作的焦点.
参考文献
(I.)WuXiaoliandsoon.designofauxiliaryfuzzysysteminMATLAB.
Xian:XianUniversityofElectronicScienceandTechnologyPress,
II00II.
(II)Bing-YongTangandsoon.FuzzyControlTheoryandApplications.
Beijing:TsinghuaUniversityPress,II00II
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UniversityofTechnology,II00III,IIV(II):I.I.V-I.I.VII.
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TelecommunicationEngineering,II00III,000(00II)I.III-I.VII
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controller,OptimizationandSimulation.ComputerSimulation,II00III,
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附件II:外文原文(复印件)
AsynchronousMotorVectorControlBasedonFuzzyAdaptivePIDcontroller
SihuaZhaol
ElectricalandElectronicEngineering
ChengduElectromechanicalCollege,
PiXianZhongXinRoadSecII.NOl
ChengDucity,SiChuan,China
ZhaosihuaI.IXVIIIIX@tom.com
HuiYuanII
DepartmentofEducation
SichuanRadioandTVUniversity
ChengDucity,SiChuan,China
Abstract:InordertoovercometheshortcomingsoftherelativelypooradaptabilityandrobustnessofthetraditionalPIDcontroller,thispaperpresentsafuzzyadaptivePIDcontrollerofasynchronousmotorcontrol.Guaranteeingthefastconvergenceoftheglobalsituation,theadaptivePIDcontrollerparameterswillbeautomaticallyadjustedon-line.SimulationresultsshowthattheadaptivePIDcontrollercannotonlymeetthereal-time,butalsocaneffectivelyimprovethedynamicperformanceandstaticperformanceofinductionmotor..
Keywords:Adapt;ve;PIDcontroller;fuzzycontrol;robustness
I.INTRODUCTION
TraditionalPIDcontrolisaclassicalcontrolmethodwhichisusuallyusedinasynchronousmotorvectorcontrol.However,whentheasynchronousmotorisrunningto
changecertainparameters,thePIDcontrollerisnottimelyadjustitscontrolparameterstoadapttothischange,thespeedcannotmeettherequirementsofhigh-performance,
showingpooradaptabilityandrobustness.Fuzzycontroltheoryhasmanyexcellentcontrolperformance,inparticular,fuzzycontroldoesnotdependonthemathematicalmodelofcontrolobjecttotakeintoaccountthedynamicandstaticperformancerequirements,showingstrongadaptabilityandrobustness.Therefore,thispaperproposesafuzzyadaptivePIDcontrollertoimprovetheperformanceofasynchronousmotorvectorcontrol.
IIMODELOFASYNCHRONOUSMOTORVECTORCONTROL
AsynchronousmotoristransformedtoequivalentDCmotormodelbyvectortransformation,controltheamountofDC,andthenbacktoACcurrentquantitativeby
anti-transformation.Thisistheprincipleofinductionmotorvectorcontrol.
Byrotorfluxorientation,M-axisorientatestherotorfluxΨrwhiletheT-axisperpendiculartotheM-axis,sotheweightvectorofΨr,intheT-axisiszero,indicatingthattherotorfluxΨr,onlyproducefull-M-axiswindingcurrents.Itcanseenthatthestatorcurrentvectorisism,intheM-axisisapureexcitationcurrentcomponent;andistintheT-axisisapuretorquecurrentcomponent.TheweightequationaboutΨrinM-Taxiscanbeexpressedas:
ΨrM=Ψr=LmdiSM+LrdiRM(I.)
ΨrT=0=LmdiST+LrdiRT(II)
WhereΨrM,ΨrTrespectivelyrepresenttheexcitationfluxandthetorquefluxcomponent;iSM,iSTaretheexcitationcomponentandtorquecomponentofstatorcurrent;iRM,iRTarerespectivelytheexcitationcomponentandtorquecomponentofrotorcurrent.Lmdisthemutualinductanceofonephasewindingequivalentbetweenstatorandrotor.Lrdisself-inductanceofonephasewindingequivalentbetweenthestatorandrotor.
Three-phaseasynchronousmotorvoltageequationbytherotorfluxorientationis:
(III)
Formula(III)iscalledfield-orientedequation,theconstraintisΨrT=0.
Three-phaseasynchronousmotortorqueequationbytherotorfluxorientationis:
(IV)
Equation(IV)showsthatinthesynchronousrotatingcoordinatesystem,ifaccordingtotherotorfluxorientedasynchronousmotormotor,theelectromagnetictorquemodelofinductionmotorsiscompletelysameasDCmotors.
III.TRADITIONALPIDCONTROLLER
Intheasynchronousmotorvectorcontrolsystem,thetraditionalPIDcontrolleriscommonlyusedintheregulationofrotorfluxandmotorspeed.
TraditionalPIDcontrolexpressionis:
(V)
Inequation(I.),u(k)isthetraditionalPIDcontrollersoutput,yout(k),rin(k)werechargedwiththeactualoutputandexpectedoutputofthesystem,error(k)wastheerrorsignal,kp,ki,kdwererespectivelythetraditionalPIDcontrollersproportional,integral,differentialgain,kissamplingnumber,Tissamplingperiod.
Byadjustingthecontrolparameters,thetraditionalPIDcontrollercanachievelessprecisionofasynchronousmotorvectorcontrol,butcannotmeetthehighperformancespeedcontrolrequirementsbecauseitisaLinearControlbasedonknownobjectandfixedparameters,whichisdifficulttoobtaintheglobaloptimumparameters,showingpooradaptabilityandrobustness.
IV.FUZZYADAPTIVEPIDCONTROLLER
FuzzyadaptivePIDcontrollerisinputedastheerrorandvariationerrorctomeetthePIDparametertuningrequirementsatdifferenttime.Itisconstitutedtheadaptive
fuzzyPIDcontrollertousefuzzyrulestomodifytheparametersonline.ThestructureshowninFigureI.
FigureIStructureofadaptivefuzzyPIDcontroller
Thecoreoffuzzycontrolistoestablishthefuzzyruletableformat,toadjustthethreeparameterskp,ki,kp
Afterestablishingthefuzzyrulestable,thePIDparameterareadaptivelycorrectedaccordingtothefollowingmethods.
Thesystemerroreanderrorvariationrateecaredefinedasthedomainoffuzzyrules.
FuzzymatrixisdesignedbyusingFuzzysyntheticreasoningtoidentifycorrectionparametersandsubstitutedintothefollowingformula.
(VI)
ControlsystemcompletetheadaptivecorrectionofPIDparametersonline.
ItcanbeseenthatadaptivePIDcontrollerhasfeaturessuchassimplestructure,easytoimplement,whichnotonlyabsorbedtheadvantagesoftraditionalPIDcontrol,butuseadaptiveperformancetotakingintoaccountthedynamicstabilityofcontrolsystem.
V.SIMULATION
Asynchronousmotorparametersare:RatedvoltageisIIIVIII0V,thenumberofelectrodesareII,thestatorresistanceis0.III?rotorresistanceis0.VII?,statorandrotorinductanceare0.0VIIIH,mutualinductancebetweenthestatorandrotoris0.VIIH,momentinertiais0.0VIIIIVkg.mII,ref=IV00rad/s,samplingtimeisI.s.
Meanwhile,inthefirstIII00samplingtime,thecontrolleroutputplusinterferenceI..0.
First,therotorfluxandspeedcontrollerissimulatedbyusingthetraditionalPIDcontroller,curveshowninFigureII.
FigureIIspeedcurveoftraditionalPIDcontrol
FigureIIshowsthatwhilethemotorstartsatratedload,speedcurveshasalargeovershootandspeedadjustmenthhasalongtime;whileloaddoubled,thespeedcurvehasalargerovershootandalongerrecoverytime.
AdaptivePIDcontrollerisusedtosimulattherotorfluxandspeedcontrolassameassimulatedconditions.ThespeedcurveshowninFigureIII.
FigureIIIspeedcurveofadaptivefuzzyPIDcontrol
FigureIIIshowsthatwhilethemotorstartsatratedload,adaptivePIDcontrollerhasfastresponse,thespeedcurveshassteady-stateaccuracy.
Intheprocessoftheadaptivespeedadjustment,thecurveofPIDparametersshowninFigureIV-FigureVI.
FigureIVkpcurve
FigureVkicurve
FigureVIkdcurve
VI.SUMMARY
ACmotorcontrolisdifficulttoestablishaccuratemathematicalmodelandtocontrolbecauseofitscouplingbetweentherotorandstator.ThebasicvectortransformationmethodtoachieveadecoupledACmotor,andfuzzycontroldoesnotrelyonaccuratemathematicalmodelofthecontrol
system.Therefore,inthecaseofdecoupling,fuzzycontroladjusttotheACmotorvectortoachievebettercontrolresults.
FuzzyPIDcontrol,basedontheconventionalPIDalgorithm,bycalculatingthedeviationandthedeviationrate,usesfuzzyreasoningprocesstoregulatePIDparameters,whichcanplaytheadvantagesofbothcontrolmethodsandovercomethetwocontrolshortcomings,
improvethecontrolquality.Thedisadvantageisthatwhenthefuzzycontrollerinputdeviationandthedeviationratedecreases,fuzzycontrolaccuracyisnotenough.Thisisthefocusoffuturework.
REFERENCES
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