电动舵机模糊自适应pid控制研究Fuzzy adaptive PID control of electric actuator.docx
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电动舵机模糊自适应pid控制研究FuzzyadaptivePIDcontrolofelectricactuator
电动舵机模糊自适应pid控制研究（FuzzyadaptivePIDcontrolofelectricactuator）
FuzzyadaptivePIDcontrolofelectricactuator
CaoJingZhuJihong11,2
1、Departmentofcomputerscienceandtechnology,TsinghuaUniversity,Beijing1000842,JiangsuCollegeofInformationTechnology,Jiangsu,Wuxi214106
Caojing@
Abstract:
ThispaperpresentsafuzzyadaptivePIDcontroller,thismethodforelectromechanicalactuatorpositionservosystem,overcomessomeshortcomingsofthesimplefuzzycontrolandtraditionalPIDcontrol,reasoninganddecision-makingthroughfuzzyrules,real-timeoptimizationofPIDcontrollerparameters,thesimulationandexperimentalresultsshowthatthismethodimprovesthecontrolperformancethesystemhasagoodcontroleffect.Keywordsfuzzycontrol;PIDcontrol;electricactuator;MATLAB;
Study,of,Fuzzy,self-turning,PID,control,of,electromechanical,actuator
Caojing1,2,zhujihong1,
1,Department,of,Computer,Science,and,Technology,Tsinghua,University,Beijing100084
2JiangsuCollegeofInformationTechnologyWuxiJiangsutextintroducesakind210106Abstract:
Theofself-turningFuzzy-PIDcontroller,itisusedontheelectromechanicalactuatorpositionservosystem.ItovercomessomedefectsofsimplyfuzzycontrolandtraditionalPIDcontrol,Thereal-timeoptimizationofthecontrolparameterofPIDcontrolleriscarriedoutbyfuzzyreasoningandstrategy.Thesimulationandexperimentresultsshowthatthismethodimprovesthecontrolperformanceofsystemandhaspreferableeffects.Keywords:
FuzzycontrolPIDcontrolelectromechanicalactuator（EMA）MATLAB
1Introduction
Theelectricactuator（EMA）hastheadvantagesofsimplestructure,lightweight,loadcharacteristicandhighreliability,thusindrones（UAV）,hasbeenwidelyusedinaircraftandmissileandspacecraft.
ThetraditionalPIDcontrolwiththecharacteristicsofreal-time,easyrealization,iswidelyappliedinthecontrolsystem,aslongasthecorrectparameters,thePIDcontrollercanrealizeitsfunction,buttheautopilotsystemexistsnonlinear,time-varyinganduncertainfactors,thecontroleffectofPIDwillbedifficulttoachievethedesiredobjectives.Thefuzzycontrolhasstrongadaptabilitytothenonlinearandtime-varyingofthecontrolobject,anditsflexibilityandrobustnessarebetter,andthecontrolissimple,anditiswidelyusedinthefieldofmotorcontrol.Butinthefuzzycontrolsystem,itisdifficulttocompletelyeliminatethesteady-stateerror.Ingeneral,thecontrolaccuracyisnotideal.
Accordingtothecharacteristicsofthetwokindsofcontroller,inordertoimprovethecontrolperformanceoftheactuatorpositionservosystem,thispaperdesignedafuzzyadaptivePIDcontroller,takingintoaccounttheadvantagesofthetwokindsofcontrolmethods,reasoninganddecision-makingbyfuzzyrules,threeparameterson-linetuningofPIDcontroller,theexperimentalresultsshowthatthecontrollerhasasimplestructure.Theeffectisgood.
2themathematicalmodeloftheelectricactuator
ThemaincomponentofelectricactuatorpositionservosystemofrareearthpermanentmagnetbrushlessDCmotor,becauseoftheairgapmagneticfield,backEMFandcurrentisnonsinusoidal,thedirectuseofphasevariablestoestablishthemathematicalmodelofthemotoritself.Takethetwo-phaseconductionstartypethree-phasesixstateasanexample,inordertofacilitatetheanalysis,assumethemotor:
（1）
Themagneticcircuitisnotsaturated,ignoringtheinfluenceofhysteresisandeddycurrentloss,ignoringtheinfluenceofhigherspatialpotentialharmonic;
（2）
Thethree-phasewindingissymmetrical,theairgapmagneticfieldissquarewave,andthestatorcurrentandrotormagneticfielddistributionaresymmetrical;
（3）
Thearmaturewindingsaredistributedcontinuouslyandevenlyontheinnersurfaceofthestator;
（4）
Theeffectsofcogging,commutationandarmaturereactionareneglected;
（5）
Thereisnodampingwindingontherotor,andthepermanentmagnetcannotplayadampingrole.Accordingtothevoltagebalancerelationshipofthethree-phasewindingcircuit,thefollowingdifferentialequationscanbelisted[1]:
R
II
LMM
MLM
MML
00
.
.
.
.
.
.
.
.
.
.
.
.
U
E
A
Saaa
..
..=.
..
..
..
..+.
..
..
P
..
..+.
..
..
R
II
Zero
Zero
（1）
U
E
B
BBBS
R
II
00
U
E
C
Sccc
Type:
UA,UB,UCisstatorwindingvoltage;IA,IB,ICarestatorwindingcurrent;EA,eb,
ECisthestatorwindingelectromotiveforce;theRsrepresentsthemotorwindingresistance,andtheLisselfinductanceofeachphasewinding;theMisbetweeneachphasewinding
Mutualinductance;Pisadifferentialoperator,P
=
D/dt.
Thethreephasewindingisstarconnectedandhasnomidline
II
B
+
Ic=0
（2）
+
A
Mi
Mi=.Mi（3）
+
Therefore,available
BaC
Bymeansof
（1）,
（2）and（3）formulas,thevoltageequationis
I
R
L
M
II
00
.
00
....
.
.
.
....
..
.
.
.
....
.
.
.
Uu
E
As
Aaa
..
=
.....
+
..
..
..
+
..
..
R
I
L
M
Zero
Zero
Zero
.
Zero
（4）
Pe
B
BBBS
R
I
L
M
I
00
00
.
U
E
C
Sccc
Becausethereareonlytwophasesatanytime,thereis
D（I
IIB）U
.
A
DtR（I
A
.
I
B
）
L
.
M
.
U
（
）
（
.
）
+
+
UEe
=
BBAsa
.
.
.
Duetothesymmetryofthree-phasewinding,thereare:
u
U,u,u,u,u
=
=
=
D,B,Ba,C,C,a
II,I,I,I,I
.
.
.
=
=
=
D,B,Ba,C,C,a
.
.
.
EE,e,e,e,e,e
=
=
=
D,B,Ba,C,C,a
Ld
L
M
.
=
Omega
0
DDTN
Omega
D
Omega
K
T
Kmi,Tm
J
Tl
+
AndbecauseofE?
=
=
=
=
DD
M
WhereUDrepresentsthevoltageappliedtothemotorphasewinding,IDrepresentstheturn-oncurrentphasewinding,Kmtorqueconstant,KeEMFconstant,Jisconvertedtothemotorshaftofthetotalmomentofinertia,loadtorqueforTl,Nforthereductionratioofthereductionmechanism.
AfterfinishingtheLaplacetransformation,thetransferfunctionofwholemotorsystem（ignoringloadtorque）for:
E
DT
（==）
Gs,U,theta（（SS））,NK,s（Ts,1,+1）（Ts,+1）（5）
MmL
Amongthem,Tm,=Rs,Jistheelectromechanicaltimeconstantofthemotorsystem;Tl=Ldisthearmatureloopelectromagnetictimeconstant.KKR
EMs
3fuzzyadaptivePIDcontrolsystemdesign
3.1controlsystemstructureandworkingprinciple
ThestructureofthefuzzyadaptivePIDcontrolsystemisshowninFigure1.ItiscomposedofatraditionalPIDcontrollerandafuzzycontrolunit.Thedisplacementsensortodetectthepositionofthesystem,thesignalconversionandcomputerserialcommunication,RgivensignalandthefeedbacksignalYthedeviationbetweentheinputsignale,thedeviationsignalisdividedintotwo,allthewaydirectlyintothePIDcontroller,theotherwayanditsrateofchangeinfuzzycontrol,gettheparametersof.Kp,.Ki,.Kdcorrection,automaticcorrectionofPIDparametersKp,Ki,Kdinitial,andthenusetheinputparametersofPIDcontrolleraftercorrectionundercontrol,asthegivenspeedloop.Thesystemadoptsdoubleclosedloopcontrol,innerloopisspeedloop,PIcontrolisadopted,outerloopispositionloop,andfuzzyPIDcontrolisadopted.
Fuzzycontrollink
Parametercorrection
Kp
Ki
Kd
R
U
PIDcontroller
Y
controlobject
Fig.1blockdiagramoffuzzyself-tuningPIDcontrolsystem
Threepointtwo
FuzzyPIDcontrollerdesign
Three
2.1establishinputandoutputvariablesandpastethem
Theinputvariablesofthefuzzycontrollerarethedeviationofthesteeringangleofthesteeringgear,eandthedeviationchangerateEC,theoutputvariableisPID,andthecontrolcorrectionparametersare.Kp,.Kiand.Kd.Whetheritisthedeviationortherateofchange,itisapreciseinputvalue,andfuzzificationistomakeitdiscreteandchangeintoanelementinthesetofintegerarguments.Let'sdefineEandECasfollows:
E=k1[（k）.Thetatheta（K.1）]ec=k2[e（k）.E（K.1）]type:
K1,K2angledeviationandrateofchangescaletransformscalefactor,theactualrangeofEandECwere[.em,EM,[.ecm,ECM],thefuzzyvariablescaletransformandquantizationafterrespectivelyasE,EC,for
Thecontrolprecisionofservosystem,theEandECdomainisdefinedasE,EC={-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6}ofthefuzzysubsetis:
E,EC={NB,NM,NS,O,PS,PM,PB},subtheconcentrationofelementsrepresentingthenegative,negative,negative,zero,issmall,middle,big,fuzzymembershipfunctionwithtriangularfunction.Theoutputsof.Kp,.Ki,.Kd,domain,languagevariablesandmembershipfunctionsarethesameasthoseofEandEC.
3.2.2establishesfuzzyinferencerules
Thedesignoffuzzycontrolisthecoretechnologyoftheknowledgeoftheexpertorcontrolengineerlong-termaccumulationandpracticalexperiencebasedonthefuzzyinferencerulesofthesystemstabilityandresponsespeed,theovershootandsteady-stateaccuracysummedup.Itsgeneralformisafuzzyconditionalstatementconsistingoffuzzylanguageandfuzzylogic.ThissystemusesMamdanifuzzyinferencetype,thatis,fuzzyimplicationrelationis:
If,E,=Ai,and,EC,=Bj,then,.Kp=Cij,and,.Ki=Dij,and,.Kd=Fij
Thebasicreasoningprincipleoffuzzycontrolleris:
whenthedeviation
E
Forlarge,makesthesystemhavegoodtrackingperformance,Kpshouldtakealarger;andinordertoavoiddifferentialoverflow,Kdshouldbesmall,atthesametimetoavoidtheovershootofthesystem,dealwiththeintegralrolerestrictions,Kiusuallyzerowhenthedeviation;
E
Formediumhours,inordertoreducetheovershootofthesystem,Kpshouldbereduced;atthistime,thevalueofKdhasagreaterimpactonthesystem,andt
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