毕业设计_control of an inverted pendulum-外文文献.docx
- 文档编号:53971
- 上传时间:2022-10-01
- 格式:DOCX
- 页数:11
- 大小:305.66KB
毕业设计_control of an inverted pendulum-外文文献.docx
《毕业设计_control of an inverted pendulum-外文文献.docx》由会员分享,可在线阅读,更多相关《毕业设计_control of an inverted pendulum-外文文献.docx(11页珍藏版)》请在冰豆网上搜索。
ControlofanInvertedPendulum
JohnnyLam
Abstract:
Thebalancingofaninvertedpendulumby
movingacartalongahorizontaltrackisa
classicproblemintheareaofcontrol.Thispaperwildescribetwomethodstoswingapendulum
attachedtoacartfromaninitialdownwardspositiontoanuprightpositionandmaintainthatstate.A
nonlinear
heuristic
controlerandanenergycontrolerhavebeenimplemented
inordertoswingthe
pendulum
toanuprightposition.Afterthependulumisswungup,alinearquadraticregulatorstate
feedbackoptimal
controler
hasbeenimplemented
tomaintain
thebalancedstate.Theheuristic
controler
outputsarepetitivesignal
attheappropriatemomentandisfinely
tunedforthespecific
experimental
setup.Theenergycontroler
addsanappropriateamountofenergyintothependulum
systeminordertoachieveadesiredenergystate.Theoptimalstatefeedbackcontrolerisastabilizing
controler
basedonamodel
linearized
around
theupright
position
andiseffective
when
the
cart-pendulumsystemisnearthebalancedstate.Thependulumhasbeenswungfromthedownwards
positiontotheuprightpositionusingbothmethodsandtheexperimentalresultsarereported.
1.INTRODUCTION
Theinvertedpendulumsystemisastandardproblemintheareaofcontrolsystems.Theyareoften
usefultodemonstrateconceptsinlinearcontrolsuchasthestabilizationofunstablesystems.Sincethe
systemisinherently
nonlinear,
ithasalsobeenusefulinilustrating
someoftheideasinnonlinear
control.Inthissystem,aninvertedpendulumisattachedtoacartequippedwithamotorthatdrivesit
alongahorizontaltrack.Theuserisabletodictatethepositionandvelocityofthecartthroughthemotor
andthetrackrestrictsthecarttomovementinthehorizontaldirection.Sensorsareattachedtothecart
andthepivotinordertomeasurethecartpositionandpendulumjointangle,respectively.Measurements
aretakenwithaquadratureencoderconnectedtoaMultiQ-3generalpurposedataacquisition
and
controlboard.Matlab/Simulinkisusedtoimplementthecontrolerandanalyzedata.
Theinvertedpendulumsysteminherentlyhastwoequilibria,oneofwhichisstablewhiletheother
isunstable.Thestableequilibriumcorrespondstoastateinwhichthependulumispointingdownwards.
Intheabsenceofanycontrolforce,thesystemwilnaturalyreturntothisstate.Thestableequilibrium
requiresnocontrolinputtobeachievedand,thus,isuninteresting
fromacontrolperspective.The
unstableequilibrium
correspondstoastateinwhichthependulumpointsstrictlyupwardsand,thus,
requiresacontrolforcetomaintainthisposition.Thebasiccontrolobjectiveoftheinvertedpendulum
problemistomaintaintheunstableequilibriumpositionwhenthependuluminitialystartsinanupright
position.Thecontrolobjectiveforthisprojectwilfocusonstartingfromthestableequilibriumposition
(pendulumpointingdown),swingingituptotheunstableequilibriumposition(pendulumupright),and
maintainingthisstate.
第1页
wheremisthecartmass,misthependulummass,
c
p
thependulum,Risthemotorarmatureresistance, risthemotorpinionradius,
Iistherotationalinertia,
listhehalf-lengthof
Kisthemotortorque
m
2.MODELLING
AschematicoftheinvertedpendulumisshowninFigure1.
Figure1.InvertedPendulumSetup
Acartequippedwithamotorprovideshorizontal
motionofthecartwhilecartposition,p,andjoint
angle,θ,measurementsaretakenviaaquadratureencoder.
Byapplyingthelawofdynamicsontheinvertedpendulumsystem,theequationsofmotionare
constant,andKisthegearboxratio.Also,forsimplicity,
g
andnotethattherelationshipbetweenforce,F,andvoltage,V,forthemotoris:
第2页
Letthestatevectorbedefinedas:
Finally,
welinearize
thesystem
abouttheunstable
equilibrium(0
000).Notethatθ=0
T
correspondstothependulumbeingintheuprightposition.Thelinearizationofthecart-pendulumsystem
aroundtheuprightpositionis:
Where
Finally,bysubstitutingtheparametervaluesthatcorrespondtotheexperimentalsetup:
第3页
3.STABILIZINGCONTROLLERDESIGN
Thecontrolerdesignapproachforthisprojectisbrokenupintotwocomponents.Thefirstpart
involvesthedesignofanoptimalstatefeedbackcontrolerforthelinearizedmodelthatwilstabilizethe
pendulumaroundtheuprightposition.Thesecondpartinvolvesthedesignofacontrolerthatswings
thependulumuptotheunstableequilibrium.Whenthependulumapproachesthelinearizedpoint
- 配套讲稿:
如PPT文件的首页显示word图标,表示该PPT已包含配套word讲稿。双击word图标可打开word文档。
- 特殊限制:
部分文档作品中含有的国旗、国徽等图片,仅作为作品整体效果示例展示,禁止商用。设计者仅对作品中独创性部分享有著作权。
- 关 键 词:
- 毕业设计_control of an inverted pendulum-外文文献 毕业设计 _control pendulum 外文 文献