Construction of Three dimensional Simulation Platform for Linear Inverted Pendulum Base on Model

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1_{FacutlyofElectronicInformaitonandElectrica lEngineering,}

y g o l o n h c e T f o y ti s r e v i n U n a il a

D . Dailan,China

2_{KeyLaboratoryofI ndustria lContro lNetworkandSystem, ShenyangInsttiuteofAutomaiton,}

a n i h C , g n a y n e h S . s e c n e i c S f o y m e d a c A e s e n i h C

: s d r o w y e

K Linearinvertedpendulum, Codeautomaitcallygenerated,OpenSceneGraph(OSG).

.t c a r t s b

A Thesimulationplatformand physica lequipment ni traditiona lcontro lsystemofinverted .

r e h t o h c a e f o t n e d n e p e d n i n e t f o e r a m u l u d n e

p Researchers are more ilkely to use Simulink for

. n o i t a l u m i s m u l u d n e p d e t r e v n

i The physica lmode lissimplified ,and the curves of thesimulation e

r a t l u s e

r correctaswell. In thispaper ,amorepractica lnonlinearmodel of inverted pendulum is d

e h s i l b a t s

e . Themode land contro lalgorithmcodearegeneratedautomaticallybased onembedded t

n e m p i u q

e , andexperimenta lcurvescanbedisplayedi nrealt imei nat hree-dimensiona lscene.

n o it c u d o r t n I

, l o r t n o c f o e u s s i e h t n

O inverted pendulum device is recognized as a typica lexperimenta l t

n e m p i u q

e [ . 1] Through the research of the inverted pendulum system ,no tonly the theoretical l

o r t n o c n i s m e l b o r

p c an be solved , bu t also the mechanics , mathematics , electrictiy and .

d e n i b m o c y ll a c i n a g r o e b n a c y r o e h t n o i t a c i n u m m o

c The contro lscheme is convenient to be

t n e m p o l e v e d r a l u d o m k n i l u m i S h ti w d e t n e m e l p m

i [2]. Effective modeling and virtuailzation

n a e d i v o r p l l i w n o i t a l u m i

s effecitveguidancet ot herea lcontro lstrategy; meanwhile,i twli lavoidt he e

h t g n i g g u b e d f o r e g n a

d physicaldeviceandsimplify theexperimentprocess [3]. Thisarticleaims m

a x e n a s a m u l u d n e p d e t r e v n i e h t e k a t o

t pletodemonstratethemethod and processofcreaitng a

e e r h

t -dimensiona lexperimenta lplatform.

e r u g i

F 1 .T the hree-dimensiona lsimulationplatformconstructionprocess.

p s e h

T ecific process shown in Figure 1, include modeling ,code generation and 3D rendering , h

c i h

w isalsot heorderoft hearitcle'scontent.

d n a g n il e d o M m e t s y

S Control Scheme k n il u m i S n o d e s a B g n il e d o M m e t s y S

Shown in Figure2, themassofpendulum and sildeare

m

and M respectively ,thelength from m

u l u d n e

p gravity's center to pivo tpoin ti s l ,the angle between the pendulum and the vertica l n

o i t c e r i d d r a w n w o

d i s θ.

x

Indicates the displacemen tof theslider. FMeans the thrus tt o the r

e d i l

e r u g i

F 2 .Invertedpendulumforceanalysis.

n o it c e r i d l a t n o z i r o h e h t g n o l a t u o d e i r r a c s i s i s y l a n a l a c i n a h c e m e h

T and vertica ldirection

. d e n i a t b o e r a s n o i t a u q e m u i r b i l i u q e l a c i n a h c e m o w t d n a , y l e v i t c e p s e r

2

2

n i s s

o c )

(

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i s )

(

F l

m l

m x x m M

x l m l

g m l

m I

θ θ θ θ µ

θ θ

θ

= −

+ + +

− = +

+

 

   



 _ ( 1)

2

1 3ml

I= andEq.1isdifficutlt osolve.Firstly ,Eq.1canbet ransformedt oge tEq.2.

2 2

2 2 2

2 2 2 2

2

) (

s o c n i s )

( ) n i s (

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( ) (

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x l m I g

l m l m I l

m F x

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µ θ θ θ

θ

θ θ θ

θ

+ − +

+ +

=

− + +

− −

=

+

 _

 

   

) 2 (

k r o w e m a r f k n i l u m i

S isse tupt ocarryou tmode lsettlement.

e r u g i

F 3 .Invertedpendulummechanicsmodel.

, , , ,m l I g

M areal lconstantsinEq.2 and F,θ ,x,θareinputs asshownin theFigure3 .Afterthe .

d e v l o s s i n o i t a u q e l a i t n e r e f f i d m u l u d n e p d e t r e v n i e h t , s p e t s e v o b a

g n i w

S -upandSteady-stateControl

r o t a c i d n i n a s a y g r e n e s e k a t m u l u d n e p e h

T ,andlett hesildermoverepeatedlytoswingt hependulum . e

h t n

I intiia lstage ,thependulumisverticallydownward. W nh e reachesthestablestage ,it’senergy t

u o b a s

i 2mgl. Inaddition,t heEq.3canbeusedt ocalculatet hependulum'senergyi nanymomen.t .

q

E 4canbeusedt ocontrolt hewindingphase.

2

5 .

0 I

E= θ ( 3)

Int hesteady-statephase ,wecangett heoptima lfeedbackgainmatrixkby ilnearizingthemodel. Sincet heactua lmodeli snotl inearized,t heparametersoft hematrixneedt obeslightlychanged .In

n i n w o h s e m e h c s l o r t n o c l l a r e v o e h t t e g n a c e w , y r a m m u

s Figure4.

e r u g i

F 4.Swing-upandSteady-statecontro lscheme.

l a e

R -itmeSystemSimula itonand3D RenderingTechnology e

d o

C Automa itcallyGenerated

s l e d o m x e l p m o c g n i v l o s r o f y a l e d n i a t r e c a e v a h s r e t u p m o c y r a n i d r

O . Moreover ,i twil lcos tmuch

n o i t n e t t

a to achieve complex contro lalgorithms in computer languages. In view of the above e

h t , s m e l b o r

p Simulinkcodeautomaticgenerationw illbeused. tI w illbebenefi tfort heresearchers c

o f o

t u son the algorithm itself. In addiiton, complex models w ill deteriorateSimulink's real-time e

c n a m r o f r e

p .Downloadingi tscodet oreal-timesystemswil lovercomet heproblemofslowresponse s

e l c y

c [4].

h p a r G e n e c S n e p

O (OSG) Scene ImageSystem

i g g u b e d e v i t i u t n i d n a t h g il e r o m m u l u d n e p d e t r e v n i e h t e k a m o t r e d r o n

I ng ,the OSG 3D engine

n e

r dering technology isintroduced .Figure5 istheinvertedpenduluminOSG image .Asshown in e

r u g i

F 4, twoS-Functionmodules positionandt heta ea r reservedforcommunicationdataexchange , d

n

a OSGenginei nterfacet oachievet hei nvertedpendulumreal-timesimulationshows.

e r u g i

Simula itonandResul tAnalyssi g

n i w

S -upandContro lSimula iton

e r u g i

F a and b in Figure6 represents theangleand thedisplacemen tcurverespecitvely. Afterthe d

n a , s e e r g e d 0 8 1 o t 0 m o r f s g n i w s m u l u d n e p e h t , d o i r e p e h t f o n o i t a l l i c s

o reach steady state

eventually.Fromt hecurvepoin tofview,t hemode ldescribest herea lphysica lsystemverywell ,and y

l l u f s s e c c u s e m e h c s l o r t n o c e h

t completest hecontro loft hei nvertedpendulum.

) a

( Anglecurve (b)Thedisplacemen tcurve

e r u g i

F 6 .Swing-upandcontro lsimulation.

n o it a l u m i

S wtihout Control

n i n w o h

S Figure7 ,thesilderi si mpactedwithaninstantaneousforce, wecanseea tthein tiiallythe e

l g n a r e g r a l a e v a h l l i w m u l u d n e

p a nd then graduallydecay to 0 degrees. Simulation resutlsverify S

e h t f o y c a r u c c a e h

t imuilnkmode lagain.

e v r u c e l g n A ) a

( (b)Thedisplacemen tcurve

e r u g i

F 7 .Simulationwithou tcontrol.

n o is u l c n o C

e h t r o f d e h s i l b a t s e s i l e d o m c i m a n y d a , r e p a p s i h t n

I invertedpendulumsystem ,andSimulinkisused

e h t e v l o s o

t nonlineardifferentia lmodel .Usingcodeauto-generaitont echnologyt oimportt hemode l l

a e r d e d d e b m e o t n

i -time system. Impor tthe mechanica lmode linto the OSG rendering too land t

n e r a p a h s i l b a t s

e -childrelationshipforeachjoin.tUseUDPprotoco ltosend thedatabacktoOSG e

m i t l a e r n

i . Completed the inverted pendulum three-dimensiona lsimulation platform design .

y l e t a m i t l u

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T work waspartially supported by Nationa lNatura lScience Foundation of China underGran t (NO.91648204) ; Nationa l Science and Technology Major Project under Grant

. O N

( 2017ZX02101007- 400 ) .

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