5/25/2018 23 - Rotary Double Inverted Pendulum - User and Lab Manual

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Rotary Motion Servo Plant: SRV02

Rotary Experiment #9:Double Inverted Pendulum

Control

Double Inverted Pendulumusing QUARC

User and Lab Manual

5/25/2018 23 - Rotary Double Inverted Pendulum - User and Lab Manual

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Rotary Double Inverted Pendulum: User and Laboratory Manual

Table o Contents

1. Laboratory Objectives............................................................................................................................12. Prerequisites...........................................................................................................................................13. Experiment Design Files........................................................................................................................2. !"#$2%D&'P (o)eling an) *ontrol Design........................................................................................3

.1. !ystem (o)eling............................................................................................................................3.2. (o)el Parameters...........................................................................................................................+.3. &alance *ontroller Design.............................................................................................................,

+. 'n-Lab Proce)ure...................................................................................................................................+.1. !ystem !etup..................................................................................................................................+.2. /iring Proce)ure...........................................................................................................................

+.2.1. *able 0omenclature...............................................................................................................+.3. ypical *onnections.....................................................................................................................1$

+.3.1. /iring 4en using E! Option...........................................................................................11

+.. *ontroller !imulation...................................................................................................................12+..1. Objectives.............................................................................................................................12+..2. Proce)ure..............................................................................................................................12

+.+. *ontroller 'mplementation...........................................................................................................15+.+.1. Objective...............................................................................................................................15+.+.2. 678"* *ontroller Description...........................................................................................1........................................................................................................................................................1+.+.3. Experimental Proce)ure.......................................................................................................1

,. "e9erences............................................................................................................................................23

Document Number 723 Revision 1. Pa!e: i

5/25/2018 23 - Rotary Double Inverted Pendulum - User and Lab Manual

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Rotary Double Inverted Pendulum: User and Laboratory Manual

!" Laboratory b$e%tives

4e c4allenge in t4is laboratory is to )esign a state-9ee)bac:control system t4at balances a rotary )ouble inverte) pen)uluman) positions t4e rotary arm to a comman)e) angular position.4e system 4en running t4e balance controller is s4on inFigure 1.

4e plant is 4as to main components; t4e 6uanser !"#$2rotary motion plant an) t4e 6uanser Double Pen)ulum< i.e.D&PE0 mo)ule. 4is is )enote) as !"#$2%D&PE0 plant. 8s)epicte) in Figure 1< t4e )ouble pen)ulum is compose) o9 arotary arm t4at attac4es to t4e !"#$2 system< a s4ort 5-inc4bottom blue ro)< an enco)er 4inge< an) t4e top 12-inc4 blue ro).4e balance control computes a voltage base) on t4e angle

measurements 9rom t4e enco)ers. 4is control voltage signal isampli9ie) an) applie) to t4e !"#$2 motor. 4e rotary armmoves accor)ingly to balance t4e to lin:s an) t4e processrepeats itsel9.

!ection 2 )escribes t4e requirements o9 t4e experiment an)!ection 3 overvies t4e 9iles supplie) it4 t4e system. 4emo)eling< mo)el parameters< an) control )esign is explaine) in!ection . 'n !ection +< t4e plant iring an) setup is )escribe)9olloe) by proce)ures to run a simulation o9 t4e system an) runt4e control on t4e actual !"#$2%D&PE0 plant in real-time.

Lastly< !ection ,contains re9erences t4at are cite) t4roug4outt4is manual.

&" Prere'uisites

4e prerequisites to success9ully carry out t4is laboratory are;i= o be 9amiliar it4 your !"#$2 main components >e.g. actuator< sensors=< your )ata acquisition

car) >e.g. 6P'D=< an) your poer ampli9ier >e.g. #oltP86=< as )escribe) in "e9erences ?1@< ?2@ = t d

d

t > = t

d

d

t > = t

d

d

t > = t d

> = t t ?1$@

an) t4e )esire) state is

=d

-

< < < < < = d t $ $ $ $ $ d

> = d t t

.?11@

4e linear state-space mo)el o9 t4e !"#$2%D&PE0 in Equation ?1@ is augmente) by intro)ucing anintegrator< resulting in t4e system

=d

d

t > = t +

1 $

1 $

$ u