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Simple Inverted Pendulum with LQR,PID SimMechanics

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25 Aug 2009 (Updated )

This sample this sample show the simple Inverted Pendulum control with lqr

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Description

Hi guys this is my Simple Pendulum model and control using SimMechanics and Control toolbox, later I will include also the SolidWorks files to show how to use SolidWorks link.

Anyone who finds that I should do things in another way please fell free to post any comment and help me :)

This sample was modelled with SimMechanics and control was made with lqr command.

First I've imported the pendulum from solidworks with
mech_import;

>> mgrPend = MECH_STATEVECTORMGR;
>> mgrPend.StateNames

ans =

    'InvertedPendulumModel/Pendulo_Invertido/Revolute:R1:Position'
    'InvertedPendulumModel/Pendulo_Invertido/Prismatic:P1:Position'
    'InvertedPendulumModel/Pendulo_Invertido/Revolute:R1:Velocity'
    'InvertedPendulumModel/Pendulo_Invertido/Prismatic:P1:Velocity'

>> [A,B,C,D] = linmod('InvertedPendulumModel');

>> eig(A)

ans =

         0
         0
    2.3132
   -2.3132

>> open_plant = ss(A,B,C,D);
>> impulse(open_plant);

>> Q = diag([ 0 100 0 100]);
>> K = lqr(A,B,Q,R)

K =

  284.3487 -10.0000 126.1560 -23.6582

>> Ac = [(A-B*K)];
>> Bc = [B];
>> Cc = [C];
>> Dc = [D];
>> sys_cl=ss(Ac,Bc,Cc,Dc);
>> T=0:0.01:50;
>> U=0.2*ones(size(T));
>> [Y,T,X]=lsim(sys_cl,U,T);
>> plot(T,Y)

Acknowledgements

Rotary Double Inverted Pendulum;Sim Mechanics Model inspired this file.

Required Products Control System Toolbox
SimMechanics
Simulink
MATLAB release MATLAB 7.7 (R2008b)
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Comments and Ratings (3)
04 Sep 2013 Phodal  
25 Nov 2011 Yi seong woo

so good!!

15 Nov 2011 yudha hadibowo

My name is Yudha from indonesia, I want make controller with LQR,

my case about nonlinear equation, the example is van der pol eq.

i dont understand about linearized, can u explaint me about it.

if i used the ode45 and the next i used LQR, what i must be do?

i hope u can help me , thank you

best regards

yudha

Updates
26 Aug 2009

Added the SolidWorks files and re-modeled things with the imported plant (Inverted Pendulum) model from SolidWorks

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