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Simple Inverted Pendulum with LQR,PID SimMechanics


Leonardo Araujo (view profile)


25 Aug 2009 (Updated )

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

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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

>> mgrPend.StateNames

ans =


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

>> eig(A)

ans =


>> 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)


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

Required Products Control System Toolbox
MATLAB release MATLAB 7.7 (R2008b)
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Comments and Ratings (3)
04 Sep 2013 Phodal

Phodal (view profile)

25 Nov 2011 Yi seong woo

so good!!

Comment only
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


Comment only
26 Aug 2009 1.2

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

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