Simple Inverted Pendulum with LQR,PID SimMechanics

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

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

The author wishes to acknowledge the following in the creation of this submission:
Rotary double inverted pendulum;sim mechanics model

• Required Products: Control System Toolbox; SimMechanics; Simulink
• MATLAB release: MATLAB 7.7 (R2008b)

[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

[Yi seong woo]

so good!!