Image:Pendulum-plots.png

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[edit] Summary

Plots illustrating the behaviour of an inverted pendulum mounted on a oscillatory base. I created this image using Matlab. The following code is used in m-files to simulate the behaviour of the inverted pendulum on an oscillatory base:

The main program that creates the plot:

% initialisation
clear all % erasing all previously used variables
close all % closing open windows
clc %clear command prompt

% simulation
[T, XY] =ode45('diffxy',0,10,[0.1 0]); 
%simulate differential equation for time = 0 to 10 sec, initial disturbance angle is 0.1 radian, initial velocity is zero

% plotting commands
plot(T,XY(:,1)*180/pi)
AXIS([0 5 -90 90])
ylabel('\theta [deg]')
xlabel('t [s]')

The program that implements the differential equation:


function dxy= diffxy(t,xy)

% parameters

g=9.81;  %gravitational acceleration [m/s^2]
l=1;        %length of the pendulum [m]
A=.05;    %amplitude of the oscillation [m]
omega=1000; % frequency of the oscillation [rad/sec]

% implementation of the differential equation

theta=xy(1);
thetadot=xy(2);
thetadot=thetadot;
thetaddot=1/l*(-sin(theta)*(A*omega^2*cos(omega*t)-g));

% return result

dxy=[thetadot, thetaddot]';

[edit] Licensing

I, the creator of this work, hereby release it into the public domain. This applies worldwide.
In case this is not legally possible,
I grant any entity the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

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(del) (cur) 10:01, 19 February 2007 . . Chojitsa (Talk | contribs) . . 1076×420 (5,771 bytes) (Plots illustrating the behaviour of an inverted pendulum mounted on a oscillatory base. (I created this image using Matlab))