Code covered by the BSD License

# Comparing different methods to solve an Inverted Pendulum problem

### Roni Peer (view profile)

A simple reporting tool that shows how you can model an inverted pendulum in a few methods.

# Dynamics of a Single Link

This example illustrates how to solve a second order differential equation using one of the numeric ODE solvers in MATLAB.

## Solve the second order differential equation

Notice that a second order differential equation has to be presented to the ODE solver as a system of two first order ordinary differential equations:

where:

Define the equation parameters

rho = 1;        % link length [m]
g = 9.81;       % gravity [m/s2]


Call one of the MATLAB ODE solvers

[t,y] = ode23(@(t,y) [y(2);-3*g*cos(y(1))/2/rho],[0 5],[pi/4,0]);


Replace the name of the output vector with the original state names

theta = y(:,1);
thetaprime = y(:,2);


## Visualize the results

figure;
plot(t,theta,'r',t,thetaprime,'g',...
'DisplayName',{'\theta';'\theta'''},'LineWidth',2);
title('Time histories for \theta and \theta'' - Single Link');
xlabel('time (sec)');
legend('show');
grid('on');