Nonlinear control for rotational movement of cart-pendulum system using homoclinic orbit

In this paper, we deal with the control method for rotational movements of a pendulum using a separatrix. We design a controller that attains a homoclinic motion or a heteroclinic motion of the pendulum and the asymptotic stability of the cart by using a kind of forwarding control design. First, we derive a controller that converges to a homoclinic orbit via a Lyapunov function of the pendulum subsystem. Next, we give a nonlinear stabilizing controller via another Lyapunov function of the cart subsystem. Moreover, using the third Lyapunov function and adding a complementary control input, we guarantee that the pendulum converges to the homoclinic orbit and the cart is stabilized. Finally, the simulation and the experiment using the rapid controller prototyping system based on MATLAB/Simulink are performed to demonstrate the forward upward circling and the giant swing of the pendulum.