Robust stabilization of self erecting cart pendulum system with periodic controller

This paper achieves robust stabilization of self erecting cart pendulum system with continuous-time periodic controller. More precisely, the present work deals with the problem of global stabilization of a cart-pendulum system. First, an energy shaping algorithm is developed to bring up the pendulum to the close vicinity of its upright equilibrium point. The energy control technique employed here also takes care of the practical constraint of limited cart track length. Next, a continuous-time periodic controller does the task of keeping the pendulum at its upright position. The robust stability of the periodic controller is examined, and is found out to be superior to linear quadratic regulator (LQR). The stabilization controller also shows its ability of disturbance and noise rejection. The simulation results are presented to establish the claim.