Swing-up control of an inverted pendulum with limited pivot travel

This paper presents a new energy-based control method for swinging up an inverted pendulum under the constraints on pivot travel and control input. For this purpose, we first construct a Lyapunov function which involves the energy of the pendulum as well as the pivot velocity. We then develop a control law which switches the control signals according to the prediction of the pivot travel. The present control law ensures that the Lyapunov function is non-increasing, while fully utilizing the limited pivot travel range without violating the constraints. Simulation and experimental results demonstrate the effectiveness of the present method.