Vibration Suppression Control for a Variable Length Pendulum with a Pivot Movable in a Restricted Range

This paper considers the problem of stabilizing a pendulum whose pivot and weight can be moved in restricted ranges. Conditions for stability of the pendulum are derived using energy-based methods, and then two feedback control laws are constructed. The one moves the pivot and weight sinusoidally, which realizes a smooth control requiring smaller control efforts, and the other moves them nearly bang-bang, which gives a better control performance. Experimental results are given to illustrate the effectiveness of the proposed control laws