Periodic motion of underactuated mechanical systems self-generated by variable structure controllers: Design and experiments

A new approach in generating a periodic motion for underactuated mechanical systems using variable structure controllers without computing a reference trajectory is proposed in this paper. The design procedure, in order to find explicit expressions of the controller gain parameters in terms of the desired frequency and amplitude, is made through frequency-domain tool, particularly with describing function method. Performance issue of a self-excited system, applied to a double pendulum, is illustrated by experiments.