Output Excitation via Continuous Sliding-Modes to Generate Periodic Motion in Underactuated Systems

In this paper, we introduce a new approach in generating a periodic motion for underactuated mechanical systems using continuous sliding-mode (SM) algorithms as a feedback loop, particularly with super-twisting algorithm and power-fractional sliding-modes (PFSM), without computing a reference trajectory. Periodic solutions of the closed-loop system are found by mean of the describing function method which allows to tune the amplitude and frequency of the oscillations via corresponding gain parameters. Performance issue of a self-excited system, applied to 3-DOF underactuated robot, is illustrated by simulations