Generation of periodic motions for underactuated mechanical system via second-order sliding-modes

The generation of periodic motion for a simple underactuated manipulator, named Pendubot is made through second-order sliding-mode (SOSM) algorithms, particularly with twisting algorithm. This study is motivated by the fact that in the presence of an actuator, the transient process converge to a periodic solution. To obtain the desired amplitude and velocity of oscillations we use describing function and locus of a perturbed relay system approach to provide the corresponding gain parameters. Performance issue of the controller is illustrated in a simulation study