A survey of applications of second-order sliding mode control to mechanical systems

The effective application of sliding mode control to mechanical systems needs to face the problems related to the chattering phenomenon and the switching control signals. Higher-order sliding modes appear to be suitable to counteract these problems since, with this method, the switching signals are the higher derivatives of the mechanical controls which turn out to be continuous. In general, this approach requires the availability of a number of time derivatives of the sliding variable and, due to noise, this requirement could be a practical limitation. A class of second-order sliding mode controllers, guaranteeing finite-time convergence for systems with relative degree two between the sliding variable and the switching control, results to be suitable to both reduce the number of differentiator stages in the controller and to deal with actuators unmodeled dynamics. In this paper different, previously presented, second-order sliding mode controllers are shown to belong to the above cited class, and are exploited to address and solve challenging control problems involving mechanical systems. Simulations and experimental results are provided throughout the paper.