Sliding mode controller design for underactuated systems

In this paper we deal with one of the most challenging control problems - controlling a class of underactuated mechanical systems. The control difficulty arises when uncertainties exist in the underactuated system. Sliding mode controller (SMC) design with both linear and nonlinear sliding surface are proposed to deal with uncertainties. Both of the controllers are capable of rejecting matched uncertainties. For linear SMC, selection of sliding surface parameters are discussed and conditions are given to ensure a stable sliding manifold. For integral SMC design, it shows flexibility in designing a nominal controller to stabilize the sliding manifold and selection of sliding surface parameters to reduce the effect of unmatched uncertainties. The SMC with integral type sliding surface not only shows great robustness but also can be easily incorporated with other controllers. As an illustrative example, the proposed controllers are applied to a unicycle plus inverse pendulum system.