Robust nonlinear control via moving sliding surfaces-n-th order case

Sliding mode control is a popular method for achieving robust tracking of nonlinear systems. The state is forced onto a manifold in state space by a “bang-bang” type control. This manifold is designed so that staying on it implies convergence to the state space origin. Since the initial state in general does not lie on the sliding surface, there is a reaching phase, where the state moves to surface from its initial position, and a sliding phase, where it moves along the surface to the origin. We present a new strategy-the sliding surface is moved, in contrast to the fixed surface of the conventional case. This is done so that the state lies on the sliding surface at all times, and the dynamics is under control. The present work treats general (n-th order) sliding surfaces, as opposed to the work of Choi, et al. (1994), which was restricted to second-order systems. Example cases are presented and the hypotheses are confirmed through simulations