A new type of sliding surface for a variable structure control system is proposed to achieve fast and accurate path tracking in a class of nonlinear second-order multi-input dynamical systems. The surface is adaptable to arbitrary initial conditions, and movable towards a predetermined surface. The movement is executed in a stepwise manner according to the trajectory of representative points. We call it a moving sliding surface (MSS). Using the MSS favorable fast tracking is accomplished without increasing the magnitude of the discontinuous control gain. A two-degree-of-freedom robotic manipulator subjected to external disturbances is considered to demonstrate the efficacy of the proposed method.
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Choi et al. (1994) studied this question.