Continuous sliding mode control

Abstract

Classical sliding mode control (SMC) uses a discontinuous control action to drive the state from an arbitrary initial state to the origin along a user-specified path and exhibits excellent robustness to disturbances and parameter uncertainty. However, the control chattering due to the discontinuity in the control law is undesirable in most processes applications. The continuous sliding mode control (CSMC) approach developed in this paper satisfies the sliding condition using a continuous control law. It therefore retains the positive properties of SMC but without the disadvantage of control chattering. The concept of boundary layer equivalence is used to show that in the presence of unknown disturbances and/or parameter uncertainty, CSMC keeps the state trajectories within a boundary layer of user-specified width. It is also shown that CSMC is equivalent to a cubic feedback control law and can be reduced to a linear form (LSMC) which provides a useful link between sliding mode control and traditional linear control. Several examples demonstrate the performance and properties of SMC, CSMC and LSMC.