Design of sliding mode for chattering-free variable structure control

In this paper, a kind of sliding mode is defined for continuous-time systems. Such sliding mode can be designed using any of linear control methods, like as optimal control, pole assignment, and so on for the overall system, which is different with the general sliding mode designed in the reduced-order system. The designed feedback rule is considered as an equivalent control. For the system without any parameter uncertainty and external disturbance, the trajectories in the state space with the equivalent control for any initial state form the sliding mode, i.e. the proposed sliding mode is a set of trajectories of the system known exactly with the equivalent control for any initial state. Then for a continuous-time system with parameter uncertainty and external disturbance, a chattering-free variable structure (VS) control law is designed to move the state to the sliding mode in a finite time. Such VS control method can be easily extended to servo control, output feedback control, and discrete-time VS control problems. The simulation results show that the proposed VS controller has good control performance without chattering.