Design of variable structure controllers with time-varying switching surfaces

Abstract

Variable structure control (VSC) is a viable high speed switching feedback control and provides an effective means of controlling uncertain system in which bounded parameter variations and disturbances exist. The main feature of VSC is the sliding mode in which the system has invariance property yielding a motion being independent of the system parameter variations and disturbances, and the representative point of the system is constrained to move along a predetermined switching surface. The methods for the design of the switching surfaces has been developed by many researchers. However, in the variable structure systems (VSS) with the conventional switching surfaces, there is a reaching phase in which the trajectories starting from a given initial state off the switching surfaces tend towards the switching surfaces. Since the sliding mode does not occur in this phase, the trajectories are sensitive to the bounded parameter variations and disturbances. To overcome this problem of the reaching phase, we firstly propose the linear time-varying switching surface. This time-varying switching surface is designed using the desired model system by means of the well developed control technique such as eigenstructure assignment, optimal control theory, etc., for the regulator design of the linear time-invariant systems. The VSC with the proposed switching surface guarantees the sliding mode from a given initial state. Hence there is no reaching phase problem provided that the control law is designed to guarantee the existence condition of the sliding mode, and the system has always the same output reponses, regardless of the parameter variations and disturbances. Also, in order to obtain the better transient response, a nonlinear time-varying switching surface designed using the desired nonlinear feedback system is proposed. Since the VSS with this nonlinear time-varying switching surface has the sliding mode from a given initial condition, the system has invariance pro...