High Performance Tracking Controller for Discrete Plant Using Nonlinear Surface

In this chapter, a nonlinear surface is proposed to improve the performance of discrete-time system. Recall that, in the previous chapter a regulator design for continuous time system is considered. Due to the flexibility of implementation, most of the controllers are implemented through digital signal processor or high end microcontrollers. Due to this reason study and research on discrete sliding mode has received a considerable amount of attention (e.g., see [12, 10, 44, 8] and [54], among many). In this chapter, a step tracking control for general discrete-timemultivariable system is considered based on DSMC with nonlinear sliding surface. To relax the need of measuring the entire state vector, the multi-rate output feedback (MROF) is used. Discrete-time system represented in delta operator is also analysed in this chapter to understand the effect of change in sampling time explicitly. This chapter reconstructs the research results proposed in [1, 3] as well as some additional results are included.

The brief outline of this chapter is as follows. Section 2 contains a brief review of themultirate output feedback strategy. The structure of nonlinear sliding surface and the proof of its stability is given in Section 3. Section 4 discusses two approaches to design control law, first is based on reaching law approach and the second is based on disturbance observer. Analysis of system represented with delta operator is presented in Section 3.5. Application and simulation results are presented in Section 6 followed by the conclusion in Section 7.