Discrete-Time Block Control

This chapter deals with the adaptive tracking problem for a class of MIMO discrete-time nonlinear systems in presence of bounded disturbances. In this chapter, a recurrent high order neural network is first used to identify the plant model, then based on this neural model, a discrete-time control law, which combines discrete-time block control and sliding modes techniques, is derived. The chapter also includes the respective stability analysis for the whole system. It is proposed too a strategy to avoid specific adaptive weights zero-crossing. Applicability of the proposed scheme is illustrated via simulation of a discretetime nonlinear controller for an induction motor.

Frequently, modern control systems require a very structured knowledge about the system to be controlled; such knowledge should be represented in terms of differential or difference equations. This mathematical description of the dynamic system is named as the model. Basically there are two ways to obtain a model; it can be derived in a deductive manner using physics laws, or it can be inferred from a set of data collected during a practical experiment. The first method can be simple, but in many cases it is excessively timeconsuming; some times, it would be unrealistic or impossible to obtain an accurate model in this way. The second method, which is commonly referred as system identification, could be a useful short cut for deriving mathematical models. Although system identification not always results in a equally accurate model, a satisfactory model can be often obtained with reasonable efforts. The main drawback is the requirement to conduct a practical experiment, which brings the system through its range of operation. Besides a certain knowledge about the plant is still required.