Discrete Control of LTI SISO Plants

Abstract

The general structure, timing, algorithms and flow charts of discrete controllers are first discussed. Then the correlation of the behaviour of discrete dynamical systems with the z-plane pole locations is studied, including stability analysis. The effects of transfer function zeros are also considered.

A simple procedure is presented for converting continuous controller designs for digital implementation provided the sampling period is sufficiently small. A criterion of applicability of continuous linear time-invariant system theory is developed that determines whether or not this procedure is valid.

The remainder of the chapter is devoted to a design method applicable, in theory, with unlimited sampling periods and which caters for plants of arbitrary order. This entails pole placement in the z-plane in which a specified settling time is nearly realised if it is considerably larger than the sampling period. As the demanded settling time approaches zero for a fixed sampling time, a dead-beat response is approached, which has the shortest possible settling time and is therefore the best compromise.

Discrete polynomial control is presented, following the continuous version of Chap. 5. This has the same structure as the RST controller but a different design procedure. It is shown how this methodology enables computational delay allowance.

Finally, discrete polynomial control of plants containing pure time delays, aided by a Smith predictor, is addressed.