Pole-placement design for the time delay systems using a generalised, discrete-time Smith predictor

Considers the pole-placement design of single input, single output (SISO) linear, discrete systems with time-delay. Two approaches, are discussed. The first one is based on a proportional-integral-plus (PIP) design for a delay-free system coupled with Smith´s principle to handle time delays. The second approach arises naturally as an inherent part of the PIP method. This control scheme is related to the extended Smith predictor (ESP) method and it is shown that, under certain conditions, it will produce exact equivalence. Since the method is more general than ESP, the authors feel that the resulting control scheme might be conveniently termed a `generalised Smith predictor´ (GSP) control system. The paper also shows how to construct a suitable non-minimal state space form for the GSP, such that the state vector consists of only the directly measured input and output variables, thus eliminating the usual requirement for state reconstructor (observer) design. In this manner, closed loop pole assignment follows naturally and easily from the normal state variable feedback design method