On the geometry of stability regions of Smith predictors subject to delay uncertainty

In this paper, we present a geometric method for describing the effects of the delay induced uncertainty on the stability of a standard Smith Predictor control scheme. The method consists of deriving the stability crossing curves in the parameter space defined by the nominal delay, and delay uncertainty, respectively. More precisely, we start by computing the crossing set, which consists of all frequencies corresponding to all points on the stability crossing curve, and next we give their complete classification, including also the explicit characterization of the directions in which the zeros cross the imaginary axis. This approach complements existing algebraic stability tests, and it allows some new insights in the stability analysis of such control schemes. Several illustrative examples are also included.