Delay‐difference approximations of PD‐controllers. Improperly‐posed systems in multiple delays case

Abstract

SummaryIn this paper, we study the behavior of characteristic roots of a class of strictly proper LTI SISO systems that are subject to a PD controller for which the derivative action has been implemented by means of a delay‐difference approximation scheme that uses multiple delays. To such an end, the improperly‐posed case is discussed in depth, that is, the situations where “small delays” induce instability in the closed‐loop system. The effect of adding more delays on the improperly‐posed case is analyzed and a methodology for determining the set of parameters that produces such a situation for a given number of delays is derived. Some illustrative examples complete the presentation.