Systems with Time Delays

Mathematical models of systems with time delays were introduced in Section 2.2.2. If there is a time delay in a linear system, then its transfer function includes a term e ^−hs where h > 0 is the delay time. For this class of systems, transfer functions cannot be written as ratios of two polynomials of s. The discussion on Routh-Hurwitz and Kharitanov stability tests, and root locus techniques do not directly extend to systems with time delays. In order to be able to apply these methods, the delay element e ^−hs must be approximated by a rational function of s. For this purpose, Padé approximations of delay systems will be examined in this chapter.