Making a polynomial Hurwitz-invariant by choice of feedback gains†

An integrated design procedure is developed for a modified Smith predictor and associated controller for linear time-delay systems having transfer functions of the form k ₁, A exp (—sT)/B, where A and B are monic polynomials in s of degree n — l and n, respectively. A is Hurwitz and B has a single right-half-plane root at s = λ. For l=1,2,3, an augmented PI controller guarantees asymptotic stability for λT less than an l-dependent limit. The procedure for l = 3 is extended to l = 4 with the introduction of derivative action into the controller. Design arguments are on root locus topology, and on Nyquist analysis applied to an auxiliary system.