Analysis of a simple quasipolynomial of degree one

Abstract

Systems with internal delays in feedback loops, so called time-delay or anisochronic ones, constitute a widespread family of industrial plants. Their linear representation in the form of the Laplace transform yields transfer functions expressed as ratios of quasipolynomials, instead of polynomials, with delay (exponential) terms in denominators. In this paper, detailed pole location analysis of a quasipolynomial of degree one is presented. This quasipolynomial is capable to express the dynamics of conventional high order systems, even without internal delays, as a model transfer function denominator. The presented analysis represents also a powerful tool for controller tuning in pole-placement control algorithms for delayed systems.