Control of first-order time-delay plants affected by parametric uncertainty

Abstract

This paper deals with an approach to control of singleinput single-output first-order time-delay systems with parametric uncertainty. The presented method consists of an algebraic synthesis of control systems in the ring of proper and stable rational functions and subsequent graphical robust stability analysis. The applied robust stability tests are based on combination of plotting the value sets of a family of closed-loop characteristic quasi-polynomials with the zero exclusion principle. Three successive cases of controlled plants with uncertain gain, uncertain time constant and uncertain time-delay term are analyzed in the illustrative example. All of these systems are controlled using two differently tuned realistic PID controllers. Obtained results are visualized and discussed.