Relay-based autotuning with algebraic control design

Abstract

In this paper, a combination of relay feedback identification and an algebraic control design method for stable systems is studied. Models with up to three parameters are estimated by means of a single asymmetrical relay experiment. Then a stable low order transfer function is identified. Then the controller is analytically derived from general solutions of Diophantine equations in the ring of proper and stable rational functions. The controller parameters are tuned through a pole-placement problem as a desired multiple root of the characteristic closed loop equation. A first order identification yields a PI-like controllers while a second order identification generates PID ones. The approach enables a scalar tuning parameter m>0 which can be adjusted by various principles.