An algebraic approach to control design for systems with periodically time-varying parameters

Abstract

This paper deals with the application of simple PI and PID algorithms to control of systems with periodically time-varying parameters. The proposed algebraic synthesis method is based on general solutions of Diophantine equations in the ring of proper and stable rational functions and subsequently on selection of appropriate controller from the set defined by Youla-Kucera parameterisation. An advantage of the technique is that the controllers can be tuned by a single positive scalar parameter. The capabilities of obtained control laws are demonstrated on three simulation examples.