Control of systems with periodic time-varying parameters: An algebraic approach

The main aim of this contribution is to present the possibilities of simple PI and PID-like robust algorithms in control of systems with periodic time-varying parameters. The proposed algebraic synthesis is based on general solutions of Diophantine equations in the ring of proper and stable rational functions and sequentially on selection of appropriate controller from the set defined by Youla -Kucera parameterization. An advantage of the method is that regulators can be tuned by a single scalar positive parameter. The capabilities of obtained control laws are demonstrated on three simulation examples.