Single-parameter tuning of PI controllers: Theory and application

The paper deals with the influence of a single tuning parameter on performance properties of the closed control loop which contains algebraically designed continuous-time PI controller while the response quality is evaluated by the size of first under- or overshoots. The controllers are obtained from general solutions of Diophantine equations in the ring of proper and stable rational functions and can be subsequently tuned via the only parameter. This article brings simple tuning rules, verifies their validity by means of simulation example and, moreover, it presents their possible practical application during control of real laboratory model assumed as system with parametric uncertainty.