Guaranteed tuning of PID controllers for parametric uncertain systems

This paper presents a methodology for tuning the controller of a parametric uncertain plant in order to guarantee the satisfaction of specifications. These specifications are defined by means of an interval reference model that represents the set of satisfactory time or frequency behaviors. The controller synthesis is then formulated as a set-inclusion problem in the frequency domain. Interval techniques for the solution of constraint satisfaction problems are applied to design fixed-structure controllers in a guaranteed manner. In particular, PID controllers are considered since they are widely used in industry.