Design of gain-scheduled PI-type compensators for linear parameter-varying systems

In this paper, SISO linear parameter-varying systems, whose dynamics depend on a single time-varying parameter, are considered. For such a system a double-input single-output linear parameter-varying compensator is designed by the gain scheduling technique, so that the closed-loop system is stabilized and its output tracks step inputs with satisfactory transients. The frozen compensator at a fixed value of the parameter is a three-gain PI-type compensator. An algorithm is presented by which the frozen PI-type compensators at fixed values of the parameter are optimally tuned. Another algorithm-is presented by which a small number of the frozen PI-type compensators are optimally tuned and are linearly linked together in order to render a stabilizing frozen compensator for all values of the parameter. This stabilizing frozen compensator is then used for the parameter-varying system in which the parameter is time varying. An example is given to illustrate the design of the compensator and its performance