Robust Discrete-Time Gain-Scheduled Guaranteed Cost PSD Controller Design

The most widely used controllers in industry are still the proportional, integral, and derivative (PID) and discrete-time proportional, summation, and difference (PSD) controllers, thanks to their simplicity and performance characteristics. However, with these conventional fixed gain controllers we could have difficulties to handle nonlinear or time-variant characteristics. The introduction of linear parameter-varying (LPV) systems led to various gain-scheduled controller design techniques in both state-space and frequency domain during the last 30 years. In spite of all these, there is still a lack of general approaches for advanced guaranteed cost PID/PSD controller design approaches for LPV systems. In this paper a new advanced controller design approach for discrete-time gain-scheduled guaranteed cost PSD controller design with input saturation and anti-windup is presented for uncertain LPV systems. In addition, the controller design problem is formulated in such a way, which gives convex dependency regarding the scheduled parameters. It results in a less conservative controller design compared to approaches using quadratic stability or the multiconvexity lemma and it's relaxations. Finally, a numerical example shows the benefits of the proposed approach.