Fixed-Order Linear Parameter-Varying Feedback Control of a Lab-Scale Overhead Crane

This brief presents a numerically attractive approach to design fixed-order H 2 /H ∞ controllers for discrete-time linear parameter-varying (LPV) systems. In this approach, the controller order that is completely determined by the number of states and the parameter dependence is selected in advance. For a prefixed controller order, parameter-dependent sufficient linear matrix inequalities (LMIs) are presented, relying on an a priori computed full-order LPV controller that stabilizes the LPV system for all the possible parameter trajectories. Pólya's theorem and polynomial approximations are used to obtain numerically tractable LMI problems that guarantee the feasibility of the parameter-dependent synthesis conditions. The practical viability of the approach is demonstrated by experimental validations on a lab-scale overhead crane with varying cable lengths.