Linear Parameter-Varying Control for Engineering Applications

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This brief illustrates a procedure for applying linear parameter-varying (LPV) control to dynamic systems through a systematic synthesis of gain-scheduling controllers that ensure stability and performance. Current LPV control theories utilize H-infinity or H2 norms for performance specification, but engineers face challenges in practical applications. There is no systematic approach to implement LPV control theory from modeling to design, nor is there a synthesis theory for designing LPV controllers with hard constraints, which are often necessary due to physical system limitations on performance outputs, sensors, and actuators. The existing H-infinity and H2 criteria do not accommodate these hard constraints, complicating their application in industry. To address these issues, the brief covers gain-scheduling control with practical applications, including LPV modeling, control problem formulation, and performance specification. A new performance specification is introduced to facilitate LPV control design with hard constraints. The procedures are demonstrated through examples such as an engine air-to-fuel ratio control system and a variable valve timing control system. Readers will gain the ability to apply LPV control synthesis techniques to design gain-scheduling controllers for their engineering needs, bridging the gap between H-infinity and H2 control theory and real-world applications.