Advanced linear parameter varying control for systems with delays, saturation and implementation constraints

Linear parameter-varying (LPV) control is a systematic and rigorous gain scheduling control method. It has drawn great attention in the past decade. In this work, the definition of LPV system and controller design are briefly reviewed. The implementation problem of the LPV controller is investigated. A motivating example and subsequent analysis show that the LPV controller implementation problem is not only a special problem resulting from Jacobian linearization of the original nonlinear plant, but also a general problem for the LPV systems. An appropriate implementation is suggested to ensure that the closed-loop system is well-behaved.;The second part of the thesis deals with the control of time varying delay systems. First, the stability analysis and state-feedback control synthesis problem for LPV systems with time-varying state delays is addressed. New LMI-based synthesis conditions that depend on both the delay bound and its rate bound for stabilization and induced L2 norm control are developed. The obtained LMIs are less conservative than the current result in the literature. Second, the reference tracking problem of dominant time varying delay systems is solved via a novel LPV two-degree-of-freedom (2-DOF) control scheme that is scheduled based on the real-time measurable time delays. The stability and performance of the proposed 2-DOF control system are explored using parameter-dependent Lyapunov functions.;The third part of the thesis details the design of an LPV air-fuel ratio control strategy for lean burn spark ignition (SI) engines. A first-order lead-lag gain-scheduled feedback controller that includes polynomial forms of the controller gains as a function of the control loop delay is obtained to satisfy desired transient and steady-state response characteristics. An input shaping method is used to reduce the cost of feedback, and improve tracking performance for transient operations. The two-step design falls into the proposed LPV 2-DOF control scheme.;In the last part of this thesis, an LPV anti-windup scheme based on the stability analysis of sector bounded nonlinearities has been successfully applied to provide anti-windup protection for an adaptive LPV controller for active microgravity isolation. Both the LPV controller and the anti-windup gain are scheduled based on the measurement of the rack displacement. The design approach followed a classical two-step anti-windup paradigm.