Stability Analysis And Anti-windup Design For Systems Subject To Actuator Saturation

Saturation is the most commonly encountered nonlinearities in control systems;Therefore, due to the important theoretical and practical significance;the research on the system subject to actuator saturation has attracted tremendous attention in the control theory field. Linear parameter-varying systems are typical time-varying control systems of very importance, and it is characterized as a linear system that depends on time-varying smooth parameters that are unknown but measurable. The measurement of these parameters provides real-time information on the variation of the plant's characteristics.The basic idea for dealing with actuator saturation in this thesis is to first neglect the saturation and design a linear controller that meets the performance specifications and then using the difference between the controller output signal and the saturated control signal, design an antiwindup compensator to weaken the influence of saturation. Generally, as the exact domain of attraction is hard to be achieved, it is always estimated by means of invariant ellipsoid. In this thesis, based on the Lyapunov approach, linear matrix inequality (LMI) approach are employed to investigate the estimation problems of the domain of attraction and performance for a class of the Linear Parameter Varying systems subject to actuator saturation. The main work and research results of this thesis are as follows:(1). An alternative algorithm to enlarge the domain of attraction (DOA) of the closed-loop LPV system is proposed by means of a linear difference inclusion. Firstly a parameter-dependent compensator design which depends on the time-varying parameter is introduced in such a way that the conservativeness in the estimation is reduced. Consider a quadratic Lyapunov function and a parameter-dependent one, and by the introduction of two slack variables, local asymptotical stability conditions are given. Then, under the given compensator gains and some given reference sets, the estimation of DOA problem can be solved by an optimization problem with some linear matrix inequalities (LMI) constraints using Schur complement lemma. At last,considering the compensator gains as some unknown ones, the estimation of DOA is optimized by an alternative LMI algorithm.(2). Based on a linear difference inclusion, an alternative algorithm to enlarge the performance of the closed-loop LPV system is proposed. Consider a parameter-dependent Lyapunov function, the performance of the closed-loop system is estimated, within a guaranteed region of the state space, under some given parameter-dependent anti-windup compensation gains. This problem is formulated and solved by a LMI optimization problem. Then the compensation gains are designed to further improve the closed-loop system performance and the gain design is formulated and solved as an iterative optimization problem with LMI constraints.(3). Based on a modified sector condition, a direct optimization method with LMI constraints is proposed for designing an anti-windup gain that maximizes an estimate of the domain of attraction of the closed-loop LPV system. The closed-loop system is first locally modeled by a linear system with a deadzone nonlinearity. Based on the use of a new modified sector condition and a quadratic Lyapunov function, the stability conditions are stated in LMI form. Then these conditions are considered as a convex optimization problem in order to maximize the estimation of DOA through computing the anti-windup gains. At the same time, considering asymptotically stable open-loop systems, the anti-windup gains are designed to ensure global stability.