Stability Analysis And Anti-windup Design For Systems Subject To Input Constraints

Due to the practical significance and theoretical challenges, problems for systems subject to input saturation have attracted tremendous attention in recent years. All real world control systems must deal with constraints, especially the input constraints. Input constraints exist in various physical systems, such as chemical plants, mechanical systems, and even communication networks. More often than not, the occurrence of actuator saturation can greatly deteriorate the performance of the systems, and even drive the systems to be unstable.This thesis deals with the stability analysis and anti-windup design issues for systems subject to input constraints. Generally, the stability of the whole systems with actuator saturation can not be guaranteed, especially for the unstable systems. Therefore, much effort has been spent on the local analysis. A new saturation-dependent Lypunov function method is presented, together with the vertex criterion, which can great reduce the conservatism of the estimation of domain of attraction (DOA). Thus the estimation of DOA can help the design of the controller better. Optimization problems in the form of linear matrix inequalities (LMIs) are presented to maximize the estimation of DOA with the help of given reference sets. By the LMI tools in Matlab, these optimization problems can be easily solved.The disturbance rejection ability of systems subject to both input constraints and exogenous disturbance was analyzed. First, amplitude bounded exogenous disturbance is considered and sufficient conditions that ensure the asymptotical stability of the origin of the systems is derived. The definition of the maximal tolerable disturbance is given, which can be computed by optimization problems in the form of LMIs. Moreover, uncertainties in the structure of the systems are also considered, which are also incorporated into the optimization problems in the form of easily solvable LMIs.Moreover, L₂ gain is used to analyze the disturbance attenuation ability of systems subject to both input constraints and exogenous disturbance. A new method is presented to compute the bound of the L₂ gain, which is less conservative compared with some other methods. At the same time, the robust regional stability of the systems is also maintained. Given an amplitude bounded disturbance, optimization problem in the form of LMIs computing the bound of L₂ gainis presented.Nonlinear systems with time-delay are common mathematical models of real phenomenon in electrical industry, chemical industry, network-based control systems and other related fields. The presence of time-delays in control loops usually degrades the performance of the system and complicates the analysis and design of the control systems. Actuator saturation and time-delays may be observed together in control systems. Novel method is constructed to deal with this kind of systems. Much less conservative results are obtained compared with other methods in the literature. Systems with time-delay in input and state are considered respectively.Finally, the problem of anti-windup compensator design is issued. A so called two step anti-windup strategy is adopted. Firstly, dynamic controller is designed according to the performance requirements for the linear systems assuming the absence of the input saturation. Then anti-windup compensator is designed such that the stability of the systems is maintained while enlarging the estimation of the domain of attraction. Anti-windup compensator can make the performance of the systems degrade gracefully.