Study Of Theory And Application For Control Systems Subject To Actuator Saturation

Although saturation characteristics exist extensively in practical control systems, it had been rarely studied in conventional control theory until several disasters happened. As a hard nonlinearity, saturation's non-smooth characteristic makes system analysis and design more complex. As for the systems subject to actuator amplitude saturation, many research results have been recently achieved, however, the system analysis of actuator amplitude and rate saturation still remains harder with less results. In addition to practically encountered actuator saturation, system model uncertainties and smooth non-linearities really exist and should be appropriately taken into consideration, due to the factors such as the variation of the system modeling parameters, the variation of the operating environment and so on. Since there exists amplitude and rate saturation in rudder manipulation systems of steering, the appropriate consideration and management must be paid. However, the present results of ship steering controller design can't provide a perfect solution to the rudder saturation.It's definitely difficult to achieve the global stability of systems subject to actuator saturation, therefore most work concentrate on system local analysis. In this paper, local stability and performance analysis methods are improved for linear systems subject to actuator amplitude saturation. As for the systems with both amplitude and rate saturation, however, the present anti-windup control theory is inapplicable because of the assumption of the algebraic loop well-posedness of the closed-loop system. The theory is improved in this paper that the closed-loop well-posedness is guaranteed for the special formed systems with anti-windup compensator, therefore, also guaranteed is the existence and uniqueness of the solution to the system dynamics. The tricks of this paper include the convex hull manipulation of saturation characteristics with less conservative results, estimating the system domain of attraction via ellipsoids and the reference sets, manipulating the uncertain smooth nonlinear terms of the system model via linear differential inclusions, introducing the magnitude and rate saturation (MRS) model and state variable augmentation to deal with the actuator amplitude and rate saturation, and finally transforming all the control problems into (convex) optimizations subject to linear matrix inequalities (LMI) and/or bi-linear matrix inequalities (BMI) constraints. All the problems can be sufficiently optimized using MATLAB.The main research contents are as follows:Four kinds of saturation control systems are concerned in the theory and the corresponding results are presented. Furthermore, the theory research results of one kind of them are applied to well solve the problem of the rudder amplitude and rate saturation in the ship course control.(1). For linear systems subject to amplitude saturation and feedback matrix perturbation, the stability is analyzed via convex hull method. The sufficient condition of determining the closed-loop system's contractively invariant ellipsoid is obtained based on the quadratic Lyapunov function. Therefore the maximum domain of attraction is estimated by choosing the reference sets as polytopes and the problem can be transformed into the LMI constrained convex optimization.(2). For linear systems subject to amplitude saturation and parametric uncertainties, the guaranteed cost control problem is solved via the convex hull method. The sufficient conditions are respectively proposed based on the quadratic and non-quadratic Lyapunov functions, with the closed-loop robust stability and the guaranteed robust performance. Furthermore, the controller synthesis problems are transformed into the LMI and/or BMI constrained convex optimization problems.(3). For linear systems subject to both amplitude and rate saturation, the static anti-windup control problem is discussed with the actuator dynamics of certain form. The amplitude and rate saturation problem is simplified to the amplitude saturation problem by augmenting the state variables. Under the assumption that the closed-loop system's algebraic loop is well-posed, the sufficient conditions are respectively proposed based on the quadratic Lyapunov function and the polytopic/norm-bounded differential inclusions, with closed-loop stability and better performance. Furthermore, the anti-windup compensator design problems are transformed into the LMI constrained convex optimization problems.(4). For a class of nonlinear uncertain systems subject to amplitude and rate saturation, the static anti-windup problem is addressed. The first step involves the nonlinear uncertain terms' management using linear differential inclusions and the second, via introducing the MRS model, the transformation of the amplitude and rate saturation problem into the amplitude saturation problem. The key point is that the necessary and sufficient condition of the closed-loop algebraic loop well-posedness is obtained and transformed into the LMI constraint, thus the above-mentioned assumption is removed. By employing the norm-bounded differential inclusions, the sufficient conditions are obtained based on the quadratic Lyapunov function, with the closed-loop robust stability and robust performance. Furthermore, the anti-windup compensator design problems are transformed into the LMI constrained convex optimization problems.(5). Based on the linear ship motion model and the static anti-windup control theory, the course keeping controller is designed to perfectly solve the problem of the rudder rate saturation.(6). Based on the nonlinear uncertain ship motion model, the ship course changing static anti-windup controller is designed. By comparison with the saturated finite interval course changing controller, simulation results show that the anti-windup controller achieves better ship course changing performance since it can perfectly solve the problem of the rudder amplitude and rate saturation.The conclusions and perspectives are given in the end of the paper.