Analysis And Design Of Control Systems In The Presence Of Actuator Saturation

Every system has constraints in their nature. In special, actuator saturation is the most common phenomenon in real world. However, most of the controller design methods in the modern control theory often assume that the control input of the system is infinite and ignores the presence of actuator saturation. If these control methods designed controller inputs reach beyond the scope that the real systems can tolerate, the closed-loop performance of the systems will degradation dramatically, thus, will lead to very serious consequences. Therefore, analysis and design of control systems with actuator saturation is of great importance in the control theory and its applications. This dissertation will dedicate our efforts on some kind of typical control systems, such as singular systems, switched systems, and large-scale decentralized systems, etc, in the presence of actuator saturation.This dissertation mainly deals with the following aspects.-For singular linear systems under a saturated linear feedback, a set of conditions under which an ellipsoid is contractively invariant are established. These conditions can be expressed in terms of linear matrix inequalities, and the largest contractively invariant ellipsoid can be determined by solving an op-timization problem with LMI constraints. With the feedback gain viewed as an additional variable, this optimization problem can be readily adapted for the design of feedback gain that results in the largest contractively invariant ellipsoid.——Based on the result on stabilization, an analysis of the (?)2 gain and (?)∞performance for singular linear systems under actuator saturation is carried out. The notion of bounded state stability (BSS) with respect to the influence of (?)2 or (?)∞disturbances is introduced, and the assessment of the disturbance tolerance and rejection capabilities of the system under a given state feedback law is formulated and solved as LMI constrained optimization problems. By viewing the feedback gain as an additional variable, these optimization problems can be readily adapted for control design.——For a group of linear systems, each under a saturated linear, not nec-essarily stabilizing, feedback law, a switching scheme is designed such that the resulting switched system is locally asymptotically stable at the origin with a domain of attraction extending well beyond the linear regions of the actuators.The problem of disturbance tolerance/rejection for a family of linear systems subject to actuator saturation and (?)2 or (?)∞disturbances is considered. For a given set of linear feedback gains, a given switching scheme and a given bound on the (?)2 or (?)∞norm of the disturbances, conditions are established in terms of linear or bilinear matrix inequalities under which the resulting switched system is bounded state stable With these conditions, both the problem of as-sessing the disturbance tolerance/rejection capability of the closed-loop system and the design of feedback gain and switching scheme can be formulated and solved as constrained optimization problems.-Motivated by the merits of switching control, a switching anti-windup design is proposed, which aims to enlarge the domain of attraction of the closed-loop system. Multiple anti-windup gains along with an index function that or-chestrates the switching among these anti-windup gains are designed based on the min function of multiple quadratic Lyapunov functions. In comparison with the design of a non-switching anti-windup gain which maximizes a contractively invariant level set of a single quadratic Lyapunov function as a way to increase the size of the domain of attraction, the use of multiple Lyapunov functions and switching in the proposed design allows the union of the level sets of the multiple Lyapunov functions, each of which is not necessarily contractively invariant, to be contractively invariant and within the domain of attraction. As a result, the resulting domain of attraction is expected to be significantly larger than the one resulting from a single anti-windup gain and a single Lyapunov function.——Based on a composite quadratic Lyapunov function, which was origi-nally proposed to study the stabilization problem for linear systems under actu- ator saturation, this dissertation proposed an alternative algorithm for designing anti-windup gains. The algorithms result in nonlinear anti-windup gains, but with an estimate of the domain of attraction of the closed-loop system in the form of the convex hull of a group of ellipsoids, instead of a single ellipsoid that would have resulted from the use of a single Lyapunov function.——This dissertation also deals with the design of decentralized controllers for large-scale linear systems under actuator saturation. Saturation in the mag-nitude of the control input is first considered. For the closed-loop system under a saturating decentralized state feedback law, conditions are identified under which an ellipsoid is contractively invariant and thus within the domain of attraction, or the restricted (?)2 gain from the disturbance to the output is less than or equal to a pre-specified valueγ. Based on these conditions, the designs of decentralized state feedback laws that achieve large domains of attraction or low (?)2 gains can be formulated as optimization problems with bilinear matrix inequality (BMI) constraints. Numerical algorithms are developed to solved these BMI problems. These developments are also extended to the situation where the actuators are subject to nested saturation, such as rate saturation.