Research On Control Of Nonlinear Systems Subject To Actuator Saturation

In engineering practice, saturation phenomenon are often encountered since actua-tors cannot deliver unlimited signals. The performance of the closed-loop systems maydeteriorate，and for open-loop unstable systems even instability may be induced dueto actuator saturation. Several disasters caused by actuator saturation have promptedresearchers attaching great importance to saturation phenomenon. In the past severaldecades, researches on control problems for saturated systems including stabilization andanti-windup compensator design have advanced signifcantly along with the deepgoingof studies on saturation nonlinearity. Until now, many diferent control strategies andoptimization algorithms have been proposed for solving the stabilization and anti-windupproblems. However, the majority of existing techniques regards linear systems and onlyfew works are committed to nonlinear systems with some”linearizable” features. Hence,the existing techniques cannot be applied to general nonlinear systems. For this reason,the dissertation frstly propose new control strategies to overcome the defciencies of theexisting techniques and then extends the techniques to general nonlinear systems.The main research content and primary innovation of the dissertation can be sum-marized as follows:1. Research status of stabilization and anti-windup synthesis is introduced for sat-urated linear and nonlinear systems. More attention has been paid to the discussionand analysis of diferent methods tackling saturation nonlinearity and the evolution ofanti-windup frameworks.2. The existing static anti-windup strategies for rational systems are based on DARtechnique. In order to obtain LMI-based synthesis conditions an additional constrainton the ellipsoid E(P) has been introduced which may cause a slightly large conservatismwhen estimating the region of attraction. In order to reduce the conservatism, the dis-sertation proposes the dynamic (and static) anti-windup synthesis methods based on theLFR technique by which an additional constraint can be avoided. Hence, it is expect-ed that the proposed methods would be less conservative for the purpose of stabilityanalysis. When the pre-designed controller is linear a modifed anti-windup strategy inwhich the measurable nonlinearity is introduced into the traditional anti-windup con-troller is proposed to increase the optimization degree of freedom and to further reducethe conservatism.3. By LFR technique, the research object can be extended to a class of more generalnonlinear systems. On this basis, the stabilization problem, i.e. designing a nonlinear state feedback controller such that the closed-loop system is asymptotically stable, forthe general nonlinear systems is frstly investigated. Compared with the traditional linearfeedback control law,the nonlinear version can further enlarge the stability region of theclosed-loop system.4. Static anti-windup synthesis for two classes of more general nonlinear systemsis investigated and LMI-based synthesis conditions are proposed. The modifed anti-windup strategy are extended so that it is applicable to the class of saturated nonlinearsystems. Numerical examples have shown the modifed anti-windup controller can furtherenlarge the region of attraction and also improve the L2performances tremendously.When a pre-designed controller is unavailable, LMI-based conditions for the synthesis ofa simultaneous nonlinear and anti-windup controller are proposed under the assumptionof constant input matrices of the controlled nonlinear systems. Numerical examples haveshown the efectiveness and superiority of the proposed synthesis method.Finally, the main results of the dissertation are concluded and some issues for furtherresearch and exploration are proposed.