Optimal Sliding Mode Control For Singular System

The optimal control theory which has maturational theory and design flexibility isan important branch of modern control theory. The optimal control theory also has theeffective engineering application. There are many theories and practical problems tobe solved after the optimal control theory being perfected and substantiated. Slidingmode control (SMC) as an effective method of stabilization for control systems iswidely concerned at present. The essence of SMC is a kind of special non-linearitycontrol and the performance is discontinuity of the control. The greatest feature ofSMC is insensitivity to internal parameter perturbation and external disturbance andcan harmonize the contradiction between steady state and dynamic performance byapplying the simple control law. But the disadvantage of SMC is that the controloutput has jitter, which limits its application to some extent. The optimal control andSMC have their own merits and demerits, so the combination of their merits isnecessary and feasible. The result of the combination is the optimization of the slidingmode.In this thesis, the optimal sliding mode control for singular system is studied. Theoptimal sliding mode control methods for classes of different singular systems aregiven.The main contents consist of several parts as follows.1. The historical development and broad research situation about optimal controland SMC is introduced. The optimal control and SMC for singular system aresummarized. Finally, the researching results are proposed.2. The optimal sliding mode control for linear continuous singular system isstudied. Firstly, the system is decomposed into two low dimensional subsystems by arestricted system equivalent decomposed method. Secondly, the quadraticperformance index optimal control technique is introduced to design the optimalsliding mode for the restricted equivalent subsystems. Thirdly, by applying reachinglaw approach, the control law is selected to ensure the solution trajectories of the system reach the switching surface in finite time and have low chattering in thesliding motion. Finally, a simulation example is given to illustrate the feasibility andvalidity of the proposed method.3. The optimal sliding mode surface and variable structure control (VSC) law areproposed for discrete singular system. Firstly, the sliding mode controller is designedbased on the restricted equivalent subsystems by a restricted system equivalentdecomposed method. The quadratic performance index optimal control technique isintroduced to design the optimal sliding mode. Secondly, by applying theexponentially reaching law approach, the selected control law ensures that thesolution trajectories of the system reach the switching surface in finite time and havelow chattering in the sliding motion. Finally, a simulation example is given toillustrate the feasibility and validity of the proposed method.4. Synthetic problem of VSC for singular system with input and state time-delays isstudied. Firstly, the original system with both input and state time-delays is writteninto a form without time-delay by a linear transformation. Secondly, the systemwithout time-delay is decomposed into two low dimensional subsystems by arestricted system equivalent decomposed method. Thirdly, the sliding mode controlleris designed based on the restricted equivalent subsystems. The quadratic performanceindex optimal control technique is introduced to design the optimal sliding mode. Byapplying reaching law approach, the selected control law ensures that the solutiontrajectories of the system reach the switching manifold in finite time and have lowchattering in the sliding motion. Finally, a sufficient asymptotic stability condition ofthe original system is proposed and a simulation example is given to illustrate thefeasibility and validity of the proposed method.5. The conclusion of the thesis is summarized, and the future work is also lookedahead.