Research On Sliding-Mode Control Of Discrete Uncertain Systems With Time-delays

With the development of computer techniques, the stability analysis and control algorithm design of discrete systems are important research subjects in control theory. Moreover, in aeronautics and astronautics, process control, and networked control systems, due to the delay in signal transmission and computation time, time delays are commonly encountered. The presence of time delays could seriously degrade performances of the control system, or even drives the system to instability. On the other hand, practical control systems are frequently subjected to various external disturbances. These disturbances can not only lead to working-position shift, but worsen the dynamic and stable characteristics of the system, or even destabilize the system and result in control failure. So it is of great significance to cancel or attenuate the effect of exogenous disturbances, both in theory and practice.In recent years, sliding mode control receives wide attention because of its simplicity, quick response, robustness and easy realization. In this dissertation, the effective sliding mode controllers and trackers are designed based on sliding mode control theory, robust control, adaptive control and Lvapunov stable theory for discrete uncertain systems with time-delays. The contents of this dissertation are arranged as follows:In the preface, an overview of the sliding mode control theory is given, and the relative studies on the methods of sliding mode control for continues systems, for the uncertain systems with time-delay and for discrete-time systems and their relevant control problems are reviewed. The research subject and significance of this dissertation are also shown.Chapter 2 deals with the problem of how the discrete system is controlled effectively by using a variable rate reaching law. First, the dissertation constructs a new discrete variable rate reaching law based on the exponential reaching for discrete system without time-delay, and it is proved that the system with new controller designed by using this new reaching law not only can decrease system chattering and hold fast reaching speed, but also can fast approach to zero at last. Then, a discrete sliding mode surface is designed for discrete system with time-delay by using pole deployment method, and a new sliding mode controller is designed by using the new reaching law and the system is controlled stably. At last, an example is studied and its simulation results illustrate that the system not only can decrease chattering and have fast reaching speed, but also can quickly approach to zero by using the proposed scheme.In chapter 3, three different methods to decrease or cancel the system chattering are proposed for uncertain discrete system with time-delay with different external disturbances. First, a discrete approximate sliding mode control method is adopted for the system with known boundary of external disturbances, and it is proved that the system can arrive the sliding mode layer in finite steps and the approaching movement is stable. Secondly, a novel discrete reaching law with dynamic disturbance compensator is presented for a class of uncertain systems with limited bounded in varying rate of external disturbance boundary, and the problem that the controller containing unrecognized states couldn't be actualized is solved. At last, a control law that can be actualized in physics based is designed based on multi-output feedback technique and the reaching law method, and it is proved that the controller can control the uncertain discrete system with time-delay effectively. The simulation results illustrate the proposed algorithms are more effective than the conventional methods.The chapter 4 considers the problem how to design a model tracker by using model reference adaptive sliding mode control algorithm for uncertain system with time-delay. A novel model reference adaptive sliding mode control algorithm is presented, and the system can track the model reference system effectively by using the new controller where the boundary of external disturbance can not be known as usually. In addition, a decentralized model reference adaptive variable structure control algorithm for a class of perturbed large-scale discrete systems with varying time-delay interconnections is investigated, and a discrete robust adaptive quasi-sliding-mode tracking controller is presented. It is proved that by using the adaptive controller the output error decreases to zero and the trajectories of each subsystem traverse the sliding hyperplane in each step, and the globally asymptotically stability of the system is also proved based on the Lyapunov-Razumikhin stability theorem. Finally, an example is presented and its simulation results illustrate the efficiency of the proposed approach.The chapter 5 considers the chaos synchrony problem for a class of discrete uncertain systems with time-delays. First, a switching function is designed to guarantee that the movement of the system is asymptotically stable in the switching manifold. And the equation of the switching surface is given based on pole assignment theorem; Then a discrete robust adaptive quasi-sliding-mode tracking controller is presented by constructing the two adaptive gains, and the globally asymptotically stability of the system is proved based on the Lyapunov-Razumikhin stability theorem. At last, the simulation examples illustrate that this algorithm is effective and robust with respect to some exogenous disturbances for Duffing-Holmes system. In addition, a discrete terminal sliding mode controller is proposed by applying terminal sliding mode control technique and selecting adaptive reaching law, and the chaos synchrony problem can be solved effectively by using this method. At the same time, it is proved that the designed sliding surface is a terminal sliding surface and the movement of the system controlled by given controller can traverse the sliding surface in each step. At last, an example is presented and its simulation results illustrate the efficiency of the proposed approach.The last chapter summarizes the research work of this dissertation and gives an outlook on sliding mode control method for discrete uncertain system with time-delay.