On Chaos Control And Its Application

Chaos is a kind of quasi-stochastic behaviors of determinate nonlinear system. As one of the most important achievements of nonlinear science, chaos attracted common attention and had been extensively studied in the last four decades. Recently, how to apply chaos has become the researching focus, chaos control and anticontrol is the basic problem of the application of chaos. To deal with this problem, the history of chaos research is retrospected, several tendencies of chaos research are pointed out, some basic concepts about chaos control and anticontrol are given, some existing methods are reviewed and their features are analyzed, and then, this paper places emphasis on chaos control and anticontrol. Diversity chaotic systems are, diversity control methods are. Therefore, looking for effective and feasible methods for special plants and control aims is a very interesting work.The tracking control method based on feedback linearization is proposed for nonlinear systems demonstrating chaos. In this method, the feedback linearization method is used to convert the nonlinear system into the linearized system, for which the tracking controller is designed, by this way, the nonlinear chaotic system can be forced to track variable reference input. The control objective of this method can be a time variant function or an equilibrium, this method is not affected by the initial condition of the system, the method also demonstrates robustness against model error and measurement noise. Simulation results with continuous chaotic system, chaos in the liquid level control system and chaos in rollingprocess show the validity and effectiveness of the method. At the same time, this method can be used for chaos synchronization and anticontrol of chaos.The optimal control method based on feedback linearization is proposed for the control of chaos in the liquid level control system to solve the problems existed in the local linearization method. Simulation results show the validity of the conclusion and effectiveness of the algorithm.According to the input and output data of the chaotic systems without exact mathematical model, the radial basic function neural network is employed to learn the dynamics of the chaotic system. In the design procedure of the controller, the neural network model is firstly used to counteract the original model of the system, a new desired dynamics can be obtained by designing a new model for the system, on the other words, the chaos can be diminished. The affect of neural network error is studied and the relative theorem is developed and testified. Simulation results with Logistic mapping and Henon mapping show the validity of the theoretical analysis and effectiveness of the algorithm.The fuzzy neural network is used to identify the dynamics of the system to be controlled, the trained fuzzy neural network is used in the inverse system method for chaos control and chaotifying control. The error of fuzzy neural network model and its affect on chaos control and chaotifying control are studied, two theorems are given and testified. Simulation results show the effectiveness and feasibility of the method.Chaos in three typical topology power electronic converters with a close loop controller is studied. The discrete iterative model is established and analyzed for the chaos in close loop BOOST converter working in discontinuous conduct mode. The tracking control method is used to control chaos of this converter, simulation results show its effectiveness.Chaos in permanent magnet synchronous motor (PMSM) is studied. To overcome the drawback of some existing methods, time delay feedback method is proposed to control chaos in PMSM. This method is simple, feasible and effective. Simulation results show thevalidity of the theoretical analysis.Nonlinear feedback control is used to control chaos in PMSM. The objective of this method is more suitable for the real application, and this method is robust against model error and measurement noise. Simulation results show the effecti...