| Permanent magnet synchronous motor (PMSM) is widely used in the industry of Numerical Control Machines because of its outstanding features such as simple structure, small size, high efficiency and reliable operation. However, PMSM is a multivariable and strong coupling nonlinear system,whose control performance is still influenced by the parameter variations and perturbations in practical applications. And these problems directly affect the stable operation of the control system, that is to say, chaos phenomenon. In order to meet the requirement of PMSM’s application in the industry, great progress in the PMSM control methods has to be made in order to ensure areliable development of PMSM applied to the field of numerical control machine.In this paper, the research focuses on the chaotic control system of PMSM applied to numerical control machines. Based on the thesis of "973" subject which indicates the mathematical mechanization method and its application in design and manufacturing, there are some related researches on the strategy of nonlinear control system. For example, chaotic backstepping synchronization control, chaotic pulse synchronization control, chaotic fuzzy synchronization control and chaotic fuzzy pulse synchronization control.In addition, the chaotic synchronization method of how to make PMSM process stable and how to design a simple practical controller is put forward. It is essential to both theory and engineering.First of all, the chaotic mathematical model of PMSM is established, and chaotic behaviors of PMSM are investigated. It illustrates that PMSM is sensitive to the input parameter, that is to say, a chaotic phenomenon happens easily when there is a parameter. It should be avoided because this phenomenon is harmful to PMSM. Therefore, this paper emphasizes the chaotic synchronization control method. Furthermore, considering of some uncertain parameters in the research, the existence of chaotic phenomenon is also analyzed. To be more specific, physical deterioration, model error or measuring error can lead to the uncertainty of parameter. In the meantime, based on Poincare mapping and Lyapunov functions which are new tools for analyzing nonlinearity system, the chaotic phenomenon of nonlinear system is also stated.Next, in terms of the nonlinear chaotic synchronization control method of PMSM applied to numerical control machines, the main results can be showed as follows:(1) The chaotic backstepping synchronization control method upon fixed parameters is studied. According to the theory of Lyapunov functions and nonlinear backstepping strategy and the chaos mathematical model, the backstepping synchronization controller is formed. This kind of controller contains a small number of parameters, which is easy to achieve in the industry. Moreover, it is stable because of following the stability of Lyapunov functions.(2) According to the phenomenon of low accuracy in the process of backstepping synchronization control when the parameter is not certain, the chaotic pulse synchronization control method on uncertainty is introduced. Therefore, the system realized synchronization. According to the theory of Lyapunov and impulse control, the pulse is synchronous in the chaotic system of PMSM. It also implies a sufficient condition to the asymptotic stability and exponential stability of PMSM with uncertain parameters. And with theoretical analysis and numerical simulation, that method is proved to be effective. As a result, that method requires less control energy and can be used widely.(3) The method of chaotic fuzzy synchronization control with uncertain parameters is established. Firstly, confirm the mathematical model of fuzzy synchronous control. Next, design some related regulations, and find out the stability of the system, then obtain a sufficient condition of the asymptotic stability and exponential stability of PMSM with uncertain parameters. Based on the Lyapunov, a fuzzy synchronization controller is designed. Finally, with the above results, to carry out some related numerical simulations. And the experiment makes further proof of the effective results in this paper.(4) After researching the pulse synchronization control and fuzzy synchronization control, the fuzzy mathematical model of fuzzy pulse synchronization control is stated. There is also a controller which combines with the advantages of both pulse synchronization control and fuzzy synchronization control. Then the stability, a sufficient condition of the asymptotic stability and exponential stability of PMSM with uncertain parameters are found out. At last, numerical simulations indicate the result to the stable control of PMSM.To sum up, the paper shows a new idea based on nonlinear backstepping theory, pulse synchronization theory and fuzzy synchronization theory to PMSM. According to backstepping theory, pulse differential equation, fuzzy synchronization control theory and Lyapunov theory, the stability and control method of PMSM are pointed out with the structure of backstepping synchronization control, pulse synchronization control, fuzzy synchronization control and fuzzy pulse synchronization control. It lays a foundation for the application and development of PMSM.In the end of the paper, some achievements and deficiencies are stated briefly, and some research areas in the future are forecasted. |
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