Research On Chaos Of Fractional Mathematical Models Of The Motor Drive And Its Control

At present, although there has been some success in the research on chaos analysis, chaos control and application of the motor system, but it is only in its infancy, has not yet formed a complete chaotic theory and systems. Traditional study on motor system’s chaos is always based on the integer order mathematical model. With the upgrading of modern science and technology and the development of modern industry, true and accurate mathematical models are required in the research in the motor system analysis and synthesis, the maximum of improvement in system performance, to achieve the purpose of high precision. The application of fractional-order theory and chaos theory has important theoretical and practical value in the motor drive and its system. It is a full of exploration, challenging research topic. Around this issue, this dissertation has made the following aspects:1. This dissertation studies on the chaos theory and fractional chaos, describes the basic characteristics and recognition methods of chaotic systems, studies on the solutions for the largest Lyapunov exponent by Wolf method and small-data method, and prepared for calculating the largest Lyapunov exponent from time series by MATLAB program.2. The difficulties of solving fractional differential equations restricted the application of fractional-order theory in practice. The dissertation studied the method for solving fractional differential equations and the solutions for the largest Lyapunov exponent of fractional order dynamic systems. First we use predict-correct method for solving fractional differential equations, and then calculate the largest Lyapunov exponent from the time series obtained. Finally, we solve the fractional order unified system and get its largest Lyapunov exponent to verify the accuracy of the algorithm used in this article.3. The dissertation established fractional order mathematical model for the two mode controlled DC motor drive, and respectively analyzed the chaos of current control mode, voltage control mode of the motor drive, to identify the chaos phenomenon when the system parameters changed, and verified the existence of chaos in the DC motor drive system.4. Fractional order control and synchronization of chaotic systems is a research hotspot in recent years. In this thesis, fractional order dynamical system chaotic control is studied. Taking voltage controlled mode fractional DC motor drive for example, based on time-delayed feedback control method, we achieve chaos control of fractional motor drive.