The Research Of Finite-Time Method For Synchronization Of Chaotic System And Observing Flux Of The Induction Motor

Finite-time control method based on synchronization of chaotic systems and rotor flux observer of the induction motor is researched in this paper. As a result of the continuously development of the research of chaotic system, the application of chaotic system theory has been got into several fields. It is important to study the finite-time synchronization of two chaotic systems. In modern variable frequency speed regulation system, the accurate observation of rotor flux is a condition for obtaining high performance. Therefore the study of rotor flux observer has important significance. The main contribution of this paper is as follows:Firstly, the finite-time synchronization of two chaotic systems is considered. A sufficient condition for the existence of finite-time observer of chaotic system is derived and the state observer is reached. The simulation of the Duffing-Holmes chaotic system is presented to show the effectiveness of the proposed method. In finite-time, the synchronization error of the state variables can convergence to a finite boundedness, then convergence to zero.Secondly, in this paper the design of fast convergence finite-time controller of chaotic system is discussed. A new terminal sliding mode controller is designed by applying a new exponential nonlinear terminal sliding mode manifold and selecting exponential reaching law. Then, the control method is presented to realize the finite-time synchronization of two chaotic system with nonmatched uncertainties. It is shown that, by this design the system state variables can be realized finite-time fast convergence and further improved the convergence rate. At the same time, good dynamic stability properties can be obtained. The simulation of the Multi-scroll chaotic system indicate the controller can make the system have good stability. It showed that the control scheme can meet the request of chaotic system. The problem of observing rotor flux of the induction motor is researched. Most of the observer theories are based on the Lyapunov Stability. The concept of finite-time observer is presented for this paper. By analyzing the state equation of induction motor which state is used as stator current and rotor flux, finite-time rotor flux observer is introduced. The error of state variables can convergence to a finite boundedness in finite-time. By solving linear matrix inequality, the gain value can be obtained and the finite-time rotor flux observer of the induction motor is reached.