Permanent Magnet Synchronous Motor Feedback Linearization Vector Control
In order to solve the control problem of a class multiple-input multiple-output nonlinear system, the feedback linearization method is introduced. By calculating the output variables of Lie derivative, the appropriate coordinate transform and nonlinear st
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Abstract In order to solve the control problem of a class multiple-input multiple-output nonlinear system, the feedback linearization method is introduced. By calculating the output variables of Lie derivative, the appropriate coordinate transform and nonlinear state feedback are obtained, then through the coordinate transformation and state feedback, the input-output linearization is realized and the system decoupling is achieved. According to the system’s linear model, the actual control rate is designed. For illustration, a multiple-input multiple-output nonlinear system example is utilized to show the feasibility of the feedback linearization in solving the permanent magnet synchronous motor, and then combines with the vector control method. Using MatLab7.6/Simulink to build modular and simulation verifies the effectiveness of the algorithm. Empirical results show that the feedback linearization is a better method to handle nonlinear system. From the simulation results we can be obtained that the feedback linearization vector control method has a good control effect. Keywords Feedback linearization • Vector control • Effectiveness
1 Introduction In recent years, with the high performance permanent magnet material technology, power electronics technology and microelectronics technology growing fast. Make permanent magnet synchronous motor be characterized by small volume, high efficiency, and the advantages of small losses. The PMSM plays an increasingly important role in small power motion control system. With the deepening of vector control theory and automatic control principle, the permanent magnet synchronous
H. Wang (*) • X. Liu Beijing Information Science & Technology University, Beijing, China e-mail: [email protected]; [email protected] W. Wang (ed.), Mechatronics and Automatic Control Systems, Lecture Notes in Electrical Engineering 237, DOI 10.1007/978-3-319-01273-5_67, © Springer International Publishing Switzerland 2014
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motor control system has developed rapidly. As a nonlinear system, the precise control methods have been studied by many scholars, among which the one based on differential geometry feedback linearization has achieved a big development. People have successfully solved the many problems about motor control with it, and got a good control effect. Such as the PMSM control systems based on SVPWM [1], the designs of PMSM in the vector control system, which has a good control effect for PMSM [2], and research the application feedback linearization in PMSM [3].
2 Description of Problem For the following n-order multi-variable nonlinear system, using state space form to describe as follow types of equations: x_ ¼ f ðxÞ þ y1 ¼ h1 ðxÞ ym ¼ hm ðxÞ
m P
gi ðxÞui
i¼1
(1)
Here f ðxÞ; g1 ðxÞ; ; gm ðxÞ is n-dimensional smooth vector function; h1 ðxÞ; ; hm ðxÞ is a scalar function. These equations can be more compact form: x_ ¼ f ðxÞ þ gðxÞu y ¼ hðxÞ
(2)
Here gðxÞ ¼ ðg1 ðxÞ; ; gm ðxÞÞ is n m order matrix; hðxÞ ¼ ðh1 ðxÞ;
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