Linearization of Permanent Magnet Synchronous Motor Using MATLAB and Simulink

Abstract

Permanent magnet machines, particularly at low power range, are widely used in the industry because of their high efficiency. They have gained popularity in variable frequency drive applications. The merits of the machine are elimination of field copper loss, higher power density, lower rotor inertia and a robust construction of the rotor (Bose 2002). In order to find effective ways of designing a controller for PM synchronous motor (PMSM), the dynamic model of the machine is normally used. The dynamic model of PM motor can be derived from the voltage equations referred to direct (d) and quadrature (q) axes (Bose 2002).The model derived essentially has quadratic nonlinearity. Linear control techniques generally fail to produce the desired performance. Feedback linearization is a technique that has been used to control nonlinear systems effectively. By applying exact linearization technique (Cardoso & Schnitman 2011) it is possible to linearize a system and apply linear control methods. But this requires that certain system distributions have involutive property. An approximate feedback linearization technique was formulated by Krener (Krener 1984) based on Taylor series expansion of distributions for non-involutive systems. Chiasson and Bodson (Chiasson & Bodson 1998) have designed a controller for electric motors using differential geometric method of nonlinear control based on exact feedback linearization. But from a practical point of view, this technique suffers from singularity issues. If the system goes into a state, during the course of the system operation, where the singularity condition is satisfied, then the designed controller will fail. Starting with the quadratic model of PMSM, we apply quadratic linearization technique based on coordinate and state feedback. The linearization technique used is the control input analog of Poincare’s work ( Arnold 1983) as proposed by Kang and Krener (Kang & Krener 1992) and further developed by Devanathan (Devanathan 2001,2004) .The quadratic linearization technique proposed is on the lines of approximate linearization of Krener (Krener 1984) and does not introduce any singularities in the system compared to the exact linearization methods reported in (Chiasson & Bodson 1998). MATLAB simulation is used to verify the effectiveness of the linearization technique proposed. In this chapter, MATLAB/SIMULINK modeling is used to verify the effectiveness of the quadratic linearization technique proposed. In particular, the application of MATLAB and SIMULINK as tools for simulating the following is described: