Analysis and Application of Quadratic Linearization to the Control of Permanent Magnet Synchronous Motor

The introduction of state equation model of the electrical machine based on direct and quadrature axes variables has paved the way for powerful control theories to be brought to bear on the problem of control of electric machines. Exact linearization has been applied to the control of permanent magnet synchronous motor (PMSM). In this paper, application of approximate linearization is proposed for the control of PMSM. Since the PMSM model is essentially quadratic, quadratic linearization is considered for the application. Conditions on the coordinate transformation and state feedback are derived for the linearization of a four dimensional permanent magnet (PM) machine model. The proposed linearization technique does not introduce singularities in the system as in the case of exact linearization. Also, to account for higher order nonlinearities including unmodelled dynamics, the linear zing transformations are adaptively tuned. Simulation studies verify the theoretical results presented. Hardware/software implementation is carried out to verify the effectiveness of the linearization technique proposed. The linearization technique proposed can also be applied to other types of electrical motors.