The dq transformation and feedback linearization of a permanent magnet synchronous motor

The dynamics of a permanent magnet synchronous motor can be described by a set of differential equations relating voltages and currents in each phase or equivalently by a set of differential equations in an orthogonal reference frame centred on the magnetic pole axis. In either case, the differential equations are coupled and nonlinear in the states. This paper applies the feedback linearisation technique of Hunt, Su and Meyer (1983) to transform these nonlinear equations into a linear time invariant state model. Unlike conventional linearisation techniques which rely on small signal perturbations, this technique uses a nonlinear state transformation and a nonlinear feedback law. The contribution of this paper is to demonstrate that the state transformation is essentially the familiar dq transformation whilst the nonlinear feedback law performs decoupling and compensation for the influence of back emf in the motor