Discrete-time model of an IPMSM based on variational integrators

Interior permanent-magnet synchronous motors (IPMSM) are widely used as automobile traction drives for electric and hybrid electric vehicles. Since motor control is commonly implemented on a digital platform, a discrete-time motor model is needed. With respect to the calculation effort the discretization is usually done via a first-order explicit Euler approximation within the rotor frame coordinates. For IPMSM traction drives this approach is leading to a systematic modeling error, since the flux trajectory degenerates from a circle to a polygon at higher speeds. Consequently, this approach leads to a speed-depending discretization error, which can have a significant impact on control performance. Hence, this contribution presents a discrete-time model of an IPMSM based on variational integrators (VI). Starting with a variational principle the Euler-Lagrange equations provide a physical continuous-time motor model. By applying a discrete version of the variational principle we receive a symplectic discrete-time IPMSM model without increasing the calculation effort in comparison to the classical Euler discretization. Simulative as well as experimental investigations confirm the benefit of a VI based discrete-time motor model concerning the transient and stationary system model accuracy.