Ideal integration of observers with sinusoidal states by Sliding Mode - Application to Direct Field Orientation of motor drives

Direct Field Orientation (DFO) is a well-established method for field-oriented control of induction motor (IM) or permanent magnet synchronous motor (PMSM) drives. In DFO, the rotor position angle is computed using the tan¹ function of the stationary reference frame fluxes or EMFs. It is typical to estimate these quantities using an observer based on the respective motor model. The paper discusses the problem of integrating the equations of this observer: generally, pure integration cannot be implemented because of the offsets in the measured signals; integration is replaced with low pass filtering. This produces estimation errors that are significant when the drive operates at low speed; the errors propagate in the rotor position. The paper discusses an interesting property of Sliding Mode Observers: under the same offset conditions, because of the discontinuous feedback used, SM Observers allow ideal integration of the observer equations. Thus, low pass filtering is avoided, the estimates have no phase errors and the resulting rotor position is more accurate than in observers with continuous feedback. The paper analyzes the general case and studies the PMSM as an example. The theoretical claims are validated with simulations and experimental tests.