This paper presents a sensorless control method of a permanent magnet synchronous machine (PMSM) with magnetic saliency estimation. This is based on a high-frequency injection (HFI) technique applied on the modified PMSM model in the γδ reference frame. Except for sensorless control, an emphasis is placed on the magnetic saliency estimation to indicate a practical approach in tracking PMSM inductance variations. The magnetic saliency is determined using calculations embedded in the speed and position algorithm through current measurements. A notable characteristic of the modified PMSM model is that the corresponding rotor flux integrates both permanent magnet and saliency term fluxes. In applying a HFI technique for sensorless control, the structure of the PMSM flux model is formatted accordingly. A novel inductance matrix is derived that is completely compatible with the HFI methodology, since its elements include terms of angle error differential and average inductances. In addition, a sliding mode observer (SMO) is designed to estimate the speed and angle of rotor flux based on equivalent control applying a smooth function of the angle error instead of a sign one to reduce the chattering phenomenon. The control strategy is principally based on the adequacy of the proposed modified model and on the appropriateness of the SMO structure to successfully track the rotor flux position with the required stability and accuracy. Simulation results demonstrate the performance of the PMSM sensorless control verifying the effectiveness of the proposed algorithm to detect PMSM saliency, speed and position in steady state and transient modes successfully.
Keywords: sensorless control of PMSM; sliding mode observer (SMO); magnetic saliency estimation; modified rotor flux; high frequency injection (HFI) Notation u d , u q = dq axis stator voltages i d , i q = dq axis stator currents λ d , λ q = dq axis stator magnetic fluxes λ m = rotor magnetic flux L d , L q = dq axis inductances ΣL =(L d +L q )/2 = average inductance ∆L = (L d -L q )/2 = differential inductance r s = stator resistance u γ , u δ = γδ axis stator voltages i γ , i δ = γδ axis stator currents λ γ , λ δ = γδ axis stator magnetic fluxes p = number of pole pairs θ = θ e = electrical angular position ω = ω e = electrical angular speed Machines 2020, 8, 14 3 of 20However, the observers in the αβ stationary reference frame suffer from phase delay between the real and the estimated EMF, since the real extended EMF is a sinusoidal signal [18,20]. This undesired phase delay is due to the observer operation, which is similar to signal filtering. Despite the αβ stationary frame, PMSM variables, such as flux and extended EMF, are constant quantities in the dq (direct-quadrature) synchronous rotating reference frame that, however, cannot be applied directly. An advantageous alternative proposal is to express PMSM mathematical model in the γδ reference frame, which is rotating at estimated angular velocityω and lagging behind the dq synchronous reference frame by electrical...