Improved Single Current Sensor Based PMSM Control under Low Frequency Ratio Using Discrete-Time Adaptive Luenberger Observer

The implementation of traditional current state observers for single current sensor (SCS) based permanent magnet synchronous machine (PMSM) control use continuous-time domain analysis and Euler or Tustin approximation for discretization. However, stability problem occurs at low sampling-to-fundamental frequency ratio condition with Euler approximation method and heavy computation burden cannot be ignored with Tustin method. To overcome these limitations, a discrete-time adaptive observer is proposed for SCS control in PMSM drives. First, commonly adopted Luenberger observers designed with Euler and Tustin methods are reviewed and analyzed. Then, a novel hybrid discretization (HY) method is proposed to design a discrete-time adaptive Luenberger observer with improved discretization accuracy while maintaining computational efficiency. In the proposed HY method, the nonlinear part of the PMSM model is discretized using the accurate Runge-Kutta discretization method, while the linear part is discretized using the computationally-efficient Euler approximation method. This HY method achieves a balance between simplicity and accuracy, resulting in a highly effective discretization of the observer. Moreover, the speed-adaptive gain is designed to guarantee stability and dynamic performance over a wide speed range. Experimental results have been performed on a laboratory interior PMSM drive to confirm the effectiveness of the proposed method.