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.