Position and Speed Estimation of PMSMs Using Gaussian Processes

In this paper, we present a novel low-cost technique to estimate both the position and the speed of a permanent magnet synchronous motor (PMSM) by sensing its stray magnetic field. At an optimal radial and axial distance, a low-cost magnetoresistive sensor is placed outside at the back of the PMSM. The magnetic field values are recorded for one complete rotor revolution at a resolution of less than a degree for different speeds of operation. Gaussian Processes (GPs) are employed to find a mapping function between the magnetic field values of the permanent magnet and the absolute angular positions. Then, by using the learned GP as a measurement function with an Extended Kalman Filter (EKF), both the angular position and speed of a PMSM can be estimated efficiently. Furthermore, we observe that the magnetic field depends not only on the position but also on the angular speed. To address this, we extend the GP to incorporate multivariate inputs. In order to take the periodicity of the data into account, we employ a periodic kernel for the GP. Additionally, a linear basis function model (LBFM) is introduced to incorporate more training points while maintaining the same computational cost. The GP and LBFM approaches are evaluated with data from a real PMSM experiment setup, and the accuracy of the position and speed state estimation is verified against a high-resolution optical encoder used as ground truth.