Well-Conditioned Identifiability Criteria With Observability Degree for Parameter Estimation of Permanent Magnet Synchronous Motors

The identifiability of parameters in permanent magnet synchronous motors (PMSMs) depends on the operating conditions. Due to disturbances and noise in actual systems, identifiability conditions that rely solely on traditional observability theorems for parameter estimation are ill-conditioned under certain operating environments, which cannot provide a definite reference for accurate outcomes. This article introduces a novel theorem regarding the degree of observability to bridge the gap in traditional parameter observability analyses and defines a quadratic function to create a unique information matrix based on the PMSM voltage model. As an example, a practical observability condition is derived for the inductances of the dq-axis of PMSMs by applying the proposed theory to the information matrix, offering guidance for selecting identifiable operating conditions in real-time systems. Moreover, comprehensive analyses are conducted to theoretically verify the correctness and stability of the proposed observability condition. Finally, experiments are performed to validate the feasibility of the proposed observability theorem for parameter estimation.