Second-Order Resistance Identification for Permanent Magnet Synchronous Motors Using Kalman Filter

Permanent Magnet Synchronous Motors (PMSM) are widely used in industrial drive systems, where control performance highly depends on the accuracy of motor parameters. As one of the key parameters, resistance drifts with temperature variations, thereby affecting control precision. This paper explores how to implement second-order resistance identification for PMSMs using Kalman filters to enhance system adaptability. The Kalman filter, as an optimal state estimation algorithm, effectively suppresses noise interference by fusing prediction and measurement data. In resistance identification scenarios, resistance and its rate of change can be modeled as second-order state variables: resistance value as the first-order state and its rate of change as the second-order state. This modeling approach tracks the dynamic variation process of resistance, making it particularly suitable for slowly varying parameters caused by temperature rise. For system implementation, an extended state-space model must be established, incorporating resistance and its derivative into the observation equation. By real-time acquisition of motor terminal signals such as voltage and current, the Kalman filter recursively updates the state covariance matrix and ultimately outputs the optimal resistance estimate. Compared to traditional offline identification methods, this approach offers three major advantages: online updating, noise suppression, and dynamic tracking. This technique can be extended to multi-parameter joint identification scenarios, such as simultaneously observing resistance and inductance parameters. Future integration with adaptive algorithms like deep learning is expected to further enhance the robustness of parameter identification under complex operating conditions. In code implementation, key functions would include: - State-space model initialization with resistance (R) and its derivative (dR/dt) as state variables - Real-time measurement processing of voltage/current signals for innovation calculation - Recursive covariance matrix updates using Kalman gain computation - Adaptive tuning of process and measurement noise matrices for optimal performance The algorithm typically follows a predict-update cycle: 1. Prediction step: Project state estimates and covariance forward using system dynamics 2. Update step: Correct estimates using new measurements and Kalman gain Critical implementation considerations include proper discretization of continuous-time models and numerical stability maintenance during matrix operations.