# Inductance Estimation Based on Wavelet-GMDH for Sensorless Control of PMSM
###### Abstract  
In permanent magnet synchronous motor (PMSM) sensorless drive systems, the motor inductance is a crucial parameter for rotor position estimation. Variations in the motor current induce changes in the inductance, leading to core magnetic saturation and degradation in the accuracy of rotor position estimation. In systems with constant load torque, the saturated inductance remains constant. This inductance error causes a consistent error in rotor position estimation and some performance degradation, but it does not result in speed estimation errors. However, in systems with periodic load torque, the error in the saturated inductance varies, consequently causing fluctuations in both the estimated position and speed errors. Periodic speed errors complicate speed control and degrade the torque compensation performance. In this paper, we propose a wavelet denoising-group method of data handling (GMDH) based method for accurate inductance estimation in PMSM sensorless control systems with periodic load torque compensation. We present a method to analyze and filter the collected three-phase current signals of the PMSM using wavelet transformation and utilize the filtered results as inputs to GMDH for training. Additionally, a method for magnetic saturation compensation using the inductance parameter estimator is proposed to minimize periodic speed fluctuations and improve control accuracy. To replicate the load conditions and parameter variations equivalent to the actual system, experiments were conducted to measure the speed ripples, inductance variations, and torque component of the current. Finally, software simulation was performed to confirm the inductance estimation results and verify the proposed method by simulating load conditions equivalent to the experimental results. P 2024 2024  
as well, resulting in a consistent error in rotor position estimation. Such a consistently sized error in the rotor position has minimal impact on the estimation error of the speed. However, in scenarios where periodic load torque occurs, the inductance parameters also exhibit periodic variations, leading to periodic fluctuations in both the position estimation error and speed error. Therefore, in environments where the magnitude and fluctuation rate of the load torque are significant, the changes in inductance, a key parameter in rotor position estimation, become pronounced, leading to increased estimation errors and consequently reduced control precision of the entire system. Particularly in environments directly exposed to external vibrations and loads, such as electric motors near engines and powertrains, pumps, and compressors for household appliances, control performance can degrade sharply. Analyzing the pattern of the external load and applying appropriate compensating currents can mitigate the influences of load torque variations [6; 10]. However, implementing such methods may lead to secondary issues such as increased eddy currents due to the increased magnitude of compensating currents, resulting in increased ripples in speed estimation. Without appropriate compensation control considering these factors, mechanical instability and NVH (noise, vibration, and harshness) issues may arise in the overall system. Therefore, accurately estimating the actual size of the inductance and applying real-time closed-loop control can enhance the precision of sensorless speed control. Efforts have been made to address the issue of magnetic saturation resulting from changes in the inductance by constructing observer-based mathematical models to estimate the value of inductance [11; 12; 13; 14]. However, this method relies on the estimated rotor position and speed information obtained in sensorless drive systems, making the estimated inductance size sensitive to variations in back electromotive force constants and drive output voltage changes.