# Research on Permanent Magnet Synchronous Motor Control System Based on Adaptive Kalman Filter
## 1 Introduction  
In recent years, the development and availability of permanent magnet materials have made permanent magnet synchronous motors (PMSMs) develop rapidly. Moreover, PMSMs have the advantages of small volume, high efficiency, high power density, and wide speed range [1, 2, 3]. Thanks to the application of advanced methods such as vector control and space vector pulse width modulation, PMSMs can realize higher performance speed and position control in the digital control system. In this way, the application of high-performance shifting motors can become widespread. At present, PMSMs are widely used in new energy vehicles, CNC machine tools, and robots, and has a good development prospect [4, 5]. To make the whole PMSM control system operate stably, the motor needs to get the position and speed of the rotor in real-time [6]. To detect the rotor position information, the universal solution is to install mechanical position sensors, such as photoelectric encoders, rotary transformers, etc. However, the mechanical sensor has several disadvantages [7, 8]. Firstly, the mechanical position sensor increases system cost and circuit size, limiting the promotion application of products. Secondly, mechanical sensors are susceptible to noise, and the operating temperature range is limited, reducing the system's operational reliability [9]. Thus, installing mechanical position sensors is not an optimal way to obtain the position and speed of the rotor in real time. Due to the limitations of the mechanical sensors, a number of studies use various non-sensor techniques to estimate speed and location. They can be divided into active methods and passive methods: the first is to inject high-frequency signals using rotor anisotropy [10, 11], and the second is based on observer [12]. For example, the authors in [13] developed the model reference adaptation method that used adaptive parameter identification theory for sensorless control of PMSMs. The method consists of an adjustablemodel, reference model, and adaptive law, according to the error of the current state variable adaptive adjustment adjustable model parameter. This method can keep the output of the reference model consistent with the adjustable model. Authors in [14; 15] developed a sliding model observer method. This method performed closed-loop correction and adjustment on the observed current to be consistent with the actual current. The control function then output the back EMF through a low-pass filter and obtained the position angle error through arctangent. Authors in [16; 17] developed the EKF-based approach, which performed an online estimation of the system state to implement online control. Among the above methods, the model reference adaptive method is susceptible to stator resistance variation during the operation process [18]. The sliding mode observer has a discontinuous switch function, which will produce large jitter and noise. The EKF can suppress noise while overcoming other algorithm defects and is easy to implement in discrete time domains. Therefore, the EKF algorithm is widely used to estimate the speed and position of PMSMs [19]. Authors in [9; 20] proposed a speed estimation method using the EKF algorithm, and achieved the closed-loop speed control system of PMSMs, which proved that the EKF algorithm is feasible for PMSM closed-loop control. The EKF algorithm considers the impact of system and measurement noise, providing a random method for status and parameter estimation. However, the EKF algorithm requires complete dynamic model parameters and statistical model parameters to achieve optimal performance, which is the accurate known system process noise covariance. In practical applications, the process noise covariance uncertainty and inaccuracy will lead to the deviation of the filter and seriously affect the filter's performance. Therefore, research on the filtering problem of inaccurate or mismatched system noise covariance is essential [21].