Abstract: High-performance permanent magnet synchronous motor (PMSM) vector control systems require real-time updates of motor parameters. This paper presents an online parameter identification method for PMSMs. This least-squares-based parameter identification method is performed in a rotor synchronous rotating coordinate system. The parameter identification of PMSMs based on the least-squares method was simulated using MATLAB/SIMULINK. Simulation results show that this motor parameter identification method can update motor control parameters in real-time and accurately. Keywords: Permanent magnet synchronous motor; Parameter identification; Least-squares method [b][align=center]Simulation of PMSM based on least squares online parameter identification WANG Hong-shan, ZHANG Xing, XIE Zhen, YANG Shu-ying[/align][/b] Abstract: This paper presents a method to determine the parameters of a PMSM online, which are necessary to implement the vector control strategy. The presented identification technique, based on least squares, reveals its suitability for PMSM. The estimation is based on a standard PMSM model, expressed in rotor coordinates. The method is suitable for online operation to continuously update the parameter values. The developed algorithm is simulated in MATLAB/SIMULINK. Simulation results are presented, and accurate parameters for PMSM are provided. KEY WORDS: PMSM; Parameter Identification; Least-Squares 0 Introduction There is a large body of literature and rich research results on motor parameter identification. Research on parameter identification technology began in the late 1970s and early 1980s. Even today, new research findings continue to emerge in this field, and numerous methods for parameter identification exist, each with its own unique characteristics. However, generally speaking, existing identification methods can be categorized into five types: signal injection method, direct estimation method, compensated coordinate system method, least squares method, and model reference adaptive method. The signal injection method injects test signals or harmonics with known characteristics into the motor and utilizes spectral characteristics to identify motor parameters. However, the injection of harmonics or test signals can adversely affect the control system. Extended Kalman filtering and model reference adaptive control strategies can accurately estimate motor parameters even when system and measurement noise is present; however, this approach is difficult to implement. Least squares theory was proposed by Gauss when solving problems related to celestial orbits. Least squares identification is one of the most important system identification methods and a primary method for parameter model identification, and it has been widely applied. This paper analyzes the equations of a permanent magnet synchronous motor in a synchronous rotating coordinate system and uses the least squares method to identify the parameters of the permanent magnet synchronous motor through a MATLAB/Simulink simulation environment. The results show that this parameter identification method can accurately identify the parameters of the permanent magnet synchronous motor. 1 Parameter Identification of Permanent Magnet Synchronous Motor Based on Least Squares Method 1.1 Necessity of Motor Parameter Identification In AC speed control systems, vector control technology enables AC motors to obtain the same control characteristics as separately excited DC motors. The performance of AC speed control systems using vector control technology reaches the level of DC speed control systems. Sensorless vector control is developed based on conventional vector control with speed sensors. In sensorless vector control, motor parameters must be used. In engineering, the parameters of the motor used on site cannot be predicted, and it is impossible to use conventional no-load tests and stall tests to measure motor parameters. Furthermore, with the aging of the motor and changes in the surrounding environment, there is a large difference between the actual parameters of the motor and the given parameters. Therefore, as a general-purpose frequency converter, it is necessary to have the function of self-determination of motor parameters. Parameter identification methods before a motor is put into normal operation, especially those that rely solely on the motor speed control system itself without adding any additional circuitry, have become a new feature of modern AC motor parameter identification. From a control perspective, one way to solve the problem of inaccurate parameters of the controlled object is to identify the parameters of the controlled object online and continuously update their parameter values ​​so that the controller setpoint matches the actual value. 1.2 Basic Principles of the Least Squares Method The least squares method was originally proposed to solve overdetermined equations and find the optimal solution. Let y be a function of a set of independent variables. If m observations are performed, then: But when m=n, as long as A[sup]-1[/sup] exists, the undetermined parameters can be found: a=（a[sub]1[/sub],a[sub]2[/sub]...,a[sub]n[/sub]), and the above equation has a unique solution: a=A[sup]-1[/sup]y When m>n, it is called an overdetermined system of equations. Usually, it is not possible to select a set of parameters to satisfy all m equations, so estimation methods are needed to estimate the optimal value. The least squares method can be used for estimation: 1.3 Parameter identification of permanent magnet synchronous motor based on least squares method The key to the parameter identification of motor based on least squares method is how to obtain the linear equation with the parameters to be identified as unknowns. The following explains how to obtain the motor model with the parameters to be identified as unknowns in the rotor synchronous rotating coordinate system. First, the mathematical model of permanent magnet synchronous motor is analyzed using the synchronous rotating coordinate dq axis system fixed to the rotor. Take the axis of the fundamental excitation magnetic field of the rotor permanent magnet (pole axis) as the d axis, the angle θr between the d axis and the A phase winding, and the q axis (quadrature axis) leads the d axis by 90 electrical degrees in the counterclockwise direction. The xy coordinate system is a rotating coordinate system fixed on the stator, the direction of the stator flux linkage is the positive direction of the x axis, and the dq axis rotates together with the rotor with an electrical angular velocity ωr. The components on the dq axis can be obtained from the three-phase stator windings through a three-phase coordinate system or vector transformation, that is, the transformation from a three-phase axis system to a two-phase rotating axis system dq. Taking the rotational transformation of the current as an example, we analyze how to obtain the motor model under the rotor synchronous rotating coordinate system. In the formula, θr is the rotor position; is the d-axis and q-axis current of the stator; and is the current of the A-axis, B-axis and C-axis. Through the coordinate transformation of formula (4), the model equation of the motor under the rotor synchronous rotating coordinate system can be obtained: In the formula: Rs is the stator resistance; Ld is the d-axis inductance; Lq is the q-axis inductance; Lmd is the magnetizing inductance; and if is the equivalent magnetizing current. In the motor, if the effect of temperature change on the magnetization of the permanent magnet is ignored, the fundamental magnetic field of the permanent magnet can be considered to be constant, that is, i[sub]f[/sub] is a constant. In fact, it is the kinetic electromotive force generated by the excitation magnetic field of the d-axis permanent magnet in the q-axis coil, that is, the no-load electromotive force e[sub]0[/sub]. Equation (5) can be simplified to: Equation (6) can be written in matrix form: From equation (7), it can be clearly seen that after coordinate transformation, a linear equation with stator resistance R[sub]s[/sub], q-axis inductance L[sub]a[/sub] and d-axis inductance L[sub]d[/sub] as unknowns is obtained, and the least squares method can be used to identify the motor parameters. 2 Simulation model of permanent magnet synchronous motor parameter identification based on least squares method In the Simulink environment of Matlab7.0, based on the analysis of the mathematical model of permanent magnet synchronous motor, a simulation model of permanent magnet synchronous motor parameter identification system was established as shown in Figure 1. [align=center]Figure 1 System Principle Block Diagram Based on Least Squares Parameter Identification[/align] The system adopts a control scheme: based on the idea of ​​modular modeling, the control system is divided into functionally independent sub-modules, mainly including: permanent magnet synchronous motor body module, motor operation status measurement module, and least squares parameter identification module. Through the organic integration of these functional modules, a simulation model of the permanent magnet synchronous motor parameter identification system can be built in Matlab/Simulink, and the motor parameter identification algorithm can be implemented. Among them, the least squares parameter identification module requires a large number of matrix operations, so it is written in M ​​language and embedded as a module in the Simulink environment, making full use of the modular environment provided by Simulink and the flexibility of M language to achieve an effective combination of the two. 3 Simulation Results The simulation model established above was used to conduct simulation tests on the permanent magnet synchronous motor system. The parameters of the permanent magnet synchronous motor are shown in Table 1: Table 1 Simulation parameters During the simulation, a torque of -30 Nm/s is added to the rotor shaft of the permanent magnet synchronous motor, so that the permanent magnet synchronous motor is running in the power generation mode while the motor is in a state of continuous acceleration. The purpose of this is to make the motor's state equation satisfy equation (7). The maximum step size of the simulation is 0.53s. The parameter identification module written in M ​​language starts at 0.53s and performs parameter identification every 0.01s. Thus, every 0.01s, the newly identified motor parameters are used to update the previously identified motor parameters to obtain accurate real-time motor parameters. Figure 2 shows the simulation results of parameter identification during the control process of the permanent magnet synchronous motor when the initial values ​​of the motor parameters to be identified are all 0: the dashed lines represent the actual parameter values ​​of the motor, and the solid lines represent the results of parameter identification. From Figures a, b, and c of Figure 2, it can be seen that from the start of the 0.53s algorithm, the d-axis and q-axis inductances of the permanent magnet motor, including the stator resistance, monotonically converge to the corresponding actual parameters of the motor from the initial value of 0, and infinitely approach the actual values ​​of the corresponding motor parameters. Simulation results show that the parameter identification algorithm based on the least squares method can accurately identify motor parameters online in real time, with good convergence and identification accuracy. [align=center] (a) d-axis inductance (b) q-axis inductance (c) stator resistance Figure 2 Motor parameter identification results[/align] 4 Conclusion To improve the control performance of permanent magnet synchronous motors, this paper uses the least squares method to identify motor parameters in the synchronous rotating coordinate system of the permanent magnet synchronous motor rotor. A simulation model of the permanent magnet synchronous motor parameter identification system is built in Matlab/Simulink. Simulation results show that the parameter identification algorithm based on the least squares method can accurately identify motor parameters online in real time, with good convergence and identification accuracy.