Vector Control of Permanent Magnet Synchronous Motor

0 Introduction
With the development of high-performance permanent magnet materials, power electronics technology, large-scale integrated circuits and computer technology, the application field of permanent magnet synchronous motor (PMSM) has been continuously expanded, and it has been widely used in high-precision control fields such as CNC machine tools and robots. Due to the increasing requirements for motor control performance, the permanent magnet synchronous motor vector control system can achieve high-precision, high-dynamic performance, and a wide range of speed regulation or positioning control. The research on the permanent magnet synchronous motor vector control system has become one of the focuses of small and medium-capacity AC servo system research, and how to establish an effective simulation model has attracted more and more attention. Based on the analysis of the mathematical model of the permanent magnet synchronous motor, this paper uses the Simulink and Power System Block modules in the MATLAB language to establish a simulation model of the control system, and analyzes the simulation results.

1 Mathematical model
of permanent magnet synchronous motor The mathematical model of permanent magnet synchronous motor is based on the following assumptions:
(1) Ignore the influence of saturation, eddy current and hysteresis effect;
(2) The current of the motor is a symmetrical three-phase sinusoidal current:
(3) The magnetomotive force of the permanent magnet is constant, that is, the equivalent excitation current is constant;
(4) The three-phase stator winding is symmetrically distributed in a star shape in space, and the armature resistance and armature inductance of each stator winding are equal;
The permanent magnet synchronous motor is the main link of the AC synchronous speed regulation system, and the analysis of its mathematical model is particularly important for grasping its speed regulation characteristics. Take the axis of the rotor permanent magnet fundamental wave excitation magnetic field as the d-axis, and the q-axis leads the d-axis by 90 degrees in the direction of rotation. The dq axis system rotates with the rotor at an angular velocity ωr. Its spatial coordinates are expressed by the electrical angle θr between the d-axis and the reference axis α. The mathematical model of the ideal permanent magnet synchronous motor in the dq rotating coordinate system can be written as follows:

According to the mathematical model, the module of permanent magnet synchronous motor was established using Simulink as shown in Figure 2.1:

2 Control Principle of Permanent Magnet Synchronous Motor AC Servo System

It can be seen from the above formula that the electromagnetic torque of the permanent magnet synchronous motor basically depends on the component of the stator current on the q axis. Since the rotor flux of the permanent magnet synchronous motor is constant, vector control oriented by the rotor flux is generally adopted. The essence of control is to achieve torque control of the AC permanent magnet synchronous motor by controlling the stator current. When the speed is below the base speed, under the condition of a given stator current, controlling id=0 can more effectively generate torque. At this time, the electromagnetic torque Tem=Pniqψr. It can be seen that the electromagnetic torque changes with the change of iq. This control method is the simplest. However, when the speed is above the base speed, because the excitation flux of the permanent magnet is a constant, the motor induced electromotive force increases in direct proportion to the motor speed. The motor induced voltage also increases, but it is limited by the voltage upper limit of the inverter connected to the motor end.
In actual control, the system detects the three-phase stator current flowing into the motor, so coordinate transformation must be performed to transform the current component on the three-phase stator coordinate system into the current component on the rotor coordinate system through park and clarke. To achieve the transformation from the stator coordinate system to the rotor coordinate system, the position of the motor rotor must be detected in real time during the control. Common rotor position detection sensors include incremental photoelectric encoders, absolute photoelectric encoders, and resolvers. The position signal command is compared with the detected rotor position, and after adjustment by the position controller, the speed command signal is output. The speed command signal is compared with the detected rotor speed signal, and after adjustment by the speed regulator, the current component i*q of the control torque is output. The current component given signal is compared with the actual current component of the motor after the coordinate transformation, and is calculated by the current controller. The output is used to calculate the PWM drive IGBT through the inverse park transformation, and the three-phase sinusoidal current with variable frequency and amplitude is input into the motor stator to drive the motor to work.

3 System Simulation
Figure 4.1 Simulation Block Diagram of Three-phase Permanent Magnet Synchronous Motor Vector Control The simulation block diagram of the three-phase PMSM vector control system based on rotor magnetic field orientation is shown in Figure 4.1. The PI module in the figure is a speed loop PI controller, which determines the current torque component according to the actual motor speed and the given speed; the PWM module adopts current hysteresis control (as shown in Figure 4.2) to make the actual motor current follow the given current change, and the specific implementation is shown in Figure 4.3; the module dq2abc realizes 2r/3s transformation, and the specific implementation is shown in Figure 4.4, in which the function modules Fcn, Fcnl and Fcn2 realize 2r/3s transformation together; the MMD module is a motor measurement module, which measures the speed, current, rotor position and other signals of the motor in real time: the PMSM module provides a permanent magnet synchronous motor model for MATLAB, and its specific implementation is shown in Figure 2.1.

4 Simulation graphics and result analysis

The motor parameters used in the simulation are as follows: stator resistance is 2.875Ω, stator direct axis inductance and quadrature axis inductance are both 8.5e-3H, the flux linkage between the permanent magnet pole and the stator winding is 0.175Wb, the moment of inertia is 0.8e-3kgm2, the number of pole pairs is 6, the given speed is ωr=500rpm, and at t=0.03s, the load torque suddenly changes from ON·m to 6N·m, as shown in Figure (5.1).
From the above simulation results, it can be seen that when the ordinary three-phase permanent magnet synchronous motor adopts a vector control scheme based on rotor magnetic field orientation and the speed outer loop adopts PI control, there is a certain overshoot in the speed response process, as shown in Figure (5.2). When the load is suddenly added, the speed drops immediately and then gradually recovers to stability, as shown in Figure (5.3): If PID control is used in the speed outer loop, that is, a small differential link D is added to the speed outer loop and the proportional gain factor P is appropriately reduced, the overshoot can be effectively reduced, and the time for the motor to reach a steady state when the motor starts and suddenly adds load can be shortened. The actual current of the quadrature axis always tracks the given current of the quadrature axis, see Figure (5.5), and during the starting process and when the load is suddenly added, the two change greatly, while both are basically constant when stable. The electromagnetic torque is constant in steady state, see Figure (5.4), in order to balance the external load; when the speed is stable, the three-phase stator current is a regular sinusoidal current, and the phase difference is about 120°.