Design of vector control system for permanent magnet synchronous motor based on SVPWM

Introduction
Permanent magnet synchronous motor (PMSM) based on sine wave has the advantages of high power density, high efficiency and low rotor loss, and has been widely used in the field of motion control. Vector control mainly uses pulse width modulation (PWM) technology to control the output voltage and reduce harmonics. Among them, SVPWM has the advantages of high system DC bus voltage utilization, low switching loss and small motor torque fluctuation. Therefore, the vector control of PMSM has been proved to be a high-performance control strategy.
With the help of PMSM mathematical model, this paper analyzes the vector control principle and SVPWM modulation method of synchronous motor. At the same time, with the help of Matlab's powerful simulation modeling ability, a simulation model of SVPWM synchronous motor vector control system is constructed and verified by simulation experiments.

1 PMSM mathematical model
The vector control of permanent magnet synchronous motor is based on the dqO coordinate system of the motor. Before establishing the mathematical model, the following assumptions can be made: that is, the core saturation is ignored, the eddy current and hysteresis loss are ignored, there is no damping winding on the rotor, the conductivity of the permanent magnet material is zero, and the motor current is a symmetrical three-phase sinusoidal current. Based on the above assumptions, the mathematical model of PMSM under the dqO axis can be obtained by applying the coordinate transformation theory.
The voltage, flux, electromagnetic torque and power equations (i.e., Parker equations) of this model are as follows:


2 Vector control system
2.1 Basic principles of vector control The
basic idea of ​​vector control is to decompose the current vector into two mutually perpendicular and independent vectors id (excitation current component that generates flux) and iq (torque current component that generates torque) on the magnetic field oriented coordinates. In other words, controlling id and iq can control the torque of the motor. The
control method based on rotor flux orientation (id=0) is to make the stator current vector located on the q axis without d-axis components. At this time, the torque Te and iq are linearly related (from the above torque equation). Therefore, as long as iq is controlled, the purpose of controlling the torque can be achieved. Since all the stator current is used to generate torque, the voltage equation of PMSM can be written as follows:

From the above simplified process, it can be seen that as long as the angle θ of the rotor spatial position is accurately detected and the three-phase stator synthetic current (magnetomotive force) is located on the q axis by controlling the inverter, the electromagnetic torque can be well controlled by controlling the amplitude of the stator current. At this time, the control of PMSM is similar to the control of DC motor.
2.2 Control composition of vector control speed regulation system
When the motor starts, the system should be initially positioned by software to obtain the actual position of the rotor. This is a necessary condition for permanent magnet synchronous motor to achieve vector control. First, the rotor angular position ωr should be detected by the rotor position sensor, and the rotor speed n should be calculated at the same time. Then, the stator (any two phases) current is detected and vector transformed to obtain the detection values ​​id and iq, and then the AC and DC shaft voltage values ​​ud and uq are output respectively through the PI regulator, and then the voltage values ​​uα and uβ are generated after coordinate transformation. Finally, the SVPWM method is used to output the 6-pulse inverter drive control signal. Figure 1 shows the principle diagram of PMSM vector control.

As shown in Figure 1, the speed of the outer loop and the current loop of the inner loop can form a double closed-loop control system of the PMSM. The space voltage vector (SVPWM) pulse width modulation technology is applied in this control system. Since the switching loss of SVPWM is small, the voltage utilization rate is high, and the harmonics are few, the speed regulation performance of PMSM is greatly improved.

3 SVPWM principle
The inverter PWM in the vector control system of this paper adopts the voltage space vector pulse width modulation (SVPWM) technology. SVPWM technology is mainly based on the perspective of the motor. It focuses on how to make the motor obtain a circular rotating magnetic field with a constant amplitude (i.e., sinusoidal flux). The three-phase load phase voltage can be replaced by a space voltage vector (target vector). By controlling the on and off of the three-phase inverter switching device, the basic vector for synthesizing the target vector can be obtained. Figure 2 shows a typical three-phase inverter circuit and its SVPWM vector sector diagram. The figure introduces the switch variables Sa, Sb, and Sc of the A, B, and C bridge arms. When the upper tube of a bridge arm is turned on and the lower tube is turned off, the switch variable value is 1; when the lower tube is turned on and the upper tube is turned off, the switch variable value is 0. Therefore, the entire three-phase inverter has 8 switching states, that is, (SaSbSc) is (000) to (111), corresponding to the 8 output voltage vectors of the inverter, of which 2 are zero vectors and 6 non-zero vectors can divide the plane into 6 sectors. Figure 3 shows the specific implementation steps for generating SVPWM. Its implementation can be built through the Simulink module library.

Now take the first sector as an example to calculate the action time of the basic vector, and the position of its spatial voltage vector Vd is shown in Figure 4. If the action time of vectors Vx, Vy, and V0 is Tx, Ty, and T0 respectively within the switching cycle Ts, then:

In formula (7), Vph is the phase voltage fundamental amplitude. The action time of the basic vectors Vx, Vy, and V0 in the sector can be obtained from formula (7), and the action time of each switching state of the inverter can be determined accordingly.
4 Simulation analysis
The simulation model of the vector control system established under MATLAB/simulink is shown in Figure 5. The system adopts dual closed-loop control, with the outer loop being the speed loop and the inner loop being the current loop. The simulation parameters are: PMSM rated voltage is 380 V, frequency is 50 Hz, pole pair number p=2, Rs=2.85, vertical and horizontal axis inductance Ld=Lq=2.21mH, rotor flux ψf=0.175Wb, triangle carrier period T=0.0002s, and amplitude is T/2. The DC side voltage Ud=310 V, and the initial speed setting value is 500 rad／s.

The purpose of this experiment is to observe the dynamic and static responses of the motor output as the torque command value changes. In the experiment, given a reference speed n = 500rad/s, the torque TL = 0 is simulated, and then the torque is changed from TL = 2 N·m to TL = 10N·m in 0 to 0.2s. The current, speed and torque waveforms obtained by the simulation experiment are shown in Figure 6.

Figure 6 (a) is the simulation result of no-load operation, and its steady-state current and torque are 0; Figure 6 (b) is the simulation result when the motor is started with maximum torque. It can be seen from the figure that the stator has a short-term impact current, but the steady-state current waveform is good and the speed following is also fast. In summary, it can be seen that this experiment has the advantages of small torque pulsation, good current waveform, and rapid system response.

5 Conclusion
This paper analyzes the basic principle of permanent magnet synchronous motor vector control and SVPWM modulation method, and uses Matlab/simulink to establish a simulation model of the vector control system, and verifies it through experiments. The simulation and experimental results show that the control system has the advantages of good dynamic and static performance and high output current sinusoidality, which can provide effective means and tools for analyzing and designing PMSM control systems, and also provide new ideas for the design and debugging of actual motor control systems.