Abstract : This paper establishes a mathematical model of a surface-mounted permanent magnet synchronous motor (SPMSM) in the stator stationary coordinate system and analyzes the control principle of the direct torque control system for the SPMSM. Based on the MATLAB/Simulink simulation platform, a comprehensive simulation model of the system is established. Simulation results show that the direct torque control system can effectively achieve rapid motor speed tracking, exhibits high dynamic and static performance, effectively reduces motor flux linkage and torque ripple, and improves the steady-state performance of the AC speed control system.
Keywords: stationary coordinate system; permanent magnet synchronous motor; direct torque control
Study of Surface Permanent Magnet Synchronous Motor direct torque control
0 Introduction
Direct torque control (DTC) is a novel variable frequency speed control technology developed after vector control. It was first proposed in the 1980s by German scholar M. Depenbrock and Japanese scholar I. Takahashi for asynchronous motors. In the 1990s, scholars Zhong.L., RahmanMF, HuYW, and others proposed the theory of direct torque control for permanent magnet synchronous motors. It employs space vector analysis to directly calculate and control the torque and flux linkage of the AC motor in the stator coordinate system. Using stator field orientation, it generates pulse width signals through discrete two-point control (Band-Band control) to directly and optimally control the switching state of the inverter, thereby achieving high dynamic torque performance.
DTC (Direct Current Traction Control) boasts advantages such as simple control structure, rapid dynamic torque response, low dependence on motor parameters, and good robustness to changes in motor parameters. It is currently widely used in asynchronous motors and permanent magnet synchronous motors, playing a significant role in industrial production, including household appliances, the automotive industry, and electric locomotive traction.
This paper presents a direct torque control system based on a surface-mounted permanent magnet synchronous motor (PMSM). Based on the analysis of the mathematical model of the PMSM, the control principle of the system is analyzed, and a simulation model of the system is established using MATLAB/Simulink. Simulation results show that the proposed control method can effectively achieve rapid tracking of the motor speed. The system exhibits high dynamic and static performance, effectively reduces the ripple of the motor flux linkage and torque, and improves the steady-state performance of the AC speed control system.
1. Mathematical Model of Surface-Mounted Permanent Magnet Synchronous Motor (SPMSM)
When studying the dynamic mathematical model of an AC motor, the following assumptions are often made:
(1) The stator windings are three-phase symmetrical, and the axes of each phase winding are 120 electrical degrees apart in space;
(2) There is no damping winding on the rotor, and the permanent magnet has no damping effect;
(3) Ignoring the effects of magnetic circuit saturation, hysteresis and eddy current, the superposition principle can be used for analysis;
(4) The back electromotive force is sinusoidal. The stator current generates only sinusoidal distributed magnetomotive force in the air gap, and the higher harmonics are ignored.
The voltage equation is:
2 SPMSM-DTC Control Principle
The Direct Torque Control (DTC) method uses space vector analysis to directly analyze the mathematical model of the AC motor in the stator stationary coordinate system, constructs the algorithm model of torque and flux linkage, calculates and controls the torque of the AC motor, generates PWM signals with the help of hysteresis controller (Bang-Bang control), and directly controls the switching state of the inverter through the switching meter to achieve high dynamic torque performance.
The basic principle is to make full use of the switching characteristics of the voltage-source inverter, and make the stator flux trajectory approach a circle by continuously switching the voltage state. The slip frequency is changed by the interleaving of the zero voltage vector to control the motor torque and its rate of change, so that the flux and torque of the AC motor can change rapidly as required.
The structural principle of a permanent magnet synchronous motor direct torque control (DTC) system is shown in Figure 2-1. It consists of an inverter, PMSM (Permanent Magnet Synchronous Motor), flux linkage estimator, torque estimator, rotor position estimator, switching meter, PI controller, and hysteresis comparator. The control system uses the error between the given motor speed and the actual speed as the torque input signal via the PI controller. Simultaneously, based on the detected three-phase current and voltage values of the motor, the system calculates the magnitude of the motor's flux linkage and torque using the flux linkage model and torque model, respectively, and calculates the rotor position, the error between the given flux linkage and the actual values, and so on. Finally, based on these states, the system selects the inverter's switching voltage vector, enabling the motor to adjust its output torque according to control requirements, ultimately achieving speed regulation.
Figure 2-1 Block diagram of the direct torque control system for permanent magnet synchronous motor
3. Construction of SPMSM-DTC Simulation Model
Based on the above mathematical model, an overall simulation model of the direct torque control system of the surface-mounted permanent magnet synchronous motor was established in the MATLAB environment using the Simulink tool, as shown in Figure 3-1.
Figure 3-1 Overall system simulation model
4. Simulation Results and Analysis
Using the simulation model established in MATLAB/Simulink, a simulation was performed in MATLAB R2010a. The system parameters were set as follows:
The simulated waveforms of motor speed, stator flux vector, flux amplitude, and electromagnetic torque are shown in Figures (a), (b), (c), and (d), respectively.
Simulation results show that the motor starts quickly, and the actual speed changes rapidly without overshoot. It can quickly track large changes in the given speed, demonstrating that direct torque control indeed possesses excellent dynamic and static performance. Except during the magnetic field establishment process at startup, the stator flux linkage trajectory remains approximately circular during both static and dynamic processes, with minimal flux linkage amplitude fluctuations, effectively reducing flux linkage pulsation when motor parameters change. After applying load torque, the dynamic response of the electromagnetic torque is fast with minimal fluctuations, improving the steady-state performance of the AC speed control system.
5. Conclusion
Direct torque control (DTC) analyzes the mathematical model of an AC motor directly in the stator stationary coordinate system, controlling the motor's flux linkage and torque, resulting in a simple system structure and ease of implementation. It largely solves some major problems in vector control, such as complex computational control, susceptibility to changes in motor parameters, and difficulty in achieving theoretical performance in actual operation. This paper establishes a mathematical model of a permanent magnet synchronous motor (PMSM) in the stator coordinate system, presents a DTC control system based on a surface-mounted PMSM, and establishes a simulation model of the system in the MATLAB simulation environment. Simulation results show that the DTC control system can effectively achieve rapid motor speed tracking, exhibits high dynamic and static performance, effectively reduces motor flux linkage and torque ripple, and improves the steady-state performance of the AC speed control system.
