Abstract: The widespread use of permanent magnet synchronous motors (PMSMs) has led to increasing research on them. PMSMs employing direct torque control (DTC) are widely used due to their good responsiveness, fault tolerance, and simple structure. However, their inherent characteristics can cause torque ripple. Over the years, research on suppressing torque ripple in PMSMs and DTCs has yielded considerable results, each with its own advantages and disadvantages. This paper proposes a novel method for suppressing torque ripple in PMSMs and DTCs based on sliding mode control (SMC) and space vector pulse width modulation (SVPWM) techniques. SMC is used to replace two hysteresis comparators to obtain the direct and quadrature axis reference voltages, which are then modulated using SVPWM. This solves the torque ripple caused by the bandwidth of the hysteresis comparators, improves accuracy and response speed, and reduces torque ripple. Simulation results also demonstrate the effectiveness of this method. However, this method also has some drawbacks. It was also found that the parameters of the PI controller have a significant impact on system performance.
Keywords : Permanent magnet synchronous motor, sliding mode control, space vector pulse width modulation, direct torque control, torque ripple suppression, PI value
1. Introduction
In recent years, permanent magnet synchronous motors (PMSMs) have been used more and more widely in the manufacturing industry, the automotive industry, and even some high-speed trains. This is because PMSMs have unique advantages: high power density, environmentally friendly materials, simple structure, and easy control. Direct torque control (DTC) is an important component of PMSM control. Although DTC technology started later than field-oriented control (FOC), it has advantages such as simple control, strong fault tolerance, and fast response speed. DTC also has its drawbacks. In particular, the traditional PMSMDTC uses a hysteresis comparator to control flux and torque, resulting in unavoidable torque ripple. Coupled with torque ripple caused by other factors, the DTC control effect is not as good as FOC. However, in recent years, researchers have made great efforts to suppress DTC ripple, and there are many methods with varying effects. For example, some add a zero vector, some subdivide the interval, some add a basic vector, and some use neural network control, etc. Many of these either do not remove the hysteresis comparator, are very complex, or have poor effects. This paper uses SMC and SVPWM technology to reduce the torque ripple of PMSMDTC, that is, to remove the hysteresis comparator without significantly increasing the system complexity. Simulation results also show that the proposed solution has a very good effect on suppressing torque ripple.
2. PMSMDTC technology and its causes of torque ripple
Direct torque control (DTC) technology originated in the 1980s, initially applied to asynchronous motor control, and later to permanent magnet synchronous motors. We can analyze its basic principle using Figure 2-1. Under vector conditions, the stator voltage can be divided into a component parallel to the stator flux linkage Ψ<sub> s </sub>, denoted as u<sub> ST </sub>, and a vertical component, u <sub>sn </sub>. These two components control the amplitude and speed of the stator flux linkage. We know that the electrical time constant is much smaller than the mechanical time constant, so we assume that changing the stator flux linkage results in almost no change in the rotor position, thus altering the magnitude of δ<sub> ST</sub> . Based on...
We know that controlling the amplitude and speed of the flux linkage controls the electromagnetic torque. This is the principle of PMSMDTC. In actual operation, hysteresis comparator is used to control the amplitude of the flux linkage and the torque (the flux linkage speed is equivalent to the electromagnetic torque). A stator flux linkage range and an electromagnetic torque range (upper and lower limits) are set. Whenever the flux linkage or torque reaches the limit, a switch is triggered to perform a voltage selection, thereby achieving the purpose of controlling the electromagnetic torque.
Torque ripple in DTC torque control has many causes. The main one is that the bandwidth of the hysteresis comparison used in its control strategy means that flux linkage and torque are not precise values, but rather a range. Furthermore, the bandwidth cannot be too small or too large. Too small a bandwidth increases the switching frequency, increases losses, reduces controllability, and may even cause more severe torque ripple. Too large a bandwidth directly increases the ripple amplitude. It also performs poorly at low speeds because the stator resistance voltage drop is significant and cannot be ignored. However, DTC ignores the stator resistance when calculating flux linkage. Other causes include hardware measurement accuracy issues, real-time changes in motor and electrical parameters, and control accuracy problems.
3. SMC technology
Sliding mode control (SMC), also known as sliding variable structure control, is a comprehensive design method for a class of nonlinear control systems. It was proposed in the 1950s by Emelyanov et al. in the former Soviet Union and further developed by Utkin et al. Variable structure is achieved through switching functions. A control system can be designed with several switching functions. When the value of the switching function, determined by the system's state vector, reaches a specific value as the system moves, one structure in the system transforms into another. Sliding mode control is essentially a special type of nonlinear control, characterized by discontinuous control, i.e., a switching characteristic that causes the system's "structure" to change over time. This control characteristic can force the system to move up and down along a predetermined state trajectory with small amplitudes and high frequencies under certain conditions, i.e., sliding mode or "sliding" motion. This sliding mode can be designed and is independent of system parameters and disturbances. Thus, systems in sliding mode motion have good robustness, fast response, and simple physical implementation. However, sliding mode control also suffers from jitter, which reduces system stability.
4. SVPWM technology
SVPWM, or Space Vector Pulse Width Modulation, is based on the principle of average value equivalence. That is, within one switching cycle T, the average value of the basic voltage vectors is combined to equal the given voltage vector, as shown in Figure 4-1. After obtaining the desired voltage usref , usref can be synthesized using two relevant basic voltage vectors in the region, such that...
In practical applications, a zero vector is added because timing mismatches sometimes occur. Using SVPWM can significantly improve DTC control performance and reduce torque ripple because SVPWM does not use hysteresis comparison but directly calculates and outputs the reference voltage. Therefore, theoretically, it precisely controls flux linkage and torque, and the switching frequency is constant. SVPWM can also experience torque ripple due to other reasons, such as hardware issues, parameter inaccuracy issues, and problems with measurement and control accuracy.
5. Simulation and Discussion
The comparative experiment used controlled variables, with the simulation time being 0.4s as the invariant; the power supply being DC 310V; the inverter model being a 3-arm IGBT and anti-parallel diode, with an infinite buffer capacitor, a buffer resistor of 1e5 Ω , an on-resistance of 1e-3 Ω , Tf: 1e-6Tt: 2e-6; the motor model being a 3-phase hidden-stage type, with a stator phase resistance of 1.2 Ω , both direct and quadrature axis inductances of 8.5mH, a specified permanent magnet flux linkage of 0.175Vs, a voltage constant of 126.966, a torque constant of 1.05, a moment of inertia of 0.0008, an adhesion coefficient of 0, a pole pair number of 4, and all other values of 0; the rotor flux linkage being oriented along the A-axis; the load being 0 from 0-0.2s and 1.5Nm from 0.2s-0.4s; and the rotational speed being 600r/min. The variables are the control strategies. One uses the traditional PMSMDTC control method, and the other uses the SMC-SVPWM-PMSMDTC control method. The experimental results are collected and compared by collecting the rotor speed, stator flux linkage and electromagnetic torque waveforms.
First, a traditional PMSMDTC experiment was conducted. The initial simulation model, as shown in Figure 5-1, involved obtaining the required torque (P=0.1, I=5) through PI control at a given speed. The flux linkage was set, and the bandwidth of the two hysteresis comparators was 0.004. The switching meter did not have a zero vector. This system was controlled by a speed sensor. The load torque increased from 0 to 1.5 Nm in 0.2 s.
The simulation results are shown in Figures 5-3 to 5-8. Figures 5-3, 5-5, and 5-7 are from the traditional PMSMDTC simulation results, while figures 5-4, 5-6, and 5-8 are from the SMC-SVPWM-PMSMDTC simulation results. From the figures, we can see that compared with the traditional PMSMDTC control, the SMC-SVPWM-PMSMDTC control has a faster speed response, better speed following effect, significant torque ripple suppression effect, and reduced flux linkage ripple, thus improving the stability and accuracy of the entire motor system. This is due to the combined use of sliding mode control and space vector pulse width modulation technology. By replacing the hysteresis comparator with sliding mode control, the main ripple caused by bandwidth disappears. SVPWM accurately constructs the required stator voltage, thus significantly reducing torque ripple and flux linkage ripple. There are also shortcomings, namely, the speed overshoot is too large. When the load changes, the speed change is larger than that of traditional DTC, the torque overshoot is also large, and the flux linkage rises slowly. The main reasons are the sensitivity and jitter of sliding mode control, as well as the parameter setting of PI controller. Good PI value parameters will greatly improve system performance, while bad ones will greatly reduce system performance.
Figure 5-3
Figure 5-4
Figure 5-5
Figure 5-6
Figure 5-7
Figure 5-8
6. Conclusion
Traditional PMSMDTC control exhibits significant torque ripple but has a fast response. The improved SMC-SVPWM-PMSMDTC effectively suppresses torque ripple and also improves flux ripple and speed response time. The disadvantage of the new system is its sensitivity, stemming from the sliding mode control characteristics. When the load changes or at the start, the overshoot is too large, and the flux response is slow.
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