Variable Flux Direct Torque Control System of Switched Reluctance Motor

Direct Torque Control (DTC) strategy is very suitable for controlling Switched Reluctance Motors (SRM) due to its advantages of the simple control structure and fast system response, etc. This paper first analyzes the principle of DTC and establishes the DTC model of three-phase 6/4 SRM by Matlab/Simulink. In this paper, a three-closed-loop variable flux DTC system with velocity as the given quantity is constructed to solve the problem that the stator current of constant flux DTC is too large when the motor is in a steady state. The simulation results show that the variable flux DTC system has a better inhibition effect on the stator current and torque ripple of SRM than the conventional DTC system.


Introduction
The Switched Reluctance Motor (SRM) and its speed control system have been applied in general industry, electric vehicles, coal mining, and other fields in recent years because of their advantages of low cost, simple structure, high reliability, large starting torque, frequent start and stop, etc. [1].However, due to its inherent double salient pole structure, the motor torque ripple is relatively large, which limits the application of SRM [2].
Traditional Control strategies mainly include Current Chopper Control (CCC), Voltage Chopper Control (VCC), and Angular Position control (APC) [3].Xu et al. [4] realized three control modes of CCC, VCC, and APC, but there is a risk that IGBT will be broken down due to a large pulse current generated in the starting stage of the motor.Although the soft start is improved, the torque ripple suppression effect is not ideal.Wei et al. [5] took the new type of permanent magnet switched reluctance motor of 8/6 pole as a prototype and drew the conclusion that APC is suitable for highspeed occasions and CCC is suitable for low-speed occasions.Besides, fuzzy control is used to improve the shortcomings of traditional SRM torque ripple, but compared with traditional PID control, it is difficult to realize no-static error control.
The obvious advantage of direct torque control is that it does not require complex mathematical models.Based on the three-phase asymmetric bridge as the main circuit of the six-phase switched reluctance motor, Liang and Zhang [6] proposed a DTC system suitable for the motor.In [7], the torque and flux characteristics obtained from the study of four-phase 8/6 SRM were used to establish a nonlinear model, and then the proposed DTC scheme was calculated on the digital control platform for power loss to evaluate the drive efficiency.The results show that the efficiency and torque ripple suppression performance of the DTC method is improved compared with the conventional DTC under various working conditions.In order to realize a direct instantaneous torque control (DITC) optimization scheme based on the adaptive dynamic commutation strategy proposed in [8], the commutation moment is dynamically adjusted according to different operating conditions.Finally, the simulation and experiment of a three-phase 12/8 SRM show that the strategy can effectively reduce the torque ripple and improve the system efficiency.
In conclusion, applying the DTC strategy to the SRM speed control system can effectively reduce motor torque ripple.However, the stator current of constant flux DTC is too large when the motor is in a steady state.This paper optimizes the structure of DTC.

Mathematical model of SRM
According to Kirchhoff's law, the voltage balance equation of the KTH phase is Equation (1).The U k is k-phase winding voltage, R k is k-phase winding resistance, i k is k-phase winding current, and k  is kphase winding flux [9].
The instantaneous electromagnetic torque of the k-phase is shown in Equation ( 2), and θ is the rotor position angle.
( , ) Since each phase of the stator windings of the switched reluctance motor is driven by unipolarity, the current i k of each phase is positive.It can be seen from Equation (1) that the direction of instantaneous torque T k depends on the sign of ( , ) , namely, the following two cases can be obtained.
(1) When ( , ) (2) When ( , ) When k  is consistent with the rotation direction of the rotor, the direction of T k increases; when k  is opposite to the rotation direction of the rotor, the direction of T k decreases.
After discretization of Equation (1), Equation ( 3) is obtained by shifting terms from left to right.( ) The Ts is the sampling period.The vector relationship of this formula is shown in Figure 1.

Graph of the relationship between stator flux and voltage vector
As can be seen from Figure 1, when the absolute value of the angle  between the stator flux vector and the applied voltage vector is less than/equal to/greater than 90°, the flux amplitude increases/basically remains unchanged/decreases.Therefore, the torque control of SRM can be realized by a reasonable selection of voltage space vector.

Basic principles of DTC
DTC uses a space voltage vector to calculate flux and torque in a stator coordinate system [10].It directly controls the torque of the motor by tracking the switching state of the PWM inverter.The schematic diagram of direct torque control is shown in Figure 2. In the DTC system, the weak current signal generated by the voltage space vector can be output by alternating on and off each switch tube in the power converter.Each phase of the power converter is composed of two power switching devices (usually IGBT) and two diodes.The working state of each phase can be divided into "1", "0" and "-1".For SRM, each phase winding has three operating states of "1", "0" and "-1".In this paper, the three-phase switched reluctance motor is used as an example.There are 3 3 =27 working states.But according to the actual operation of the motor, some states are invalid.The superposition of voltage vectors of the three-phase winding produces 6 basic voltage Space Vector Pulse Width Modulation (SVPWM), as shown in Figure 3.The difference between each phase vector, 6 voltage space vector is respectively: V1(1,0,-1), V2(0,1,-1), V3(-1,1,0), V4(-1,0,1), V5(0,-1,1), and V6(1,-1,0).The angular bisector of these 6 voltage vectors is then taken as the dividing line, and the stator coordinate system is divided into 6 equal parts, namely, the interval from N1 to N6 in the corresponding figure.

SRM direct torque control system model building
Taking a three-phase switched reluctance motor as the controlled object, a double closed-loop control system model with flux and speed as the given quantity was built in Matlab-Simulink, as shown in Figure 4.In this model, the speed regulator ASR adopts the conventional PID controller.In Matlab-Simulink, the torque of the motor can be directly output, eliminating the torque estimation.The switch Tab module is the switch table.The CONVERTER module is the power conversion module.The 3/2 module and the module are the 3/2 conversion and angle calculation of stator flux, respectively, corresponding to the flux estimation module in the block diagram, ZONE module is the interval judgment module.

Theoretical analysis of variable flux DTC
After the motor tends to a steady state, the amplitude of the phase current is approximately proportional to the given flux.The main control object of the DTC strategy is flux, while the main control object of other conventional speed regulation methods is torque.Thus, we can control the flux of DTC and the required torque value increase and decrease trend.Therefore, this paper transforms the fixed flux DTC system into a variable flux DTC system so that the given flux changes with the given torque, forming a three-loop control system with speed as the given quantity.
In order to determine what link should be added between a given flux and torque, the relationship between a given flux and torque is obtained by the following method.It is assumed that the sampling period is 3 N•m/ time, and the sampling length is 6 N•m~78 N•m.The measured flux should be selected as the relative optimum, and the selection criteria are as follows: When SRM reaches the rated speed, the steady-state torque ripple is controlled at the minimum flux value between 1 N•m and 5 N•m.The data obtained from the experiment is plotted as a dot plot, as shown in Figure 5.
The measured torque-flux data can be obtained from the fitting curve in the figure, and the proportional linear function relationship can be expressed as Equation (4).* 0.001795 * 0.3141 Te  =+ (4) where *  denotes the given value of flux, and Te* denotes the given value of torque.

DTC simulation model construction with variable flux
After the relationship between torque-flux given values is known, the conventional DTC system is improved.Compared with the fixed flux direct torque control system shown in Figure 2, the improved system adds a linear fit between the given torque and the given flux, making the control system become a three-loop control system with only the speed as the given quantity.
For the variable flux DTC system of switched reluctance motor, a model was built in Matlab-Simulink, and only a linear fit was added.The other links were consistent with the fixed flux DTC simulation model shown in Figure 4.The simulation model of the linear fitter is shown in Figure 6.According to the current comparison waveform shown in Figure 7, the variable flux DTC system is compared with the fixed flux DTC system before optimization.The stator current in the motor startup stage has no optimization effect, which can ensure that the motor's instantaneous starting torque is still large.However, after the motor reaches the steady state, the stator current after optimization decreases significantly compared with that before optimization, and the stator current after optimization is only about 61% of that before optimization, which greatly reduces the damage probability of power devices and system loss.As can be seen from the torque comparison waveform shown in Figure 8, when the motor tends to steady state with variable flux DTC, the torque ripple roughly decreases from 0.1 N•m~6 N•m to 1 N•m~5.5 N•m.

Conclusion
In this paper, on the basis of fixed flux DTC, the variable flux DTC is constructed, and the simulation model of variable flux DTC is built.The simulation results show that the SRM variable flux DTC system has a good effect on reducing steady-state stator current and inhibiting torque ripple compared with the conventional fixed flux DTC system.

Figure 2 .
Figure 2. Schematic of direct torque control

Figure 4 .
Figure 4. Simulation model of DTC system for SRM

Figure 6 .Figure 7 .Figure 8 .
Figure 6.Simulation model of linear fitting device4.Simulation results and analysisThe optimized model was simulated by Matlab-Simulink, and the simulation environment and motor parameters were consistent with those mentioned above.The current waveform comparison between fixed flux DTC and variable flux DTC of SRM is shown in Figure7, and the torque waveform comparison is shown in Figure8.