Design of a Deflection Switched Reluctance Motor Control System Based on a Flexible Neural Network

Abstract

Deflection switched reluctance motors (DSRM) are prone to chattering at low speeds, which always affects the output efficiency of the DSRM and the mechanical loss of the motor. Combining the characteristics of a traditional reluctance motor with the strong nonlinear and high coupling of the DSRM, a control system for a DSRM based on a flexible neural network (FNN) is proposed in this paper. Based on the better robustness and fault tolerance of fuzzy PI control, the given speed signal is adjusted and converted into a torque control signal. As a result, the FNN control module possesses the strong self-learning ability and adaptive adjustment ability necessary to obtain the control voltage signal. Through simulations and experiments, it was verified that the control system can run stably on DSRM and shows good dynamic performance and anti-interference ability.

1. Introduction

Due to the frequent occurrence of international energy crises, a new energy technology has been developed, the switched reluctance motor (SRM). With its low cost, simple structure, easy maintenance, and superior reliability, it has wide application prospects in modern industries, such as the electric vehicle, household appliance, and textile machinery industries [1,2,3]. The double salient-pole structure and switching control mode cause the highly nonlinear and strongly coupled electromagnetic characteristics of the SRM, resulting in the problem of large torque pulsation when the SRM is running, especially at low speeds. In electric vehicle applications, motor torque pulsation can lead to noise problems in the vehicle and resonance problems at certain frequencies.

It is clear from the previous literature [4,5,6] that the main solutions to improving the performance problems of switched reluctance motors can be divided into two approaches: (1) The structural parameters of the motor body can be changed and optimized, and (2) the control strategy direction can start to optimize the motor control scheme.

In the papers, [7,8,9,10,11] the idea of optimizing the motor structure parameters was proposed based on Taguchi’s method, in which the motor structure parameters were taken as the optimization variables and optimization targets, and then the optimization scheme was determined and simulated using finite element software to confirm the feasibility of the structure optimization scheme. In studies [12,13], the rotor structure of a reluctance motor was changed. The uneven distribution of the air-gap magnetic-field density between the stator and rotor of the motor leads to fluctuations in the output torque, so the rotor structure was optimized to improve the air-gap magnetic-field density, thereby increasing the torque density and reducing the torque fluctuations to increase the efficiency of the motor. In reference [14], the magnetic pole surface of the stator was optimized, and the response surface method was used to optimize the structural parameters of the motor stator. The optimized model showed that the torque ripple decreased significantly through numerical testing. Study [15] proposed the optimization of a switched reluctance motor by particle swarm optimization algorithm. First, the Audze–Eglais Latin hypercube design method was used to build the optimal third-order response surface model, and then the structural parameters on the stator of the motor were set as design variables. It was found that the torque fluctuation of the optimized model was reduced and the efficiency was improved.

Due to the high saturation and nonlinear characteristics of switched reluctance motors, traditional linear control methods, such as PI control, cannot meet the requirements of the high-performance system. Therefore, people began to optimize the control systems of switched reluctance motors. In studies [16,17,18,19], a variety of modern control theories, such as adaptive control, model predictive control, synovial variable structure control, and intelligent control, were applied to the speed control of the switched reluctance motor. Study [20] used an RBF neural network and a BP neural network for SRM model identification and speed control, respectively, proposing a neural network PID control strategy with strong adaptive ability and adjustable parameters. The speed regulation system built with a robust governor in study [21] effectively reduced the overshoot, rise time, and setting time of the system and achieved a faster response speed and a stronger robustness of the SRM. Reference [22] uses a genetic algorithm to determine the optimal PID control parameters of linear switched reluctance motors to optimize their control speed.

This paper proposes a kind of torque control strategy for deflection switched reluctance motors (DSRM). Due to the deflectable double-stator structure of the deflection switched reluctance motor (DSRM), the stability of rotor rotation and deflection are reduced when the rotor is running. Therefore, the direct instantaneous torque control strategy is used for reference in this paper. Fuzzy control and flexible neural network control are added to the control system. After the difference between the input speed fixed value and the feedback value is transmitted to the fuzzy PID speed regulator, the reference value of the torque signal is input to the flexible neural network (FNN) of the PID torque control system. Finally, the power converter distributes the switching signal to complete the control work of the deflection switched reluctance motor (DSRM). Through the simulation and verification of the control through the flexible neural network in the Matlab/Simulink environment, it was found that the speed waveform and torque waveform of the deflection switched reluctance motor were significantly improved. The feasibility of the control system was verified by experiments, which contribute to the further research on the deflection motion control of the deflection switched reluctance motor (DSRM) in the future.

2. The Working Principles of the Deflection Switched Reluctance Motor

2.1. Basic Structure of the Deflection Switched Reluctance Motor

The material of the rotor and stator of DSRM in Figure 1 is laminated silicon steel sheet, The inner structure of the tooth pole of the outer stator is concave spherical, the outer structure of the inner stator-tooth pole is convex spherical, and the number of teeth is 12. The outer structure of the tooth pole of the outer rotor is a convex spherical shape, the outer structure of the inner rotor-tooth pole is a concave spherical shape, and the number of teeth inside and outside the rotor is 8. Figure 2 shows that, through the cooperation between this special salient-pole structure and the rotor, the DSRM can complete the deflection motion at an appropriate angle.

Centralized winding is wound around the salient pole of the stator, while no winding and a permanent magnet exist in the rotor, which avoids the excitation loss and eddy-current loss on the rotor of traditional motors. It can be seen from the magnetic-field-line distribution diagram for the deflection reluctance motor in Figure 3 that the rotor is divided into inner and outer parts through the addition of a magnet vane with good performance, preventing the magnetic circuit of the inner and outer rotors from crossing and reducing the waste of magnetic field energy.

The working principles of the DSRM are the same as those of the traditional SRM. The SRM follows the “minimum reluctance principle” and the magnetic flux of the motor is a closed loop formed along the path of minimum reluctance. When the tooth axes coincide, the magnetic resistance between the two is the smallest, and when the rotor slot axis coincides with the stator tooth axis, the magnetic resistance between the two is the largest. Therefore, when the motor is operating, it is first necessary to add excitation to the single-phase winding to generate magnetic lines of force.

As can be seen in Figure 3, after the magnetic lines of force form a closed loop through the path of minimum reluctance, the tangential magnetic pull generated by the twisted magnetic lines of force is used to pull the rotor to move. The control circuit is used to cooperate with the concentrated winding to run the deflection switched reluctance motor in such a cycle.

2.2. Mathematical Model of the Deflection Switched Reluctance Motor

Without considering the influence of magnetic circuit saturation, the most important factor affecting the operating characteristics of the DSRM is the phase inductance in the reluctance motor. Equation (1) shows the inductance expressions when the stator winding is at different conduction angles:

$$L\left(\theta \right)=\left\{\begin{array}{ll}{L}_{min}& {\theta }_1\le \theta \le {\theta }_2\\ \frac{(L_{max}-L_{min})(\theta -{\theta }_2)}{{\theta }_3-{\theta }_2}+L_{min}& {\theta }_2\le \theta \le {\theta }_3\\ L_{max}& {\theta }_3\le \theta \le {\theta }_4\\ L_{max}-\frac{(L_{max}-L_{min})(\theta -{\theta }_4)}{{\theta }_3-{\theta }_4}& {\theta }_4\le \theta \le {\theta }_5\end{array}\right.$$

(1)

In Equation (1), under the above four-position angle relations, the inductance value on the stator presents different sizes. When the position angle is between ${\theta }_1$ and ${\theta }_2$, the inductance value is the minimum value. When the position angle is between ${\theta }_3$ and ${\theta }_4$, the inductance value is the maximum. Other position angles should be calculated according to the specific formula of Equation (1).

The ideal linear voltage model is established by using the K-phase of the deflection reluctance motor:

$$U_k=R_k{i}_k+\frac{d{\psi }_k}{dt}$$

(2)

Equation (2) expresses the voltage balance equation of the K-th phase winding electrical circuit, The K-th phase flux linkage ${\psi }_k$ can be expressed by the phase current $i_k$ and the rotor position angle $\theta$:

$${\psi }_k\left(\theta ,i_k\right)=L_k(\theta ,i_k)i_k$$

(3)

In Equation (3), $L_k\left(i_k,\theta \right)$is the function of the K-th phase current $i_k$ and the rotor position angle $\theta$. The variation of the phase inductance $L_k$ with the rotor position angle $\theta$ is a prerequisite for the reluctance motor to generate electromagnetic torque. The $L\left(\theta \right)$is the inductance value at different position angles, $L_{max}$ is the maximum inductance value, $L_{min}$ is the minimum inductance value, and $R_k$ is the K-th phase resistance.

In order to establish an ideal linear winding model, Equation (3) is brought into Equation (2) to obtain:

$$\begin{array}{ll}\hfill U_k& =R_k{i}_k+\frac{\partial {\psi }_k}{\partial i_k}\frac{d{i}_k}{dt}+\frac{\partial {\psi }_k}{\partial {\theta }_k}\frac{\partial {\theta }_k}{dt}\hfill \\ \hfill & =R_k{i}_k+(L_k+i_k\frac{\partial L_k}{\partial i_k})\frac{d{i}_k}{dt}+i_k\frac{\partial L_k}{\partial \theta }\frac{d\theta }{dt}\hfill \end{array}$$

(4)

It can be seen from Equation (4) that the applied phase voltage of the K-th phase winding is equal to the voltage drop of the loop resistance, the transformer electromotive force caused by the current change, and the moving electromotive force caused by the position angle change.

The voltage drops across the winding resistance $R_k{i}_k$ is small compared to $d\Psi /dt$, with a negligible resistance drop, and after arranging Equation (2), can be obtained as:

$$U_k=\frac{d{\psi }_k}{dt}=\frac{d{\psi }_k}{d\theta }\frac{d\theta }{dt}=\frac{d{\psi }_k}{d\theta }\omega$$

(5)

After finishing, Equation (6) is obtained, and $\omega$ is the rotor angular velocity.

$$d{\psi }_k=\pm \frac{U_k}{\omega }d\theta$$

(6)

When the rotor positions are at different angles, the flux linkage equation of the K-th phase winding can be expressed as:

$${\psi }_k(\theta )=\left\{\begin{array}{ll}\frac{U_k}{\omega }(\theta -{\theta }_{on})& {\theta }_{on}\le \theta \le {\theta }_{off}\\ \frac{U_k}{\omega }(2{\theta }_{off}-{\theta }_{on}-\theta )& {\theta }_{off}\le \theta \le {\theta }_{on}\end{array}\right.$$

(7)

Combining the laws of mechanics with the reluctance motor structure, the rotor mechanical motion equation of the DSRM can be obtained as:

$$T_e=J\frac{d^2\theta }{dt}+D\frac{d\theta }{dt}+T_L$$

(8)

The calculation of the torque of the DSRM is the key to the analysis of the dynamic operation of the DSRM. The electromagnetic torque of the DSRM is expressed as:

$$T_x={\left.\frac{\partial W{}^{\prime }}{\partial \theta }\right|}_{i=const}={\left.-\frac{\partial W}{\partial \theta }\right|}_{\psi =const}$$

(9)

In Equation (9), $W{}^{\prime }$ is the magnetic co-energy of the winding, $\partial W{}^{\prime }$ is the internal magnetic co-energy increment of the coupled magnetic field in the rotor displacement increment $\Delta \theta$, and $W$ is the winding energy storage. The $W{}^{\prime }$ and $W$ expressions are:

$$W{}^{\prime }={\displaystyle \underset{0}{\overset{i}{\int }}\psi di={\displaystyle \underset{0}{\overset{i}{\int }}l(\theta ,i)idi}}$$

(10)

$$W={\displaystyle \underset{0}{\overset{\psi }{\int }}i(\psi ,\theta )}d\psi$$

(11)

3. Design of the Flexible Neural Network Torque Controller

This section introduces the overall design idea of torque control system based on a flexible neural network. A set of fuzzy PID speed controllers are added before the flexible neural network controller to convert the speed into a torque reference value. Then the calculation of the flexible neural network is carried out to obtain the control signal for the deflection switched reluctance motor.

3.1. Design of the Fuzzy PID Speed Regulator

The fuzzy PID controller makes self-adaptive adjustments to the low precision and poor anti-interference ability of the PID control so that the output PID parameters can reach a certain precision. Fuzzy PID control structure is shown in Figure 4. The speed difference, e, is set as the fuzzy PID speed controller input. First, the speed difference e is integrated to obtain the speed deviation change rate, ec, then e and ec are jointly imported into the two-dimensional fuzzy controller to use the membership function to fuzzify it; the obtained fuzzy quantities EC and E are reasoned according to the adjusted fuzzy control rules, and the fuzzy output value U* is determined, and finally, the fuzzy output value is clarified and the PID output value Tref is obtained.

In order to more intuitively reflect the adjusted fuzzy control rules, the fuzzy inference rules are represented by three-dimensional diagrams in this paper. As shown in Figure 5, the inputs of the 2D fuzzy control module are the speed deviation e and the rate ec of the speed deviation as abscissa, and the correction values of the three parameters U_p, U_i and U_d are the ordinates.

3.2. Flexible Neural Network Control

The FNN PID control structure is shown in Figure 6. With the advantage of a flexible neural network using the fastest descent method, the weights are constantly modified, and the structure features are as follows: the parameters of the excitation function of the hidden layer and the output layer are adjustable, which can accelerate the learning speed of the neural network. It can effectively prevent the neuron excitation function from entering the false saturation state so that the network weight cannot be modified. T_ref comes from the previous fuzzy controller, and Ts comes from the switched reluctance motor model.

As shown in the Figure 6, the constructed flexible neural network learning structure adopts the 4-6-3 network structure, with four input vectors x = [Te, T_ref, e(k), 1]; in this way, the hidden layer–node threshold can be incorporated into the weight vector for online adjustment, and the outputs of the network are the PID parameters, which are K_P, K_I, and K_D, respectively.

The control algorithm in the BP block is:

$$\begin{array}{l}u(k)=u(k-1)+\Delta u(k)\\ \Delta u(k)=k_p\cdot d_1+k_i\cdot d_2+k_d\cdot d_3\end{array}$$

(12)

In algorithm Equation (12), $d_1$ = e(k) − e(k − 1), $d_2$ = e(k), $d_3$ = e(k) − 2e(k − 1) + e(k − 2).

The excitation function of the hidden layer node in the structure of the flexible neural network is selected as the flexible bi-polar S function:

$$f(x,a)=\frac{1-e^{-2xa}}{a(1+e^{-2xa})}$$

(13)

The partial differential expressions of the variables x and a in the function f(x,a) are, respectively, as follows:

$$\left\{\begin{array}{l}\frac{\partial f}{\partial x}=\frac{4e^{-2xa}}{{(1+e^{-2xa})}^2}\\ \frac{\partial f}{\partial a}=\frac{4ax{e}^{-2xa}+e^{-4ax}-1}{a^2{(1+e^{-2xa})}^2}\end{array}\right.$$

(14)

The flexible excitation function of the nodes at the output level of the network is:

$$g(x,b,c)=\left|b\right|\frac{1}{1+e^{-2xc}}$$

(15)

Then take the partial derivatives of variables X and b in the flexible excitation function:

$$\left\{\begin{array}{ll}\frac{\partial g}{\partial x}=\frac{2\left|b\right|c{e}^{-2xc}}{{(1+e^{-2xc})}^2}& \\ \frac{\partial g}{\partial x}=\frac{2\left|b\right|x{e}^{-2xc}}{{(1+e^{-2xc})}^2}& \\ \frac{\partial g}{\partial b}=\frac{1}{1+e^{-2xc}}& b\ge 0\\ \frac{\partial g}{\partial b}=-\frac{1}{1+e^{-2xc}}& b>0\end{array}\right.$$

(16)

FNN learning adopts the error-feedback learning method [23], and its performance index function is set as:

$$E(k)=\frac{1}{2}{[r(k)-y(k)]}^2=\frac{1}{2}e{(k)}^2$$

(17)

where r(k) is the reference torque signal and y(k) is the instantaneous torque signal output by the motor.

The weight and parameters of the excitation function of the FNN are adjusted online, and the adjustment algorithm of the output layer is:

$$\left\{\begin{array}{l}{\omega }_{lj}(k)={\omega }_{lj}(k-1)+\Delta {\omega }_{lj}(k)\\ \Delta {\omega }_{lj}(k)=-\beta \frac{\partial E(k)}{\partial {\omega }_{lj}(k)}+\alpha \Delta {\omega }_{lj}(k-1)\end{array}\right.$$

(18)

$$\left\{\begin{array}{l}{b}_l(k)=b_l(k-1)+\Delta b_l(k)\\ \Delta b_l(k)=-\eta \frac{\partial E(k)}{\partial b_l(k)}+\alpha \Delta b_l(k-1)\end{array}\right.$$

(19)

$$\left\{\begin{array}{l}{c}_l(k)=c_l(k-1)+\Delta c_l(k)\\ \Delta c_l(k)=-\eta \frac{\partial E(k)}{\partial c_l(k)}+\alpha \Delta c_l(k-1)\end{array}\right.$$

(20)

In the above algorithm formulas, ω_lj, b_l, and c_l, are the three functions of the weight of the nodes, the hidden layer containing function ω_lj, and the output layer containing functions b_l, c_l, the b parameter of the l node excitation function in the output layer, and the c parameter of the l-node excitation function in the output layer, respectively.

In order to accelerate the convergence of the above algorithms and save calculation time, in this paper, the gradient method for the driving quantity term is adopted; this method also helps overcome the problem of local minima. α is momentum factor, β and η represent the learning efficiency of weight and parameter adjustment, respectively, as follows:

$$\begin{array}{ll}\frac{\partial E(k)}{\partial {\omega }_{lj}(k)}=& \frac{\partial E(k)}{\partial y(k)}\frac{\partial y(k)}{\partial \Delta u(k)}\frac{\partial \Delta u(k)}{\partial o_l{}^{(3)}(k)}\cdot \\ & \frac{\partial o_l{}^{(3)}(k)}{\partial ne{t}_l{}^{(3)}(k)}\frac{\partial ne{t}_l{}^{(3)}(k)}{\partial {\omega }_{lj}(k)}\end{array}$$

(21)

$$\frac{\partial E(k)}{\partial b_l(k)}=\frac{\partial E(k)}{\partial y(k)}\frac{\partial y(k)}{\partial \Delta u(k)}\frac{\partial \Delta u(k)}{\partial o_l{}^{(3)}(k)}\frac{\partial o_l{}^{(3)}(k)}{\partial b_l(k)}$$

(22)

$$\frac{\partial E(k)}{\partial c_l(k)}=\frac{\partial E(k)}{\partial y(k)}\frac{\partial y(k)}{\partial \Delta u(k)}\frac{\partial \Delta u(k)}{\partial o_l{}^{(3)}(k)}\frac{\partial o_l{}^{(3)}(k)}{\partial c_l(k)}$$

(23)

where $ne{t}_l{}^{\left(3\right)}\left(k\right)$ and $o_l{}^{\left(3\right)}\left(k\right)$ are the total output and output of the l node in the network output layer, respectively.

Because $\partial y\left(k\right)/\partial \Delta u\left(k\right)$ is an unknown quantity, we use the sign function $sgn(\partial y\left(k\right)/\partial \Delta u\left(k\right)$ to take its place, and adjusting the learning rate can correct the calculation error in time. The adjustment algorithm in the hidden layer is:

$$\left\{\begin{array}{l}{v}_{ij}(k)=v_{ij}(k-1)+\Delta v_{ij}(k)\\ \Delta v_{ij}(k)=-\beta \frac{\partial E(k)}{\partial v_{ij}(k)}+\alpha \Delta v_{ij}(k-1)\end{array}\right.$$

(24)

$$\left\{\begin{array}{l}{a}_{ij}(k)=a_{ij}(k-1)+\Delta a_j(k)\\ \Delta a_j(k)=-\eta \frac{\partial E(k)}{\partial a_j(k)}+\alpha \Delta a_j(k-1)\end{array}\right.$$

(25)

where $v_{ij}$,$a_j$ are the weights between the i node in the network input layer and the j node in the hidden layer and parameter a of the excitation function of the j node in the hidden layer, respectively. Finally, the partial error function of the parameter can be derived:

$$\frac{\partial E(k)}{\partial v_{ij}(k)}=\frac{\partial E(k)}{\partial y(k)}\frac{\partial y(k)}{\partial \Delta u(k)}\delta \cdot \frac{\partial o_j{}^{(2)}(k)}{\partial ne{t}_j{}^{(2)}(k)}\frac{\partial ne{t}_j{}^{(2)}(k)}{\partial v_{ij}(k)}$$

(26)

$$\frac{\partial E(k)}{\partial a_j(k)}=\frac{\partial E(k)}{\partial y(k)}\frac{\partial y(k)}{\partial \Delta u(k)}\delta \frac{\partial o_j{}^{(2)}(k)}{\partial a_j(k)}$$

(27)

$$\delta ={\displaystyle \sum _{l=1}^3\left[\frac{\partial \Delta u(k)}{\partial o_l{}^{(3)}(k)}\frac{\partial o_l{}^{(3)}(k)}{\partial ne{t}_l{}^{(3)}(k)}\frac{\partial ne{t}_l{}^{(3)}(k)}{\partial o_i{}^{(2)}(k)}\right]}$$

(28)

where $ne{t}_j{}^{\left(2\right)}\left(k\right)$, $o_j{}^{\left(2\right)}\left(k\right)$ are the sums of the inputs and outputs, respectively, of the j-th node in the hidden layer of the network.

4. Simulation Analysis and Experimental Verification

4.1. Simulation Analysis

In this section, the outer motor simulation model of the DSRM was first built in the Matlab/Simulink environment. It can be seen from Figure 7, the DSRM simulation system diagram, in the dotted box, that the outer motor model of the DSRM motor is connected to the control system, and the bridge inverter circuit in the power converter is used to regulate the switching control of the three-phase centralized winding. The signal of the power converter comes from the torque signal output by the torque distribution module.

In this paper, the parameters of the DSRM used in the simulations and experiments are shown in

Table 1. Main parameters of DSRM.

Parameter	Value
Outer stator radius Ds1/mm	300
Inner stator radius Ds2/mm	13.5
Outer radius of rotor Dr1/mm	108
Inner radius of rotor Dr2/mm	43.3
Length of core la/mm	90
Rated current density Acd/(A/mm2)	6
Rated rotating torque n/(r/min)	200
Rated power PN/kw	2.5
Rated voltage UN/V	380

.

By setting variable speed motion to the model, the stability of the model was analyzed. The motor speed was set as 150–200–150 r/min to simulate the motor under the light load of 1 N.

Through observation, it can be found that the current in Figure 8a cannot be adjusted to a stable current state in time during commutation adjustment, especially when the current value fluctuates greatly between 2–4 A, which shortens the life of electronic devices by a long time. In Figure 8b, it can be found that the current adjustment ability is significantly improved and the current stability is strengthened.

It can be seen from Figure 9a that the output torque under ordinary PI control had a large torque fluctuation from moment 0.013 s to moment 0.1 s, and the amplitude is about 0.28 N·m. However, compared with Figure 9b, it is obvious that the torque fluctuation decreased a lot in this period, and the amplitude was about 0.038 N·m. When the speed of 0.1 s directly rose to 200 r/min, a slight instantaneous overload phenomenon appeared in the torque. Under ordinary PI control, the maximum instantaneous overload torque reached 10.3 N·m, while under flexible neural network control, the maximum instantaneous torque reached 10.05 N·m. When the speed decreased to 150 r/min at 0.2 s, the torque fluctuation of the flexible neural network was obviously smaller than that of the ordinary PI control.

As can be seen from Figure 10, during variable speed motion, the speed stability of flexible neural network control was significantly higher than that of ordinary PI control, and this phenomenon became more obvious when the speed was increased.

We further verified that the control performance of the flexible neural network (FNN) control system based on the deflection switched reluctance motor (DSRM) is better than that of the ordinary PI control system. In this paper, the outer motor control model of the deflection switched reluctance motor (DSRM) was built in the Matlab/Simulink environment, and the speed was set as 130 r/min. DSRM operated at no-load rotation at 0 s until three groups of loads with different values of 2 N, 5 N, and 7 N were added at 0.03 s. Then, the flexible neural network control (FNN) and ordinary PI control were substituted into the set conditions to run the simulation. Finally, we observed the three groups of simulation results for comparison. The torque waveform and torque fluctuation of the DSRM model were analyzed under the general PI control system and the flexible neural network control system (FNN).

According to Figure 11a, it can be observed that the starting part under ordinary PI control exceeded the rated torque by 10 N·m. The torque began to decline at 0.007 s until 0 N. When the load was added at 0.03 s, the torque fluctuation began to occur. When the fluctuation reached the maximum, the instantaneous torque amplitude could reach 6.5 N·m, which is half of the rated torque of the DSRM. After a period of time, the torque output value was stable at about 2 N·m at 0.0375 s; by comparing the output torque of the flexible neural network (FNN) control, Figure 11b shows that the starting torque did not exceed the rated torque by 10 N·m and the torque fluctuation was small. Compared with the waveform of the ordinary PI control, there was almost no torque fluctuation between 0.007 and 0.03 s. After increasing the load, the torque could rise directly and start adjustment, and the final torque fluctuation dropped below 5.6 N·m. When the adjustment time dropped to 0.003 s, i.e., 0.035 s, the torque fluctuation tended to be gentle, and the subsequent torque fluctuation amplitude decreased significantly in comparison with that shown in Figure 11a.

Figure 11b shows that the starting torque did not exceed the rated torque by 10 N·m and the torque fluctuation was small. Compared with the waveform of the ordinary PI control, there is almost no torque fluctuation between 0.007 and 0.03 s. After increasing the load, the torque could rise directly and start adjustment, and the final torque fluctuation drooped below 5.6 N·m. When the adjustment time dropped to 0.003 s, i.e., 0.035 s, the torque fluctuation tended to be gentle, and the subsequent torque fluctuation amplitude decreased significantly in comparison with that shown in Figure 11a. Therefore, flexible neural network control can effectively improve DSRM torque control under load.

From Figure 12 and Figure 13, the torque fluctuation trend of load 5 and 7 N was the same as the simulation result of load 2 N. In the second group of the comparison simulation, it can be seen that the load regulation time added by the flexible neural network control at 0.03 s decreased from 0.034 to 0.0324 s, and the amplitude range of torque fluctuation decreased from 4.72–5.3 N·m to 4.96–5.07 N·m. In the third group of the comparison simulation, the load adjustment time added by the flexible neural network control at 0.03 s decreased from 6.695–7.315 N·m to 6.936–7.096 N·m. In summary, the motor torque fluctuation phenomenon after the use of the flexible neural network control is obviously improved.

4.2. Experimental Verification

The STM32C8T6 development board and MATLAB automatic code generation tool were combined to carry out experimental verification. STM32CubeMX software was used to generate the underlying configuration code, and the optimized algorithm was imported to complete the experiment, which improved the work efficiency. The experimental verification platform is shown in Figure 14. The experimental platform was built with a drive board, control board, the deflection switched reluctance motor, and other hardware facilities. As the controlled object, DSRM used the code generation tool to generate the control algorithm C code, and then transmitted it to the STM32C8T6 development board for algorithm verification, completing the experimental verification of the DSRM.

The experimental platform of the deflection switched reluctance motor was built, and the traditional PI control and the control which is proposed in this paper were respectively built for comparative experimental verification. Figure 15 shows the contrast in the control system running speed at the different given speeds of 40, 60, and 80 r/min. Figure 15a shows the running speed of the two control systems at a given speed of 40 r/min. Contrasting with the traditional PI control, the control system designed in this paper has smaller overshoot and shorter adjustment time. Speed jitter after smooth operation is also greatly reduced. Figure 15b,c shows the comparison of the operating speeds of the two control systems at given speeds of 60 r/min and 80 r/min. At the given speeds of 60 and 80 r/min, the two control systems run similarly. The control system designed in this paper has a smaller overshoot and a smaller jitter.

Through simulation and experimental verification, the control system designed in this paper is shown to have better dynamic performance and stronger anti-interference ability compared with the traditional PI control.

5. Conclusions and Prospects

For improving the chattering phenomenon of the DSRM at low speeds, in this paper, the DSRM was used as the control object to design a set of fuzzy PI control and FNN control systems. The fuzzy PI control module has strong robustness and fault tolerance ability to effectively adjust the control parameters online, combined with fast response speed and the optimization computing ability of the flexible neural network. Through simulation and experiment, the advantages of the control system designed in this paper were verified and can improve the stability of the DSRM during operation, reduce the oscillation time and amplitude in the rotation process, and significantly enhance the adaptive ability and anti-interference ability. This paper provides a new idea for the control algorithm of deflection switched reluctance motors. Compared with traditional PI control, the control parameters of the flexible neural network can be adjusted in a better and more timely manner, thereby greatly optimizing the stability of the DSRM during operation. It also lays the foundation for the control of the DSRM in the deflection state in the future. On this basis, we will conduct a detailed study on the motor control under different deflection angles so as to better control the deflecting double-stator switched reluctance motor.