Feedforward Neural Network-DTC of Multi-phase Permanent Magnet Synchronous Motor Using Five-Phase Neural Space Vector Pulse Width Modulation Strategy

In multi-phase motors (MPMs), the five-phase permanent magnet synchronous motor (FP-PMSM). It is the most used and famous. This type of motor provides greater torque than conventional electric motors. Among the characteristics of these electric motors, we mention: lowering of the stator current per phase, reduced electromagnetic torque ripples, improved fault tolerance, greater efficiency, and minimized stator flux ripples compared to three-phase PMSMs (TP-PMSMs) [1, 2]. Despite these positives, the FP-PMSMs are quite large, and controlling it is very difficult compared to TP-PMSMs.

To control electrical machines there are several different types of controls. The most famous of them is direct torque control (DTC). This strategy was first introduced to control induction motors in the early 1980s. Among the characteristics of this type is that it is very simple and inexpressive materials and improves the performances of the electric motor. Compared with the field-oriented control (FOC), the DTC control is best in all respects. However, this method has several disadvantages, as is all other controls. Among its drawbacks are the following: frequent electromagnetic torque and stator flux ripples, the values of total harmonic distortion (THD) are great, fall in electromagnetic torque in the event of low frequencies and it is affected by the change of the parameters of the electric motor [3, 4]. Several articles addressed the negatives of the DTC method, using the latest technologies. Among these new technologies, we mention the following: fuzzy logic (FL), sliding mode controller (SMC), multi-level inverter (MLI), space vector pulse width modulation (SVPWM), artificial neural networks (ANNs), super-twisting sliding mode algorithm (STSM), adaptive-network-based fuzzy inference system algorithm (ANFIS), Second-order sliding mode control (SOSMC) and genetic algorithm (GA).

A new DTC control based on the ANN controller was proposed to control the induction motor (IM) [3]. The seven-level hysteresis comparator (HC) of the DTC control was proposed based on the ANN [5]. A new DTC method was proposed to regulate the stator flux and electromagnetic torque of IM drives, where the switching table (ST) is replaced by the ANN algorithm and the proportional-integral (PI) controller of speed was replaced by the FL controller [6]. This proposed method is robust and reduced the THD value of stator current compared to classical DTC. DTC control of PMSM was proposed for low-speed operation [7]. The 3-phase IM drive is controlled by sensorless DTC control using the ANN selector table [8]. Four-level DTC-ANN control based on the ANFIS controller of speed is designed to control the IM drives [9]. A novel DTC strategy using STSM was proposed to control a DFIG [10]. SMC algorithm and FL controller are combined to minimize the torque and stator flux ripple of the IM controlled by DTC control [11]. The neural DTC-STSM method is proposed to regulate the active and reactive powers of the DFIG based wind turbines [12]. Five-level DTC control based on fuzzy logic is proposed to control the IM drives, where the torque HC was replaced by the fuzzy controller. This proposed strategy is a simple structure and minimizes the torque ripple compared to the traditional DTC control [13]. DTC with neural ST minimized the torque ripples of IM compared to DTC with fuzzy PI of speed and DTC method with neural HCs [14]. Speed control of FP-PMSM through fractional integral terminal sliding mode control (FITSMC), SMC, and PI controller is presented [15]. The authors [16] propose a DTC-ANN method with ANFIS controller of speed for IM fed by 3-level NPC inverter, where a comprehensive analysis is provided. A hybrid control was proposed based on ANN and ANFIS of the DTC to control IM [17]. The authors [18] propose a Dual DTC for DFIM using ANN. A novel STs of 12 sectors DTC was proposed for IM drive [19]. Four-level DTC based on the ANN algorithm was proposed to control 3-phase PMSM using neural PI of speed [20].

On the other hand, some papers deal with DTC of MPMs, among them: a novel DTC method is proposed to control five-phase induction motor (FPIM) using open-phase fault [21]. Classical DTC strategy is proposed to regulate the stator flux and electromagnetic torque of the FPIM drives [22]. DTC strategy with common-mode voltage is proposed to minimize the current harmonics of FPIM [23]. A modified DTC strategy was proposed to control FPIM drives [24]. DTC method and FL controller are combined to regulate the torque of FPIM [25]. The FPIM drive is controlled by the DTC-SVM method using the MRAS estimator [26]. ANNs algorithm and DTC-SVM method are combined to regulate the flux/torque of FPIM, where the PI controllers of the DTC-SVM are replaced by ANN algorithms and this proposed DTC control improved 17% the performances of FPIM compared to DTC with PI controllers [27]. DTC method with a sinusoidal stator current waveform was proposed to regulate the current of FP-PMSM [28]. DTC technique with load capacity enhancement was proposed to control FP-PMSM drives [29]. DTC technique with optimized vector tables of FP-PMSM is introduced [30]. Modified ST of DTC strategy controlled six-phase PMSM drives [31]. DTC-SVM strategy was proposed to control the FP-PMSM by using the biogeography based optimization (BBO) algorithm [32].

In this work, the DTC-SVPWM system with the application of the feedforward neural networks (FNNs) algorithms has been considered. The original contribution of this work is the application of the FNN algorithms in the DTC-SVPWM system with FP-PMSM and simulation investigation of this new structure.

This work is divided into seven sections. The 5-phase neural SVPWM strategy has been discussed in Section 2. In Section 3, the classical DTC method of the FP-PMSM is described. In Section 4, the DTC-SVPWM technique is presented. Section 5 deals with the description of the DTC-SVPWM technique with the application of FNN algorithms. Simulation studies are presented and discussed in Section 6. The work is concluded with a summary.

Traditionally, DTC control is robust and simple control scheme used to control any machines. This strategy of control is based on the ST to control the inverter. The latter feeds the electric motor. In our article, we will pay attention to FP-PMSM. In DTC control, we use the 3-level HCs to control the torque and 2-level HCs to control the stator flux. The sector level is 10. On the other hand, mathematical equations of an FP-PMSM are expressed in the park reference (d-q-x-y) [2]:

The stator voltage:

$\left\{ \begin{align}  & v_{ds}^{{}}={{R}_{s}}i_{ds}^{{}}+\frac{d}{dt}\Phi _{ds}^{{}}-{{w}_{r}}\Phi _{qs}^{{}} \\ & v_{qs}^{{}}={{R}_{s}}i_{qs}^{{}}+\frac{d}{dt}\Phi _{qs}^{{}}+{{w}_{r}}{{\Phi }_{ds}} \\ & v_{xs}^{{}}={{R}_{s}}i_{xs}^{{}}+\frac{d}{dt}\Phi _{xs}^{{}} \\ & v_{ys}^{{}}={{R}_{s}}i_{ys}^{{}}+\frac{d}{dt}\Phi _{ys}^{{}} \\ & v_{0s}^{{}}={{R}_{s}}i_{0s}^{{}}+\frac{d}{dt}\Phi _{s0}^{{}} \\\end{align} \right.$      (1)

The magnetic equations:

$\left\{ \begin{align}  & \Phi _{ds}^{{}}={{L}_{d}}i_{ds}^{{}}+{{\varphi }_{f}} \\ & \Phi _{qs}^{{}}={{L}_{q}}i_{qs}^{{}} \\ & \Phi _{xs}^{{}}={{L}_{ls}}i_{xs}^{{}} \\ & \Phi _{ys}^{{}}={{L}_{ls}}i_{ys}^{{}} \\ & \Phi _{s0}^{{}}={{L}_{ls}}i_{0s}^{{}} \\\end{align} \right.$      (2)

For the FP-PMSM, the expression of the electromagnetic torque is:

$T_{e m}=\frac{5}{2} P\left(\left(L_{d}-L_{q}\right) i_{d s} i_{q s}+\phi_{f} i_{q s}\right)$    (3)

The dynamic equation is:

$J \frac{d w_{r}}{d t}=p T_{e m}-p T_{r}-f w_{r}$     (4)

The main objective of the DTC strategy is to directly control Φ_s and T_em. The flux and torque are controlled quantities. The errors between the reference values (Φ_s* and T_em*) and the actual values (Φ_s and T_em) are introduced into two HC which determine the switching state of the switch. In classical DTC method, the switching table of multi-phase machine is proposed by Listwan and Krzysztof [26]. This table contains the error flux εΦ_s, the error torque εT_em, and the sector number (S₁,..S₁₀). The optimal vector stator voltage of the FP-PMSM is presented in Table 2 [35].

Table 2. Switching table of the classical DTC of FP-PMSM

The stator flux components can be written by the stator currents and the voltage in the reference frame (α, β):

$\left\{\begin{array}{l}\Phi_{\alpha}=\int\left(v_{\alpha}-R_{s} i_{\alpha}\right) d t \\ \Phi_{\beta}=\int\left(v_{\beta}-R_{s} i_{\beta}\right) d t\end{array}\right.$     (5)

The amplitude of the stator flux is determined by:

$\Phi_{s}=\sqrt{\Phi_{\alpha}{ }^{2}+\Phi_{\beta}{ }^{2}}$     (6)

The torque formula of the FP-PMSM is expressed in terms of flux and stator current as:

$T_{e}=\frac{5}{2} P\left(\Phi_{\alpha} i_{\beta}-\Phi_{\beta} i_{\alpha}\right)$     (7)

Position of the stator flux:

$\theta_{s}=\tan ^{-1} \frac{\Phi_{\beta}}{\Phi_{\alpha}}$     (8)

DTC using PI regulators is a traditional technique used to control FP-PMSM. However, PI regulators for application to an FP-PMSM have some drawbacks, where this technique gives more flux and torque ripples and thus reduces the robustness of the system. The VC technique based on the hybrid control of an FP-PMSM has been proposed [36], where the PI controller of the speed of an FP-PMSM has been replaced by an FLC and SMC controller. The DTC based on an SVM using the FL algorithm is proposed to minimize the flux and torque ripple of the FP-PMSM [37]. The authors [35] used a DTC-SVM technique for the FP-PMSM drive, where the PI controllers of the speed are replaced by SMC algorithms and this proposed DTC control improved the performances of systems compared to DTC with PI controllers.

In this part, the DTC based on the FNNs of the FP-PMSM drive was proposed, where the SVPWM was replaced by the NSVPWM technique and the PI regulators of the flux, speed and torque were replaced by the FNNs algorithm. This proposed new DTC structure is a simple command and easy to implement. The block diagram of the NDTC-NSVPWM applied to FP-PMSM is shown in Figure 6.

The structure of the FNNs controller is shown in Figure 7. On the other hand, the gradient descent W/MALRB characteristic and the training performance of the rotor speed are shown in Figure 9 and Figure 10. The FNNs consists of an IL comprises 02 neurons (See Figure 8); one HL has 06 neurons (See Figure 11), and an OL 01 neuron (See Figure 12).

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Figure 6. Block diagram of the NDTC-NSVPWM applied to FP-PMSM

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Figure 7. Block diagram of FNNs

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Figure 8. Layer 1

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Figure 9. The gradient descent W/MALRB characteristic

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Figure 10. Training performance

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Figure 11. Block diagram of HL

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Figure 12. Layer 2

In this work, a novel structure of DTC based on FNNs of the FP-PMSM drive fed by an NSVPWM inverter is presented. The proposed control design to improve the performance and robustness of the DTC method. The simulation results confirmed the good static and dynamic performance, the reduction of stator flux ripples, torque ripples, and robustness of the proposed control structure compared to the DTC-SVPWM and conventional DTC. Indeed, we proposed a new modulation 5-phase NSVPWM strategy; it was clear in the stator current THD that the use of the NSVPWM minimizes the THD more and more than the traditional SVPWM and PWM technique. Therefore, the NDTC-NSVPWM structure is simple and easy to implement.