Smart Controls for Switched Reluctance Motor 8/6 Used for Electric Vehicles Underground Mining Security

Different techniques have been proposed in the past to minimize torque ripples. Warpatkar and Dalvi [1] presented a new approach for minimizing torque ripple in an SRM 8/6 poles using computational methods for the design calculation. According to this, the combination of calculations including mechanical, electromagnetic, and electrical design as well as laboratory tests and appropriate investments play an essential role in the development of a successful SRM design. Nagesh et al. [2] modeled and analyzed the SRM 8/6 with a simple PI controller and showed after simulation that torque ripples were reduced for different load values.

Pratapgiri and Narsimha [3] have put in evidence that theDTC technique can minimize torque ripple by regulating torque with a specified hysteresis band. A four-phase non-symmetrical converter has a total of 81 space voltage vectors while only 8 space voltage vectors are sufficient to apply the DTC technique to the SRM.

Ghani et al. [4] asserted based on the simulation results that the fuzzy logic controller produces better results. When compared to the results obtained by the ANN controller, the torque ripple has become weaker and the current waveform has become smoother.

In 2015, Shrivastava [5] used the fuzzy logic controller of the SRM 8/6 in combination with the DTC. This proposed technique reduced torque ripples and current distortion, produced a very fast torque response and good control precision.

This article compares the use of two intelligent speed controls associated with direct torque control (DTC) to minimize torque ripples caused by peripheral discontinuities imposed by the shape of the SRM rotor. The DTC associated with the fractional order controller (PI^α) is better than that associated with the controller of the artificial neural network (ANN).

4.1 Switched reluctance motor model

SRMs are similar in their mode of operation, but for reasons of simplification, the characteristics mentioned below in Table 3 of the SRM taken as the object of our study, are identical to those appearing in Ref. [8].

The selection of ferromagnetic material characterizes the magnetic properties capable of significantly increasing the motor's efficiency. Because the surface of the latter determines the magnetic losses, ferromagnetic materials for SRMs are chosen using the criterion of the narrowest hysteresis cycle possible. Figure 1 shows the first magnetization curve B=f(H) of the ferromagnetic material used here (Steel M19). It is important to specify that the simulation will be made for the magnetic unsaturation zone.

Table 3. The main characteristics of the SRM chosen

The basic practical design of SRM was developed with higher efficiency than induction motors of the same size thanks to the work of Lawrenson et al. [9], among other things; he established the design rules for the polar arcs of the stator and the rotor, as well as the flux waveforms in the different positions of the rotor.

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Figure 1. Magnetization curve of M19 steel, B=F (H)

After the interest and acceptance of SRM technology has grown huge. Miller [10] presented the first book dealing only with SRM technology which allowed manufacturers to develop series of SRM products, with half the volume of conventional DC and AC motors.

The main idea of the operation of the SRM is that windings housed in the stator teeth are energized alternately, while the rotor teeth, without windings or magnets, are attracted adequately to the stator windings [7]. The figures below depict the design topology of the prototype of the rotor and stator object of our simulation with a four-phase power supply of the SRM 8/6. Figure 2 depicts the rotor structure with SRM 8/6 poles. Figure 3 is a clear picture of the poles lamination of the stator without winding and the different parts of the previous figures have been assembled in Figure 4 which shows the whole machine with its different parts.

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Figure 2. Structure showing the rotor of the SRM and its poles

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Figure 3. The stator lamination of the SRM 8/6poles without winding

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Figure 4. The entire structure of SRM 8/6poles with its different parts

The principle of operation of an SRM is essentially based on the position of the rotor tooth with the stator tooth. Figure 5 shows schematically how the 4 phases are connected around the stator poles. When a phase is supplied, the rotor turns to the position where the flux created by the stator is maximal [11]. This case is called the conjunction position. The opposition position is the opposite position with the least amount of flux. The torque is created by magnetic variation between the stator pole and the rotor pole, hence its name “Switched reluctance motor” [12, 13]. During a cycle of variation of the magnetic permeability four periods are observed [14]:

$\begin{array}{ll}L_{\min } & 0 \leq \theta<\theta_{1} \\ L_{\min }+p \theta & \theta_{1} \leq \theta<\theta_{2} \\ L(\theta)=L_{\max } & \theta_{2} \leq \theta<\theta_{3} \\ L_{\max }-p\left(\theta-\beta_{r}\right) & \theta_{3} \leq \theta<\theta_{4} \\ L_{\min } & \theta_{4} \leq \theta<\theta_{5}\end{array}$      (1)

L(θ): Inductance variation over one rotor pole pitch,

L_min: Unaligned inductance (H),

L_max: Aligned inductance (H),

β_s: Stator pole arc(rad),

β_r:Rotor pole arc(rad) β_r>β_s.

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Figure 5. Connection of the 4 phases of the stator for SRM 8/6

$p=\frac{L_{\max }-L_{\min }}{\beta_{s}}$     (2)

The idealized form of the inductance of a phase as a function of the rotor position is shown in Figure 6.

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Figure 6. Inductance profile for switched reluctance motor

The electric supply voltage of the stator winding of the motor is given by:

$v=R i+\frac{d \psi(\theta, i)}{d t}$     (3)

dψ(Ɵ,i) is the phase flux linkage as a function of rotor position θ and stator current I. We deduce:

$v=R i+\frac{d \psi(\theta, i)}{d i} \frac{d i}{d t}+\frac{d \psi(\theta, i)}{d \theta} \frac{d \theta}{d t}$      (4)

The mechanical energy [8] is shown as:

$d W_{m}=i \frac{d \psi(\theta, i)}{d \theta} d \theta-\frac{d W_{f}}{d \theta} \frac{d \theta}{d t}$      (5)

The torque equation is defined as:

$T \approx i \frac{d \psi(\theta, i)}{d \theta}$     (6)

4.2 DTC for SRM 8/6 poles used for electric vehicle

The technique known as direct torque control is a protocol to reduce vibrations and acoustic noise due to torque ripples caused by the rotor shape of the SRM. The performance of the DTC control of the SRM 8/6 and its impact on the torque ripple in the steady and the transient state, are used in this article in conjunction with, on the one hand, control by Artificial Neural Network and on the other with fractional-order control. A comparison between the two controls is made under the Matlab/Simulink environment.

Direct Torque Control, does not require speed or position sensors and uses only voltage and current measurements. Magnetic flux and torque are estimated and maintained when selecting the corresponding voltage vector. This makes the DTC very suitable for electric vehicles.

According to Eq. (6), the phase flux depends on the position of the rotor (θ) and the stator current (i). The DTC technique for SRM can be explained as follows [15, 16]: The unbalanced converter is often used for SRM drives (As shown in Figure 7). Each power phase has three possible voltage states.

When both switches are turned ON, current flows through two switches and a coil to apply a positive voltage to the motor phase (as shown in Figure 8a).; "Magnetizing state".

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Figure 7. Asymmetric converter

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Figure 8. SRM voltage states: a- State (1); b- State (0); c- State (-1)

Figure 8.b depicts what happens when the switch is turned OFF, current flows through the diode and coil, and a zero voltage loop occurs "freewheel state 0 ". In Figure 8.c, the two switches are deactivated, the current flows through the diodes and the phase winding, however, a negative voltage is applied "it is the state (-1) said demagnetizing". The unbalanced 4-phase converter (Figure 7) can have up to 81 different Space Voltage Vectors, but for the DTC applied to the SRM, only eight spatial voltage vectors are sufficient as shown clearly in Figure 9.

The proposed technique is a 4-phases spatial vector modulation (SVM) based DTC for SRM 8/6 by choosing an appropriate set of 8 spatial voltage vectors. Pulse Width Modulation (PWM) is not used. The inverter receives the commands directly and successively (see Figure 9). If the k^th sector is considered for the stator flux link vectors, the spatial voltage vectors V_k+1 and V_k+2 are selected for a required increase in torque and if a decrease in torque is requested, the voltage vectors which decelerate the vector of flux V_k-1 and V_K-2 are applied.

Based on the output of the hysteresis blocks where torque and flux are estimated, the appropriate spatial voltage vectors are shown in the following Table 4.

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Figure 9. Space voltage vectors and 8 sectors

Table 4. DTC switching table for SVM

The vectors of the fluxes of the four phases are solved in the α-β axes [17, 18] using the transformation shown in Figure 10. The equation of magnetic fluxes in the α-β axes is obtained as:

$\psi_{\alpha}=\psi_{1} \cos 45^{\circ}-\psi_{2} \cos 45^{\circ}-\psi_{3} \cos 45^{\circ}+\psi_{4} \cos 45^{\circ}$     (7)

$\psi_{\beta}=\psi_{1} \sin 45^{\circ}+\psi_{2} \sin 45^{\circ}-\psi_{3} \sin 45^{\circ}+\psi_{4} \sin 45^{\circ}$      (8)

$\psi_{s}=\sqrt{\left(\psi_{\alpha}^{2}+\psi_{\alpha}^{2}\right)}$     (9)

$\delta=\arctan \left[\frac{\psi_{\alpha}}{\psi_{\beta}}\right]$      (10)

ψ_1, ψ_2, ψ₃and ψ₄: Are flux phases

ψ_α, ψ_β: Respectively the fluxes in α and β axes

$\delta$: Angle of flux vector

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Figure 10. Vectors of fluxes of 4 phases in the α, β axes

Figure 11 shows the diagram of DTC for SRM 8/6 poles. The measured values are the voltages and currents of each of the four phases at the output of the inverter which supplies the SRM. The magnetic flux of each phase is calculated and then transformed according to the α-β axes where the flux in four phases is converted into two phases. The amplitude Ψs and the angle δ of the flux vector are automatically recognized. The amplitude of the flux vector Ψs, and the calculated motor torque T, are then introduced into the flux and torque hysteresis blocks. The reference flux is compared to the real flux as well as the reference torque and the real torque which leads to an increase or decrease in flux Ψ and torque T.

The switching tables and the asymmetric converter apply the voltage vectors suitable for the four-phase windings of the SRM.

The actual speed and the reference speed are compared and the error is transmitted to the PI controller.

4.3 The PI-ANN controller for the SMR8/6

Artificial neural networks are structures built around a collection of cells (neurons) that are linked together using weighted and modifiable links during a process known as learning [19, 20]. The formal neuron (see Figure 12) consists of three basic elements:

- A set of links, each characterized by a weight w_j (or synaptic coefficient), corresponding to the efficiency of the connection and a particular input x₀ always equal to 1, which makes it possible to add flexibility to the network by varying the threshold of triggering of the neuron by the adjustment of its weight, commonly called bias and noted b, when learning w₀ = b.

- An adder or summing unit for summing the weighted signals.

- A threshold activation function to limit the amplitude of the output value.

The objective of a learning algorithm in the ANN is to adapt the weights of the network iteratively until the error between the reference input and that measured or estimated is less than the target value.

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Figure 11. Diagram of DTC for SRM 8/6 poles

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Figure 12. Model of the formal neuron

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Figure 13. Sensorless block diagram for SRM 8/6 using Artificial Neural Network with DTC

The DTC control strategy has been implemented. As shown in Figure 13, ANN was designed with the error between the reference speed and the estimated speed as input values.

The behavior of an existing conventional controller (PI, PID) can be reproduced by a neural network thanks to its learning and approximation capacity. The proposed model makes it possible to calculate the reference torque (T_ref) from the error (e) and its derivative (Δ_e) by following the following steps [21, 22]:

- Set the number of hidden layers: apart from the input and output layers. The analyst must decide on the number of intermediate layers,

- Determine the number of neurons in the hidden layers: with each addition of a neuron, specific profiles of the specific input neurons must be taken into account,

- Determine the activation function.

4.4 The PI fractional controller of the SMR8/6

The applications of fractional calculus are very modern because we have been able to update a process whose study of their models corresponds to the fractional-order derivative and is expressed with the fractional power pole equation (PPE):

$G(s)=\frac{1}{{{s}^{\alpha }}}=\frac{K}{{{(1+\frac{s}{{{W}_{f}}})}^{\alpha }}}$      (11)

Here α is a non-integer real number or even a complex number; S is the Laplace transform of differentiation and W_f is the fractional pole (cutoff frequency). The use of this system in the SRM control was motivated by the superior performance of fractional order systems when compared to PI integer order. PI^α D^β is the form of the fractional regulator and it is an extension of the PID regulator which has the transfer function [23, 24]:

$H(S)={{K}_{p}}+{{K}_{i}}.{{S}^{-\alpha }}+{{K}_{d}}.{{S}^{+\beta }}$      (12)

α and β are both positive real numbers; K_p, K_i and K_d are respectively the proportional, integral, and derivative gain. If α = 1 and β= 1 we obtain the classic PID regulator.

In the numerical implementation of a Fractional Order Control, the most important step is the numerical evaluation of the discretization of the fractional-order derivations S^α. The fractional-order ordering system is characterized by the following transfer function [25, 26]:

$G(S)=\frac{{{b}_{m}}.{{S}^{\beta m}}+{{b}_{m-1}}.{{S}^{\beta m-1}}+.......+{{b}_{m0}}.{{S}^{\beta 0}}}{{{a}_{n}}.{{S}^{\alpha n}}+{{a}_{n-1}}.{{S}^{\alpha n-1}}+........+{{a}_{0}}.{{S}^{\alpha 0}}}$      (13)

Hence the discrete transfer function of the fractional-order system G (z) can be obtained as:

$G(z)=\frac{b_{m} \cdot\left(w\left(z^{-1}\right)\right)^{\beta m}+b_{m-1} \quad\cdot\left(w\left(z^{-1}\right)\right)^{\beta m-1}+\ldots \ldots +b_{0}\left(w\left(z^{-1}\right)\right)^{\beta 0}}{a_{n} \cdot\left(w\left(z^{-1}\right)\right)^{\alpha n} S^{\alpha n}+a_{n-1}\quad \cdot\left(w\left(z^{-1}\right)\right)^{\alpha n-1}+\ldots \ldots +a_{0} \cdot\left(w\left(z^{-1}\right)\right)^{\alpha 0}}$      (14)

w(z^-1), present the discrete equivalent of the Laplace operator S. To implement the fractional-order model in the control object of this work, we will use the singularity function method developed by Charef et al. [27] and Bai et al. [28]. For a fractional system of the first order, the approximation method targets the slope of 20 mdB/dec on the Bode plot of the PPF by the number of lines in the form of a zigzag, produced by an alternation of 20dB/dec and 0 dB/Dec such as:

p₀<z₀<p₁<z₁<. . . <z_N-1<p_N     (15)

This leads to the following expression:

$G(S)=\frac{1}{{{S}^{\alpha }}}\cong \frac{K}{{{(1+\frac{S}{{{W}_{f}}})}^{\alpha }}}\cong K.\frac{\prod\nolimits_{i=0}^{n-1}{(1+\frac{S}{{{z}_{i}}})}}{\prod\nolimits_{i=0}^{n-1}{(1+\frac{S}{{{p}_{i}}})}}$     (16)

(n+1) is the determined total number of singularities by the frequency band of the system. The singularity function can be obtained as:

${{p}_{i}}={{(ab)}^{i}}.{{p}_{0}};$ For i=0,1,2,3,........,N     (17)

${{z}_{i}}={{(ab)}^{i}}.a{{p}_{0}};$   For i=0,1,2,3,........,N-1     (18)

$p_{0}=W_{f}(10)^{\frac{\varepsilon p}{20_{\alpha}}}$     (19)

$a=(10)^{\frac{\varepsilon p}{10(1-\alpha)}}\quad$;  $b=(10)^{\frac{\varepsilon p}{10 \alpha}}$

$N=\left[ Integer\left[ \frac{\log (\frac{{{w}_{\max }}}{{{p}_{0}}})}{\log (ab)} \right]+1 \right]$     (20)

εp is the tolerated error in dB. The simulation of this method in a Matlab environment for different values of α was carried out. The transfer function that we have chosen for the present control system is for α=0.62. Figure 14 shows a sensor-less block diagram vector control for SRM 8/6 poles using fractional controllers with DTC.