An enhanced control method for torque ripple minimization of switched reluctance motor using hybrid technique

Abstract

In this manuscript, a hybrid technique is proposed for Torque Ripple (TR) minimization of Switched Reluctance Motor (SRM). The proposed technique is the consolidation of Wingsuit flying search (WFS) optimization and Gradient Boosting Decision Tree (GBDT) algorithm, hence it is known as WFS-GBDT technique. The control mechanisms consists of fractional order proportional integral derivative (FOPID) speed controller on external loop as well as current controller on internal loop with controlling turn activate and deactivate angles for SRM. The complexity of acquiring the ideal evaluation of proportional, integral and derivative gains for speed and current controller including turn activate and deactivate angles are deemed as a multi-objective optimization issue. Here, the WFS optimize the gain parameters of external speed loop along internal current loop with commutation angles for turn activate and deactivate switches. The WFS optimization processing is used to productive machine learning dataset under the types of SRM parameter. By using the satisfied dataset, the GBDT is predicted and mandatory forecasting is implemented in the entire machine operating stage. The optimized gain parameters based, the fractional order proportional integral derivative controller is tuned exactly. The proposed WFS-GBDT control technique lessens the torque ripple and quick settling time with this proper control, because of its systematic random search capabilities, thereby enhancing the dynamic execution of SRM drive. Finally, the proposed technique is activated in MATLAB/Simulink site, its performance is analyzed with existing techniques, like Base, ALO and WFS. The best, worst, mean, standard deviation for ISEspeed using proposed technique attains 230.5364, 231.5934, 230.952 and 0.05314. The best, worst, mean and standard deviation for torque ripple using proposed technique attains 0.4571, 0.6548, 0.585 and 0.472. The best, worst, mean, standard deviation for ISEcurrent using proposed technique attains 3.1257, 3.9754, 3.5783 and 0.0472.

Keywords

Switched reluctance motor torque ripple minimization speed current gain parameters and dynamic efficiency

1 Introduction

Nowadays, the SRM is gaining more interest in global industries because of its characteristics, like Stator poles are attached in centralized windings and rotor pole have no winding or permanent magnets (PM) [1, 2]. Due to environmental pollution including energy crisis of the fossil fuels, the electric vehicle without exhausting emission is more concentrated. Higher dependability, ease and rough construction, huge power/volume ratio and suitable process for a broad range of speed are the special characteristics of the SRM, which are used to adjustable-speed drives in various industrial applications [3, 4]. SRM has no winding and permanent magnet in rotor, hence it can work in difficult conditions and attractive for EV applications compared to other motor drives, like PM motors with brushless direct current motor drives [5 –8].

The advantages of SRM are ease of structure, optimal bearings for difficult environments, and significant efficiency over the range of wide speed, higher dependability and error tolerance. Previously, many methods were used to improve the efficiency of the machine by the variation of torque ripple reduction [9, 10]. However, it provides required offline calculations, but inadequate flexibility during process. Some of the offline calculations are required machine electromagnetic characteristics and lesser than neglect the magnetic field saturation, which requires the balancing calculation of current waveforms [11, 12]. In dead zone, the phase current maintains zero-stage and also needs precise nonlinear SRM model [13, 14]. In adaptive iterative learning control process, diminish the TR and loss of electromagnetic energy conversion [15], precise magnetization features of SRM are requested for determining co-energy [16].

Nevertheless, certain drawbacks are limit its utilization viz, huge TR, noise, vibration, etc. [17, 18], it is not possible to use a switched reluctance motor at maximum speed applications. A common issue of SRM is relatively maximal TR resulting in its dual salient configuration with magnetic saturation [19], which illustrates SRM is not as well-liked on industrial utilizations with definite amount [20, 21]. Current profiling torque sharing function (TSF) with direct instantaneous torque control (DITC) methods [22, 23]are introduced for the reduction of torque ripple of SRM, which produce some remarkable outcome [24, 25]. The proficiency is also critical for the SRM except the TR. But these difficulties are producing insignificant conflicts. When torque is smooth then the efficiency is low distorted loss distribution is producing on the drive [26, 27]. In the examination of the above TR and proficiency of SRM require control strategies [28, 29], like higher efficiency lower ripple (HELR) control schemes [30, 31]. In two recent decades, the TR with high noise of switched reluctance motor is researched for reduce these problems [32].

Objectives and Contribution

In the proposed work, a hybrid technique is proposed for Torque Ripple (TR) minimization of SRM. The proposed method is the joint execution of both the WFS optimization and GBDT algorithm, hence it is known as WFS-GBDT technique. The proposed technique is implemented in MATLAB/Simulink, its performance is compared with existing techniques.

The major intention of the proposed work is to acquire the overall optimal solution and the optimal solution is collected from the search space of these operators.

The proposed work contains the two significant operations to solve the optimization problem. The first stage of the torque ripple minimization in SRM is implemented using the proposed approach of WFS. Here, the WFS optimize the gain parameters of external speed loop as well as internal current loop with commutation angles for switches turn activate and deactivate.

The second stage of the torque ripple minimization in SRM is handled by GBDT. By using the satisfied dataset, GBDT can be generated and also gives the mandatory forecasting implementation by the entire machine operating stage. The FOPID controller is tuned exactly with the help of optimized gain parameters.

The rest of this manuscript is: section 2 portrays the recent investigation works with its background, section 3 illustrates about the proposed control design of switched reluctance motor drive and reduction of TR, section 4 illustrates the SRM drive converter design, section 5 explains the Gain Parameters of proposed technique, section 6 proves the simulation outcomes and discussion, section 7 concludes the manuscript.

2 Recent research work: A brief review

Numerous research works were previously existed in the literature depending on the minimization of TR in switched reluctance motor utilizing different methods with features. Some of the recent works are reviewed here,

Reddy et al., [33] have suggested an inexpensive sense winding system that estimates the motor instantaneous inductance. To diminishing the TR in switched reluctance motor, the current references were calculated from the computed values of the immediate inductance. Furthermore, a new concept of sense winding can determine the rotor angle with speed, which removes the position of external sensor requirements. The sense voltages signal processing was executed in the system on chip (SoC), field-programmable gate array, and current using speed control loops. Based on inductance change rate, the torque ripple could be diminished via regulating current.

Hao et al., [34] have presented an enhanced control technique depends on the direct force control (DFC) and direct torque control (DTC) process for decreasing the levitation force and torque ripple at single-winding bearing less switched reluctance motors (SWBSRMs), which can attain maximal torque-ampere ratio with minimal torque ripple at same time. The flux-linkage loop control was not required as vector table of space voltage enhanced. The high torque ripple restrictions the switched reluctance machine, with ripple suppression technique request could decrease that system efficiency.

Song et al., [35] have introduced a new online optimization and commutation strategy using genetic algorithm (GA) for enhancing the proficiency of switched reluctance machine and torque ripple. Besides, a purpose function was created with the torque ripple and efficiency coefficient. During the machine operation, the defined boundary angles were optimized via the GA for maximizing the objective function value.

Shuguang et al., [36] have suggested the switched reluctance motors (SRMs) torque ripple mechanism. At 3-phase SRM, the TR includes the 3^rdorder harmonic components and mostly comes from the rotor slotting, the current harmonic with their interface. In terms of analytical calculation technique, the major current harmonics influence in the torque ripple was researched, which indicates the second-order current harmonic filtering have more helpful for diminishing the torque ripple.

Selvi and Mani Malar [37] have implemented a bridgeless base Luo converter fed SRM drive depends upon the Particle Swarm Optimization tuned PI controller. The proportional integral tuned converter offers great thickness of power, great proficiency, and minute motor driver structure. The advanced converter proficient outcome voltages were associated to Switched Reluctance Motor (SRM) motor. For the drive, the SRM was selected due to its effortless development and smallest effort. SRM was medium and low power applications, it much efficient than the other types of motors with high efficiency, higher flux thickness per unit volume, lower obstruction of the electromagnetic, needs less maintenance.

Saha and Sidhartha Panda [38] have developed a Cosine adapted modified whale optimization algorithm (Cam WOA), where cosine function was integrated to the control parameter “d” selection maintains that whales location while the optimization process. Besides, during the search process, the correction factors were employed the search agent movements for modifying. These modifications offer an appropriate balance between exploitation and exploration phases in Cam WOA method. The Cam WOA efficiency was a multi objective engineering difficulty pertaining to the SRM control.

Bober and Ferkova [39] have established the comparison of simplistic firing angle modulation (FAM) model with improved torque sharing function (TSF) base SRM control. Here, the offline process for retaining and improving the parameters of selected technique off-shelf SRM was described. The major functions for optimization approaches were torque ripple, motor efficiency, ISE. Moreover, the off-line optimization utilizes SRM’s finite element method.

Mukhopadhyay et al., [40] have introduced an ANFIS base Speed with Current control along TR lessening utilizing Hybrid SSD-SFO for SRM. The aim was to get optimum current with speed performance of SRM along less TR. ANFIS structure was employed to concurrent regulator of the speed and current, which involves 2 controlling loops. The inside loop controlling current and the outside loop controlling speed. The dynamic conduct of SRM was deemed to constraint the current with speed that lessens the TR. Hybrid SSD-SFO was utilized to attain the parameter values of current with speed control of SRM. Kotb et al., [41] have introduced the use of 2 recent optimization techniques: Local Unimodal Sampling (LUS), Spotted Hyena Optimizer (SHO), to ideally tune cascaded PID controller design while controlling the speed, also lessens the TR of SRM. Rana and Ravi Teja [42] have introduced a strategy to lessen the TR in 8/6 four-phase SRM. A nonlinear modulating factor depending on rotor position with phase currents magnitude was introduced. Where, controlled the currents in 2 adjacent phases while commutation and lessens the TR. Unlike the conventionally available torque-sharing functions, the introduced strategy instantly modulates every phase current acquired mathematically depending on other phase current to maintain the stable of net torque. The introduced strategy needs less offline analysis and gives maximal feasible torque with minimal ripple.

2.1 Motivation of research work

The review of the recent research work shows that the torque ripple minimization in SRM is an important contribution factor. The SRM utilizes electronic position sensor to compute the rotor shaft angle and solid state electronics to switch the stator windings, which enables dynamic control of pulse timing and shaping. The electromagnetic characteristics of the SRM are required to predict the copper losses, which simultaneously improves the torque per ampere ratio and prevents torque overshoot. For TR minimization in SRM, the soft computing procedures are used such as field-programmable gate array (FPGA),direct torque control (DTC), genetic algorithm (GA), Particle Swarm Optimization (PSO) tuned Proportional Integral (PI) controller, Cosine adapted modified whale optimization algorithm (CamWOA), torque sharing function (TSF) and so on. The objective function of the GA corresponding to a design vector plays the role of fitness in natural genetics, and it’s difficult to branching and looping. The PSO can be search carried out by the speed of the particle, transmit the information is fast, it does not work in non-coordinative system the energy field and the moving rules of the system. DTC method is used to remove the flux-linkage loop control and upgrades the space voltage vector table to create vectors allocation more reasonable, and then the winding current conducts in negative-torque region that lessens the overall output torque. The effective value of current increases, at the same time the torque-ampere ratio will decrease. TSF is used to minimize the torque ripple and TSF can uses online turn-on and off angle calculation and simple hysteresis current controller with lesser demand on computing power Along these lines, to accomplish the optimal results of SRM, the torque ripple minimization in SRM is enhance through a productive method. In literature, a few works were suggested to tackle these issues, but the suggested works are ineffectual. These mentioned problems have motivated to do this research work.

3 Proposed control design of switched reluctance motor drive with the reduction of torque ripple

When SRM is connected to the load, the voltage and phase current are assumed as the contribution of the controller. The qualities of flux linkage have been evaluated from the signals of voltage as well as current including rotor angle are calculated from the characteristic mapping curve. The calculated rotor angle is processed with contributions of proportional integral derivative controller, then transfers the speed controller reference signal [43]. The SRM has less number of switches, it is a linear converter, the protection of strategic length through windings from the current, and for the stability a current sensor is utilized. The phase current is efficiently produced by the converter with low switches. In R-dump converter, the SRM converter has high efficiency, in C-dump converter; the SRM has the commutation speed of high phase current [44]. The coupled inductor and the execution speed are described to design the SRM converter. During the commutation if the phase current not reaches zero then it is in the range of negative torque. The switching series of the proposed converter is regulated by the rotor signal position and it is get from the position sensor which is located motor shaft. For exploiting that position of rotor dependent reluctance the electromagnetic torque in SRM is developed in every phase.

A PID controller is used to determine the module of the current signal from the current controller and the proper phase driver circuit pulse is rectified based on turn off time and assumed current signal. During the period of low impedance winding, the current control loop will give the confirmation to keep the current from working away.

3.1 Mathematical modelling of SRM

The SRM does not have permanent magnets or stator windings, which are a salient polar synchronous motor and the salient poles of rotor with stator in the SRM are located around the stator shaft with coils then linked in reverse pairs to motor phases mode. The switch series of the proposed converter is regulated by the rotor signal position and it is get from the position sensor, which is placed on the motor shaft [45]. For exploiting the position of rotor dependent reluctance the electromagnetic torque in SRM is developed in every phase. While a phase is energized, the reluctance torque is generated that tends to tune the stator with rotor poles. To every phase, mathematical modeling of SRM is created by the electric set environments [46]. SRM drive the equation of phase voltage is given as follows, $V_{ph} - r_{ph} i - \frac{d λ (θ, i)}{dt} = 0$ (1)

here the phase voltage is denoted as V_ph, electrical resistance is denoted as r_ph and the flux linkage is expressed as λ. At the SRM electromagnetic circuit the current including inductance in the function of flux linkage is, $λ (θ, i) = l (θ, i) . i$ (2)

From the above equation, the phase current with rotor position of the inductance is represented as l. By substituting equation (1) and (2) we get eqn. (3) [47]. $V_{ph} - r_{ph} i - l (θ, i) \frac{di}{dt} - \frac{dl (θ, i)}{d θ} i ω_{M} = 0$ (3)

here the angular velocity is denoted as ω, the voltage loop resistance is denoted as r_ph, the inductive drop of voltage is expressed as $l (θ, i) \frac{di}{dt}$ and the back-emf (electromotive force) is expressed as $\frac{dl (θ, i)}{d θ}$ . In winding, the back-emf is exhibited as follows, $e_{b} = \frac{dl (θ, i)}{d θ} i ω_{M} = i ω_{M} k_{b}$ (4)

From the above equation the back-emf is denoted as e_b, and when the emf is constant then it will be expressed as k_b and it is denoted as follows, $k_{b} = \frac{dl (θ, i)}{d θ}$ (5)

In nonlinear electro-mechanic scheme, the electric torque developed through the SRM as co-energy function and it is expressed as, $t_{e} = \frac{\partial w_{c} (θ, i)}{\partial θ}$ (6)

here the electrical torque is expressed as t_e, and the co-energy is, $w_{c} = \int_{0}^{1} λ (θ, i) di$ (7)

The following equations shows the torque in a phase, $t_{e} (θ, i) = \frac{1}{2} i^{2} \frac{dl (θ, i)}{d θ}$ (8)

Based on the equation of total torque, while simplifying the linearity of electricity obtains as follows, $t_{tot} (θ, i) = \sum_{ph} \frac{1}{2} i^{2} \frac{dl (θ, i)}{d θ}$ (9)

While, modifying the above equation, the mechanical equation can create a new equation which is shown as follows, $j_{M} \frac{d ω_{M}}{dt} = t_{TOT} - t_{Load} - b_{M} ω_{M}$ (10)

In the load system of the SRM, j_M represents spinning part of the inertia, b_M represents viscous friction, total angular speed is expressed as ω_M, motor produced from the total torque is expressed as t_TOT and the load torque is represented as t_Load. From the above equations the derivative device of the self-inductance is denoted as torque and the winding is denoted as the current square [46]. The formulated torque is individual at the sign of the current and when the derivative as positive then the torque is developed as positive. The nonlinear function of the current has phase winding inductance including rotor position. Overview of Switched Reluctance Motor with proposed technique is shown in Fig. 1.

Fig. 1

Overview of Switched Reluctance Motor with proposed technique.

4 Design of SRM drive converter

SRM has less number of switches and it is a linear converter and for the protection of strategic length through windings from the current and for the stability a current sensor is utilized. The phase current is efficiently produced by the converter with low switches. In R-dump converter the SRM converter has high efficiency, in C-dump converter the SRM has the commutation speed of high phase current. The coupled inductor and the execution speed are described to design the SRM converter [46]. During the commutation if the phase current not reaches zero then it is in the range of negative torque. The motor has generated high expensive ripple in the torque that is stimulated by the negative torque and it is done in the maximum speed and the rapid commutation occurs by the maximum speed. Based on the converter, the SRM can operate due to the quantity of speed. The most tremendous SRM drive rate depends on the type of converter used and denoted with associated condition, $t_{f} = τ_{e} ln [1 + \frac{r_{ph} i_{phd}}{v_{R}}]$ (11)

From the above equation, $τ_{e} = \frac{l_{a}}{r_{ph}}$ (12)

Here, from the current zero value, the required time is expressed as t_f, the constant time of electrical is τ_e, at commutation the phase current at aligned inductance is denoted as l_a, the preferred phase current is denoted as i_phd, and during the commutation the reverse voltage is applied to the phase inductance is denoted as v_R.

Based on turn activate and deactivate angles the SRM process is determined that is depending upon the speed range of torque, torque ripple and efficiency of switching angle is selected. Based on the FOPID controller the switching angles can restricts the torque ripples. When the process is negative then the current transfer through any value is different. For maintaining strategic ranges from the negative torque then want to enhance the generation of positive torque. During the early stage when the supply is not turned off correctly then it provides a loss in+ve torque. The optimum angle is chosen using the given equation. $θ_{opt} = \frac{l_{un} i_{phd} ω_{r}}{v_{dc}}$ (13)

The unaligned inductance is expressed as l_un, the required phase current denotes i_phd, the speed of angular denotes ω_r, and bus voltage of DC indicated as v_dc.

4.1 Speed design and current control loop

Here, SRM speed control along torque reduction using proposed technique is proposed. The maximum values of FOPID controller can generate the functional parameters like, PID. For improving the execution of SRM, the functional parameters of current and speed controller are utilized ahead the switching angles of the converter. The differential and fractional order of gain parameters are added in the FOPID controller is indicated as k_p, k_i, k_d. The ideal execution of SRM is defined as turns activates and deactivate angles with phase current magnitude. Based on the torque ripple coefficients, the common form of torque ripple is measured as, $T_{R} = \frac{T_{RMax} - T_{RMin}}{T_{RMean}}$ (14)

From the above equation, in total torque, the minimum, maximum and mean value is represented as T_RMax, T_RMin and T_RMean. The following equations show the current and speed of integral squared error. ${ISE}_{sp} = \int_{0}^{\infty} {(ω_{ref} - ω_{a})}^{2} dt$ (15) ${ISE}_{crnt} = \int_{0}^{\infty} {(I_{ref} - I_{ph})}^{2} dt$ (16)

Here, the actual and reference speed is expressed as (ω_ref - ω_a), likewise the actual and reference current is expressed as (I_ref - I_ph). Based on the FOPID controller the optimal tuning rules are obtained to control the ISE including torque ripple. In frequency domain the transfer function of the FOPID controller is depicted as, $G_{C} (s) = k_{p} + k_{i} S^{- λ} + k_{d} S^{μ}$ (17)

In the time domain, the effect of the controllers are given, $U (t) = k_{p} E (t) + k_{i} S^{- λ} E (t) + k_{d} S^{μ} E (t)$ (18)

From the above equation, the PID controllers gain parameters is denoted as k_p, k_i, k_d. The differentiator and integrator of the fractional order parameter is denoted as λ and μ. In the time domain, the control parameters is defined as the given equation, $U (t) = k_{p}^{b} E (t) + k_{i}^{b} S^{- λ} E (t) + k_{d}^{b} S^{μ} E (t)$ (19)

From the above equation, the PID gain parameters in the fractional order PID controller is denoted as $k_{p}^{b}$ , $k_{i}^{b}$ and $k_{d}^{b}$ . General model of SRM is shown in Fig. 2. Figure 3 depicts the block diagram of SRM.

Fig. 2

General model of SRM.

Fig. 3

Block diagram of SRM.

5 Gain parameters optimization

In this section, the proposed technique is described. WFS is inspired by the famous extreme game –Wingsuit flying and it mimics the flier intention to land within their range in the least point on the surface of earth, i.e., a global minimal of search space. GBDT is a popular machine learning algorithm [48], and has quite a little effectual execution, like XGBoost etc. [49]. The control mechanisms contains fractional order proportional integral derivative speed controller on external loop, whereas current controller on interior loop using control of turn activate and deactivate angles of SRM. Multi-objective optimization is deemed as the issue of obtaining optimal estimates of PID gains for speed and current controller with turn activate and deactivate angles, also aim of limiting the ISE for speed with TR. Here, WFS helps to switch the switches turn activate and deactivate by combining the gain parameters of outer speed loops and inner current loop along with the transfer angles. WFS optimization implementation can be used to the productive machine learning dataset era subject to SRM parameter types. Dataset is generated by the WFS, that dataset is processed by GBDT. The fractional order PID controller is adjusted exactly through the optimal gain parameters. Along this proper control, the WFS-GBDT technique reduces the torque ripple with rapid settling time owing to its proper random search capacities, thus enhancing the dynamic performance of switched reluctance motor drive.

5.1 Steps for enhancing gain parameter

Step 1: Initialization

Here, initialize the random generation and initial population of control parameters are $k_{p}^{b}$ , $k_{i}^{b}$ , $k_{d}^{b}$ in N number of population.

Step 2: Random generation

The gain parameter of WFS method is randomly generated based on the parameters of above process.

Step 3: Fitness Function

Fitness function is analyzed by initial population in each particle using the given equation, ${fit}_{obj} = min {{ISE}_{sp}, {ISE}_{crnt}, T_{R}}$ (20)

From the above equation, the speed and current of the integral square error is represented as ISE_sp, ISE_crnt respectively, and the coefficient of torque ripple is defined as T_R.

Step 4: Termination

After finishing the above process, the WFS give the best parameters and it is used in the PID controller. The FOPID controller is tuned in terms of the above process and FOPID controller output is given to GBDT input. By GBDT method the best control parameters of the input was predicted. In the following equation shows the output of FOPID controller. $[\begin{matrix} ω_{1} (s), i_{1} (s) \\ ω_{2} (s), i_{2} (s) \\ . \\ . \\ ω_{n} (s), i_{n} (s) \end{matrix}] = [\begin{matrix} k_{p}^{1} (s), k_{i}^{1} (s), k_{d}^{1} (s) \\ k_{p}^{2} (s), k_{i}^{2} (s), k_{d}^{2} (s) \\ . . \\ . . . \\ k_{p}^{n} (s), k_{i}^{n} (s), k_{p}^{n} (s) . \end{matrix}]$ (21)

5.2 GBDT for the prediction process of gain parameter

Here, the GBDT technique for the process of reference voltage is explained. Like other boosting methods GBDT generate the model at step-wise fashion, also it normalizes them by enabling an arbitrary difference to improve the loss operation [50]. This is commonly utilized to fixed size decision trees (especially CART trees) as basic learners. From the utilization of boosting approaches for regression trees the algorithm for Boosting Trees is developed. The common idea is to calculate the order of the simplest trees, for the predictive remainder of the previous tree where each successive tree is configured. The stepwise procedure of fault classification process is depicted as below,

Step 1: In this step, h(x) is denoted as the basic learner. Here, number of predicted variables is defined as $x_{n} = (x_{1 i}, x_{2 i}, \dots x_{pi})$ , the predicted label is y_i, β is denoted as the initial stable value of sample, which is shown as follows, $f_{0} (x) = Arg min_{β} \sum_{i = 1}^{N} l (y_{i}, β)$ (22)

Step 2: The objective function is calculated by evaluating the reference voltage value.

Step 3: To count of iterations m = 1, the gradient direction of residuals M is evaluated as follows, $Y_{i}^{*} = - {[\frac{\partial l (y_{i}, f (x_{i}))}{\partial F (x_{i})}]}_{f (x) - F_{m - 1 (x)}}, i = {1, 2, . . ., N}$ (23)

Step 4: To get the initial model fit the sample data then the essential classifiers are utilized. The parameter a_m is acquired then sample h (x_i ; a_m) is fitted depending on the least square method. $a_{m} = arg min_{α, β} \sum_{i = 1}^{N} {[y_{i}^{*} - β h (x_{i}; a)]}^{2}$ (24)

Step 5: Current model weight is accessed and loss function is reduced with the help of given equation. $β_{m} = arg min_{α, β} \sum_{i = 1}^{N} L (y_{i}, F_{m - 1} (x) + β h (x_{i}; a))$ (25)

Step 6: The sample is upgraded using given equation. $f_{m} (x) = f_{m - 1} (x) + β_{m} h (x_{i}; a)$ (26)

The GBDT is optimally trained as well as the optimum outputs are acquired in terms of the fitness function. The following section shows the simulation result and discussion under 3 case studies. Flowchart of proposed technique is shown in Fig. 4.

Fig. 4

Flowchart of proposed technique.

6 Result and discussion

In this section, the proposed technique depending on FOPID controller to enhance the system based stability in switched reluctance motor along TR. The reference torque and the SRM speed control are contributed. The execution of WFS optimization is used to productive machine learning dataset era subject to SRM parameter types. Using the required dataset, GBDT is predicted; also the mandatory forecasting implementation can be implemented through the entire machine operating condition. The proposed technique is used to improve the SRM to limit the torque ripple. The proposed technique is carried out in MATLAB/Simulink, its performance is evaluated under three case studies. The efficiency of proposed technique is likened with existing process like Base, ALO [51, 52] and WFS under three different case studies such as: rapid change in torque, swell change in torque and sag change in torque, which are explained as follows.

Case 1: Rapid Change in Torque

Figure 5 signifies the WFS-GBDT analysis of current. The current flows 0A to 27A at 0 sec time period then it remainders constant till the end of operation. Figure 6 indicates that proposed flux analysis. On observing this Figure, flux flows 0 Vs to 0.5Vs at 0 sec time, then it remainders constant till the operation end. Figure 7 implies the proposed speed analysis. Here, the speed flows 0 rpm to 1500 rpm then it raised upto 1900 rpm at 0 to 0.15 sec. Figure 8 represents the proposed torque analysis. Here, the torque flows 4Nm to 8Nm then it raised upto 10Nm at 0 to 1 sec time. Figure 9 displays the proposed analysis of reference torque and theta. In subplot 9(a), the analysis of torque is depicted. Here, the torque flows from 3Nm to 4Nm and it somewhat reduced up to 3Nm and it increased up to 6Nm at 0.15se time interval. Subplot 9(b) specifies the analysis of theta. On observing this, the theta slightly increased up to 0 to 39rad at 0 to 0.2 sec time interval.

Fig. 5

Proposed (a) Current (b) current Zoom analysis.

Fig. 6

Proposed (a) flux (b) flux Zoom analysis.

Fig. 7

Proposed Speed (b) Speed Zoom analysis.

Fig. 8

Proposed (a) Torque (b) Torque Zoom analysis.

Fig. 9

Proposed (a) Reference torque (b) theta analysis.

Figure 10 represents the existing performance of base under various approaches. The base in the current flows from 0 to 29A, the base in the torque flows from 0 to 10Nm, the base in the speed flows from 0 to 1700 rpm and the base in the flux flows from 0 to 0.5Vs. Figure 11 specifies the existing analysis of ALO under various approaches. The ALO in the current flows from 0 to 29A, the ALO in the torque flows from 0 to 10Nm, the ALO in the speed flows 0 to 1700 rpm, ALO in the flux flows 0 to 0.5Vs. Figure 12 signifies the existing analysis of WFS under various approaches. Here, the WFS in the current flows from 0 to 29A, the WFS in the torque flows from 0 to 10Nm, the WFS in the speed flows 0 to 1700 rpm, WFS in the flux flows 0 to 0.5Vs. Figure 13 depicts the torque comparison of WFS-GBDT and existing techniques. Here, the WFS-GBDT technique flows 0Nm to 9Nm at 0 to 0.2 sec time, the existing base flows 2Nm to 8Nm at 1 to 0.2 sec time interval, the ALO flows 2Nm to 8Nm at 1 to 0.2 sec time interval, WFS flows 2Nm to 8Nm at 1 to 0.2 sec time period. From the comparison result, the torque of the WFS-GBDT technique is higher than the existing methods.

Fig. 10

Analysis of (a) base (b) base zoom under various approaches.

Fig. 11

Analysis of (a) ALO (b) ALO Zoom under various approaches.

Fig. 12

Performance of (a) WFS (b) WFS Zoom under various approaches.

Fig. 13

Torque comparison of proposed and existing techniques (b) Zoom.

Case 2: Swell change in torque

Figure 14 portrays the proposed analysis of current and flux. Subplot 14(a) implicates the current flows 0A to 27A at 0 sec time period then it leftovers constant till the end of operation. Subplot 14(b) portrays the proposed flux analysis. The flux flows 0 Vs to 0.5Vs at 0 sec time interval then it leftovers constant till the end of operation. Figure 15 shows that proposed performance of speed, torque, and theta. In subplot 15(a), the speed flows from 0 rpm to 1500 rpm, then it maximized 1900 rpm at 0 to 0.15 sec. Subplot 15(b) displays the proposed torque analysis. The torque flows 4 Mn to 8Nm then it maximized 10Nm at 0 to 1 sec time. Subplot 15(c) portrays theta analysis. The theta slightly increased up to 0 to 39rad at 0 to 0.2 sec time.

Fig. 14

Proposed (a) Current (b) Flux analysis.

Fig. 15

Proposed (a) speed (b) torque (c) theta analysis.

Figure 16 portrays the proposed analysis of reference torque. Here, the torque flows 4Nm to 8Nm and it slightly reduced up to 4Nm, then it remainders stable at 0.15 to 0.2 sec time. Figure 17 represents that existing performance of base under various approaches. The base in the current flows from 0 to 29A, the base in the torque flows from 0 to 10Nm, the base in the speed flows from 0 to 1700 rpm and the base in the flux flows from 0 to 0.5Vs.

Fig. 16

Proposed Reference Torque analysis.

Fig. 17

Analysis of base under various approaches.

Figure 18 depicts the existing performance of ALO under various approaches. The ALO in the current flows from 0 to 29A, the ALO in the torque flows from 0 to 10Nm, the ALO in the speed flows 0 to 1700 rpm, ALO in the flux flows 0 to 0.5Vs. Figure 19 portrays the existing performance of WFS under various approaches. Here, the current flows from 0 to 29A, the torque flows from 0 to 10Nm, the speed flows 0 to 1700 rpm, the flux flows 0 to 0.5Vs. Figure 20 portrays the torque comparison of WFS-GBDT and existing methods. The WFS-GBDT flows 0NM to 9Nm at 0 to 0.2 sec time, the existing base flows 2Nm to 8Nm at 1 to 0.2 sec time, ALO flows 2Nm to 8Nm at 1 to 0.2 sec time, WFS flows 2Nm to 8Nm at 1 to 0.2 sec time period. From the comparison results, the WFS-GBDT technique is higher than the existing techniques.

Fig. 18

Analysis of ALO under various approaches.

Fig. 19

Analysis of WFS under various approaches.

Fig. 20

Torque comparison of proposed and existing process.

Case 3: Sag change in torque

Figure 21 represents the proposed current and flux analysis. Subplot 21(a) displays the current flows 0A to 27A at 0 sec time period and remainders stable till the operation end. Subplot 21(b) denotes the proposed analysis of flux. The flux flows 0 Vs to 0.5Vs at 0 sec time period then it remainders stable till the operation end. Figure 22 depicts the proposed speed, torque, and theta analysis. In subplot 22(a), the speed flows 0 rpm to 1500 rpm then it maximized 1900 rpm at 0 to 0.15 sec. Subplot 22(b) depicts the proposed torque analysis. On observing this, the torque flows 4 Mn to 8Nm then it maximized 10Nm at 0 to 1 sec time interval. Subplot 22(c) signifies the analysis of theta. On observing this, the theta slightly increased up to 0 to 39rad at 0 to 0.2 sec time. Figure 23 represents the proposed analysis of reference torque. Here, the torque flows from 4Nm to 8Nm and it slightly reduced upto 4Nm, then it remainders stable at 0.15 to 0.2 sec. Figure 24 signifies the existing base under various approaches. The base in the current flows from 0 to 29A, the base in the torque flows from 0 to 10Nm, the base in the speed flows from 0 to 1700 rpm and the base in the flux flows from 0 to 0.5Vs. Figure 25 portrays the existing performance of ALO under various approaches. The ALO in the current flows from 0 to 29A, the ALO in the torque flows from 0 to 10Nm, the ALO in the speed flows 0 to 1700 rpm, ALO in the flux flows 0 to 0.5Vs. Figure 26 represents the existing analysis of WFS under various approaches. Here, the current flows from 0 to 29A, the torque flows from 0 to 10Nm, the speed flows 0 to 1700 rpm, then the flux flows from 0 to 0.5Vs.

Fig. 21

Proposed (a) Current (b) Flux analysis.

Fig. 22

Proposed (a) speed (b) torque (c) theta analysis.

Fig. 23

Proposed analysis of Reference Torque.

Fig. 24

Analysis of base under various approaches.

Fig. 25

Analysis of ALO under various approaches.

Fig. 26

Analysis of WFS under various approaches.

Figure 27 shows that torque comparison of WFS-GBDT with existing methods. Here, the WFS-GBDT flows 0NM to 9Nm at 0 to 0.2 sec. The existing base flows 2Nm to 8Nm at 1 to 0.2 sec time interval. The existing ALO flows 2Nm to 8Nm at1 to 0.2 sec time interval. The existing WFS flows 2Nm to 8Nm at 1 to 0.2 sec time period. Here, the torque of the WFS-GBDT technique is high likened with the existing techniques. Figure 28 shows the analysis of boundary angle with count of generation. Here, hi flows from 4deg to 5deg at 1 to 14 sec time period, h2 flows stable at 20deg at 1 to 14 sec time period. Figure 29 depicts the analysis of efficiency with number of generation. Here, the maximum efficiency flows from 84% to 85% at 1 to 9 sec time interval. The average efficiency flows 83% to 84% at 1 to 7 sec time interval. Figure 30 describes that analysis of objective with number of generation. Here, the maximum objective flows from 0.12 and it lessened to 0.1, then it raised upto 0.13 at 1 to 4 sec time. The average efficiency flows from 0.14 and it reduced up to 0.11. Figure 31 represents the analysis of torque ripple coefficient with number of generation. Here, the maximum torque ripple coefficient flows from 6.2% and it reduced up to 6% and then it maximized 7% at 1 to 9 sec time interval. The average torque ripple coefficient flows from 6.8 and it decreased upto 6.2%. Figure 32 implicates the analysis of torque ripple with proposed and existing methods. The WFS-GBDT technique flows 0.2Nm to 0.27Nm. The existing base flows from 0.4Nm and it decreased upto 0.34Nm. The existing ALO flows 0.35Nm and it decreased upto 0.26Nm. The existing WFS flows 0.25Nm and it reduced upto 0.22Nm. Figure 33 signifies the current waveforms obtained by simulation by changing the time scale for Case 1, 2 and 3. The time scale is set up at the range from 0.1 to 0.12 sec for case 1, 0.05 to 0.1 sec for case 2 and 0.05 to 0.2 sec for case 3.

Fig. 27

Torque comparison of proposed and existing systems.

Fig. 28

Performance of Boundary angle with number of generation.

Fig. 29

Analysis of Efficiency with number of generation.

Fig. 30

Analysis of objective with number of generation.

Fig. 31

Analysis of torque ripple coefficient with number of generation.

Fig. 32

Analysis of torque ripple with proposed and existing techniques.

Fig. 33

Current waveforms obtained by simulation by changing the time scale (a) Case 1 (b) Case 2 (c) Case.

Table 1 shows the parameters of SRM drive. Here, the Phase number is 3, Num of stator poles is 12, Num of rotor poles 8, Load torque 3Nm, Aligned Inductance is 60 mH, Unaligned Inductance is 8 mH, Speed is 157.17rad/s and stator is 1.3ohm. Table 2 shows that statistic performance of parameters with proposed technique and existing techniques for ISE speed, torque ripple and ISE current. Likened with the existing methods the proposed technique values are low. Table 3 displays the optimal parameters of FOPID controller along turn activate and deactivate angles for ISE speed, torque ripple and ISE current. From the comparison results, the values of WFS-GBDT are lesser likened with other techniques. Table 4 displays the statistic performance of torque with each case for min, max and mean. Here, the values of WFS-GBDT are lesser likened with other methods.

Table 1

Parameters of SRM drive

Parameter	SRM drive
Phase number	3
Count of stator poles	12
Count of rotor poles	8
Load torque	3Nm
Aligned Inductance	60mH
Unaligned Inductance	8mH
Speed	157.17rad/s
stator	1.3ohm

Table 2

Statistical Analysis of parameters using Proposed and existing techniques

Solution Techniques	Parameters	Better value	Poor value	Mean value	Standard Deviation (SD)
Proposed technique	ISE Speed	230.5364	231.5934	230.952	0.05314
	TR	0.4571	0.6548	0.585	0.472
	ISE Current	3.1257	3.9754	3.5783	0.0472
Base	ISE Speed	220.762	221.0918	220.8423	0.0689
	TR	0.5751	0.854	0.758	0.6852
	ISE Current	3.9132	4.1247	4.0212	0.0579
ALO	ISE Speed	215.5257	216.8793	215.4863	0.08647
	TR	0.725	0.985	0.8563	0.7286
	ISE Current	5.1475	5.8746	5.5972	0.9548
WFS	ISE Speed	224.4268	227.8674	224.5638	0.09583
	TR	0.834	10.562	0.9457	0.8593
	ISE Current	6.1243	6.7945	6.4781	10.592

Table 3

Optimal parameters of fractional order proportional integral derivative controller along turn activate and deactivate angles

Solution Techniques	Parameters	$k_{p}^{b}$	$k_{is}^{b}$	$k_{pi}^{b}$	$k_{ii}^{b}$	θ_ON	θ_OFF
Proposed technique	ISE Speed	7.058	0.385	24.2981	0.3418	0.153	0.6872
	Torque ripple	8.264	0.765	25.678	0.7158	0.183	0.6872
	ISE Current	5.834	0.537	24.532	0.8725	0.1638	0.6824
Base	ISE Speed	7.742	0.443	25.6995	0.3604	0.1772	0.7365
	Torque ripple	9.096	0.887	29.963	0.8107	0.2012	0.7264
	ISE Current	6.671	0.682	25.6384	0.9322	0.1943	0.7301
ALO	ISE Speed	8.5257	0.8793	26.48625	0.8647	1.1852	0.8471
	Torque ripple	0.725	0.985	0.8563	0.7286	0.2151	0.8351
	ISE Current	6.958	0.721	25.9312	0.9682	0.2438	0.7931
WFS	ISE Speed	224.4268	227.8674	224.5638	0.09583	2.5634	0.8334
	Torque ripple	0.834	10.562	0.9457	0.8593	0.3652	0.8567
	ISE Current	6.1243	6.7945	6.4781	10.592	0.9234	0.8434

Table 4

Statistical analysis of torque with each case

Solution Techniques	Torque in Nm	Case 1	Case 2	Case 3
Proposed technique	minimal	0	0	0
	maximal	8.7	9.05	12.4
	mean	4.85	5.06	6.864
Base	minimal	0	0	0
	maximal	9.12	9.38	14
	mean	5.0618	6.758	6.867
ALO	minimal	0	0	0
	maximal	9.5	9.64	14.5
	mean	5.158	5.295	6.586
WFS	minimal	0	0	0
	maximal	9.8	9.8	14.8
	mean	4.9109	6.0385	6.5139

Table 5 tabulates the coefficients of torque ripple using settling time with proposed and existing technique. In proposed technique, the torque ripple coefficient is 0.5609 and the settling time is 0.038. In existing base, the torque ripple coefficient is 0.4097 and the settling time is 0.021. In existing ALO, the torque ripple coefficient is 0.4190 and the settling time is 0.021. In existing WFS, the torque ripple coefficient is 0.4035and the settling time is 0.021. Here, when analyzed to the existing techniques, the settling time of WFS-GBDT is high. Table 6 displays the coefficients of torque ripple with the efficiency of WFS-GBDT and existing techniques. Here, the WFS-GBDT technique attains the torque ripple coefficient is 10.34and the efficiency is 80.41. In existing base, torque ripple coefficient is 86.56 and efficiency is 76.88. In existing ALO, the torque ripple coefficient is 9.86 and the efficiency is 75.41. In existing WFS, the torque ripple coefficient is 8.67and the efficiency is 78.96. Table 7 shows the comparison of Quality of Solution. The computation effort for various number of trails utilizing proposed and existing techniques are tabulated in Table 8.

Table 5

Coefficients of torque ripple and settling time using WFS-GBDT and existing techniques

Solution methods	Torque ripple coefficient	Settling time
Proposed technique	0.5609	0.038
Base	0.4097	0.021
ALO	0.4190	0.021
WFS	0.4035	0.021

Table 6

Coefficients of torque ripple and efficiency using WFS-GBDT and existing techniques

Solution methods	Efficiency (%)	TR coefficients
Base	76.88	86.56
ALO	75.41	9.86
WFS	78.96	8.67
Proposed	80.41	10.34

Table 7

Comparison of Quality of Solution (QoS)

Various optimization techniques	Coefficient of variation (COV)	Error of the best (EFB)
Base	0.09	0.10
ALO	0.75	1.27
WFS	0.63	1.021
Proposed technique	0.075	0.82

Table 8

Computation effort for various count of trails utilizing WFS-GBDT and existing techniques

Solution techniques	Computation effort using various number of trails (%)
	100 trails	150 trails	200 trails	250 trails	500 trails
Base	61.930	73.48	83.36	76.096	77.009
ALO	54.118	60.91	75.10	65.920	61.123
WFS	49.04	57.29	74.93	64.101	61.002
Proposed technique	48.17	51.21	71.04	60.00	57.801

7 Conclusion

This manuscript proposes an enhanced control method for Torque Ripple minimization of Switched Reluctance Motor system. The proposed technique is the combined execution of both the WFS optimization and GBDT algorithm, hence it is known as WFS-GBDT technique. The control method consists of fractional order proportional integral derivative speed controller for external loop as well as current controller for interior loop including turn activate and deactivate angles controller for SRM. Moreover, this is the major aim of controlling the ISE of speed and TR. The performance of proposed technique is compared with other existing techniques, like Base, ALO and WFS. The experimental outcomes demonstrate that the proposed technique is more efficient to lessen the TR in the SRM. Also, the proposed system is effectual to find the optimum solution through lesser computation, also reduced complication of needed algorithm. The proposed technique is analyzed in three different case studies they are: rapid change in torque, swell change in torque and sag change in torque. Under all the cases, current, flux, speed, torque, reference torque, theta values, torque ripple are also analyzed and compared with various existing approaches, like base, ALO and WFS technique. Statistical parameters, like ISE speed, torque ripple, ISE current with better value, poor value, mean value and standard deviation of proposed and existing approaches, ISE speed, torque ripple, ISE current with optimal parameters of fractional order proportional integral derivative controller along turn activate and deactivate angles of proposed and existing approaches are also executed. Efficiency and torque ripple coefficients of the proposed technique achieves 80.41% and 10.34. The future scope of this work is to reduce the torque ripple through artificial neural networks, direct instantaneous torque control and torque sharing function modes.

Data availability statement

Data sharing does not apply to this article as no new data was generated or evaluated in this study.

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