# Mathematical Modelling and Torque Ripple Waning in BLDC Motor Using Outgoing-Phase Current Discharge Hysteresis Controlled ANFIS Controller

Authors: A. Senthilnathan; P. Palanivel; K. Ramash Kumar
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

This study focused on approaches for reducing torque ripples in Permanent Magnet Brushless Direct current motors (PMBLDC) to provide sophisticated performance and reliable machine drives for both industrial and consumer applications. Torque ripples are caused by current ripple, nonsinusoidal Back Electromotive Force (EMF), and cogging torque at the Brushless Direct Current Motor (BLDCM) output. Acoustic emissions are produced when the torque ripple creates vibrations in the mechanical system, which interacts with the motor housing and reduces the life span of the motor. The BLDC’s uses are limited due to these acoustic emissions. Proportional-Integral (PI), Fuzzy Logic Control (FLC), and Adaptive Neuro-Fuzzy Inference System (ANFIS) speed controller approaches were used to construct and analyze the mathematical model of the BLDC motor in the MATLAB environment. The Adaptive Neurofuzzy Inference System (ANFIS) speed control system has solved the shortcomings of the PI and Fuzzy Logic Control (FLC) techniques. Because of FLC interpolation and flexibility, ANFIS is one of the finest trade-offs between neural and fuzzy systems, allowing for smooth control. Model compactness, a smaller training set, and faster convergence are all benefits of the ANFIS approach over traditional feedforward NN. In this research proposal, a simple control approach based on outgoing phase current discharge hysteresis control (OGCDHC) with minimal torque ripple is presented.


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## Body

## 1. Introduction

Drives driven by brushless DC motors are becoming more popular nowadays because of their higher efficiency, higher torque-to-weight, and torque-to-inertia ratios. They are small, highly responsive to acceleration with high durability, and simple to control. A broad range of Motion-Control applications, including Biomedical, aviation, electric vehicle, and defense industries, employ BLDCMs with trapezoidal back EMFs [1–3]. The BLDCMs with electronically commutated motors are incredibly reliable and require very little maintenance as they lack high-wear components like the conventional mechanical commutator and brush assembly [4, 5].Torque ripple is one of the most prevalent problems in BLDCM applications. The three primary sources of torque ripple generation in BLDCMs are cogging, reluctance, and mutual torques. [5] These torque ripples can be decreased by (a) choosing the suitable motor, (b) using the proper control techniques, or (c) doing both. If either the rotor magnets or the stator slots in a BLDCM have skewed one slot pitch, the impact of the first two torque components is considerably decreased. The torque ripple is reduced when the phase back-EMF waveform and phase current waveform are entirely matched. However, when uneven magnetization and improper windings are considered, the exact matching of phase back EMF and phase current is problematic [10]. A three-phase inverter is required to power the motor, and the commutation is done electronically. Several studies on BLDC motor operation are currently being conducted using fuzzy logic, PID, and FPGA control [20–25].


## 2. Literature Review

The BLDCM drive system’s commutation torque pulsation is mostly responsible for aberrant vibration, undesired speed fluctuations, and sound. To maximize BLDCM drive system torque performance, it is necessary to minimize the commutation torque pulsation [6, 7, 18]. A composite switching mode has been proposed to reduce the torque ripple at all speeds during commutation periods during the inverter’s 120° and 180° electrical conduction modes [8]. A variable input voltage solution for efficient torque ripple reduction during the BLDCM’s freewheeling period was reported in [9]. With this approach, the Laplace transformation was used to predict the freewheeling zone and the ideal voltage.The rate of a BLDCM fed from a 2-degree inverter is governed by using a buck converter in between the dc supply and the 2-stage inverter [11–14]. A hybrid converter topology has been proposed incorporating a dc-dc converter to control the speed of a BLDCM in [11, 20]. Reference [7] presents unique circuit architecture with a SEPIC converter and a switch selection combination to reduce torque ripple when a 2-level inverter is used in parallel with a superlift Luo-converter [13]. An innovative approach for torque ripple suppression has been proposed using Instantaneous torque estimation in sensorless direct-torque-controlled brushless dc motors [14]. The average torque control presented in [15] is based on one-cycle control (ATC-OCC), which measures voltage and current on the DC bus instead of back-EMF measurements and rotor location exactly. Finite-state model predictive control [19] has been proposed as novel circuit architecture for torque ripple suppression in a BLDCM drive system. In conduction and commutation modes, a current optimization technique based on integral variable structure control has been devised to eliminate torque ripple for BLDCM [16].One of the most often used phase current shaping methods to control current ripple is phase advance control [28]. Depending on the motor speed and input voltage, the phase advance angle is estimated using either a phase advance circuit or a delay function to adjust for phase current distortion. Another way to correct for distorted current and boost overall efficiency by eliminating tail current is commutation pulse control. Due to limited resolution, misalignment, electrical noise, and physical vibration, both phase advance and commutation pulse controls need the employment of a sequencing algorithm based on a Hall effect sensor signal, which has poor precision. [29–31].Reference voltage controlled (RVC) PWM [26] is a revolutionary current shaping method that may reduce excitation torque ripple while increasing motor speed. This Reference voltage controlled (RVC) PWM efficiently diminishes the high peak current with the linearly reducing reference voltage. The roots of torque ripple in the BLDCM in the speed closed-loop state were investigated [30], and a novel PWM-MPC method was suggested that computed the duty cycle of the power switches during the commutation period using the predictive model, but the proposed method worked well only at lower or higher speed ranges only. Because of its superior performance in positioning and torque ripple reduction, field oriented control (FOC) is used in BLDC motor drive systems [31]. However, effective performance necessitates precise control system state monitoring, which is frequently attributed to superior sensors. A novel harmonic injection scheme is proposed, which effectively reduces the torque ripple and improves the speed stability. [31] A realistic method for compensating for specific torque harmonics is proposed by identifying the prominent torque ripple components (cogging torque and flux linkage ripple torque) and tuning the correction algorithm using a cuckoo search algorithm [32]. As the best criterion, the speed variation index is utilized in minimizing torque ripple in PMSM drive-by cuckoo search algorithm article.


## 3. Analysis of Torque during Commutation Interval

Figure1 illustrates the electrical equivalent of the BLDC motor and the electronic commutation system. Equation (1) provides the stator voltage equation of the motor in terms of equivalent electrical parameters.(1)VapVbpVcp=Rsp000Rsp000RspIapIbpIcp+LMMMLMMMLddtIapIbpIcp+eapebpecp,where “Rsp” refers to the stator resistance/phase. vap, vbp, and vcp refer to stator voltage/phase. iap, ibp, and icp refer to stator currents/phase. “L” refers to the self-inductance/phase. “M” refers to the mutual inductance/phase. eap, ebp, and ecp refer to the back EMFs induced in each phases. EM refers to the maximum back EMF/phase. IM refers to the maximum commutation current/phase. ωr refers to rotor speed.Figure 1
Electrical Equivalent circuit of a BLDCM with the commutation system.Considering the stator currents are balanced in nature and if all stator current summation is equal to zero, then equation (1) is simplified as follows:(2)VapVbpVcp=Rsp000Rsp000RspIapIbpIcp+L000L000LddtIapIbpIcp+eapebpecp.The phase voltages are equivalent and identical to the DC machine’s voltage equation. The generalized BLDC motor electromagnetic torque equation can be written as follows:(3)Te=eapiap+ebpibp+ecpicpωr.According to equation (3), the sum of all currents must attain a consistent value at particular speeds to provide a steady electromagnetic torque. As depicted in Figure 2, rectangular phase currents should result from back EMFs.Figure 2
BLDCM three-phase current and back-EMF waveforms.The nonzero inductance stator winding with a finite rise time leads the phase currents to be trapezoidal rather than rectangular. The slopes of the entering and exiting phases have a direct influence on the commutation torques.The torque ripple analysis is done by taking into account the current change from phaseA to B during the commutation period. At the start of the commutation period, MOSFET S1 is switched off to deenergize phase A. and S3 is switched ON to energize phase B, with S6 remaining in ON state. During the commutation period, the current flowing through the stator winding is supposed to be constant (Im). Im, 0, and −Im are the starting currents in the A, B, and C phases, respectively.At the beginning of the commutation,(4)Vap=Vcp=0,Vbp=Vdc,soeap=−em;ebp=em;ecp=−em.Due to the above conditions, the voltage equation can be rewritten as follows:(5)0=RIap+Ldiapdt+Eap+Vn,Vdc=RIbp+Ldibpdt+Ebp+Vn,0=RIcp+Ldicpdt+Ecp+Vn.And the neutral voltage can be written as follows:(6)Vn=13Vdc−Em.Therefore the electromagnetic torque at the conduction period will be equal to the following:(7)TConduction=eapiap+ebpibp+ecpicpωr=2ImEmωr.Resistance may be neglected and the current gradients in the phase can be represented by equations (8)–(10) when the hysteresis control frequency is large in a time frame and smaller than the electrical time constant:(8)dIapdt=−Vdc+2Em3L,(9)dIbpdt=2Vdc+Em3L,(10)dIcpdt=−Vdc+4Em3L.Let the diode and IGBT/MOSFET switch actions be negated in comparison to the commutation period, and the time frame for the disappearance of a phase current from its initial maximum value is shown in equation (11), and the time frame for the increase of “B” phase current from zero to the maximum value is shown in equation (12):(11)Ta=3LImaxVdc+2Em,(12)Tb=3LImax2Vdc−Em.The torque during commutation can be written as follows:(13)TCMP=2Em/ωrImax+Vdc−4Em/3LtThe torque ripple for BLDCM would be as per the following equation:(14)TRipple=Vdc−4Em/3LtThus, based on the torque ripple equation, certain conclusions arrived. Commutation causes the torque to rise when on time exceeds off time. Commutation results in torque decrease when off time exceeds on time. However, commutation produces a continuous torque when the off-time equals on time. Figure3 depicts the behavior of currents during the commutation period.Figure 3
Stator Current behaviors during commutation. (a)Vdc > 4Em, ta > tb. (b) Vdc < 4Em, ta < tb. (c) Vdc = 4Em, ta = tb.
(a)(b)(c)The suggested OCDHC control for BLDCMs is depicted diagrammatically in Figure4. During the commutation time, three-phase conductions occurred as a result of the armature inductance. For analysis purposes, let us consider the commutation time when the conduction transfers from phase A to phase B. During this transfer, the current referred to as incoming phase current climbs to Max, while the current referred to as outgoing phase current decreases, resulting in a zero current slew rate difference for this current control. OCDHC uses hysteresis control to alter the OGP current in relation to the reference current. When the actual current is smaller than the reference current, the duty ratio is restricted, which lowers the differential slew rate.Figure 4
BLDCM CTR control diagram.Because of their simplicity, hysteresis-band current control methods are commonly employed in PWM systems. A quick responsive current loop, the capacity to handle intrinsic current peaks, immediate reflexes, better precision, and unconditioned stability are all advantages of hysteresis-band current control [25]. Equations (15) and (16) define the output signal of a hysteresis comparator:(15)Ha=1,forIa<Ia∗−Δi2,(16)Ha=0,forIa>Ia∗+Δi2,where Ia = OGP current, Ia∗ = Reference ICP current. Δi  = Preset hysteresis band for phases.If the outgoing phase current rises to the top limit, the hysteresis comparator output ha becomes zero, and an appropriate voltage vector is chosen to reduce the out-going phase current. When the outgoing phase current lowers and hits the lower limit, the hysteresis comparator output ha equals one, and a suitable voltage vector is chosen to increase the out-going phase current.Figures5(a)–5(c) depict the three-phase stator currents, rotor speed, and torque responses of BLDC motor without commutation torque ripple control (CTR). Torque ripple of 60% is recoded at half load condition and 55% at full load condition.Figure 5
Traditional commutation simulations without CTR control.Figures6(a)–6(c) depict the three-phase stator currents, rotor speed, and torque responses of BLDC motor with SEPIC converter controlled-DC link voltage control. Torque ripple of 21.5% is noted at half load condition and 18.65% at full load condition. SEPIC converter controlled-DC link voltage control has a medium differential slew rate. Hence current ripples and torque ripples get reduced.Figure 6
Simulation result for SEPIC converter controlled-DC link voltage control.Figures7(a)–7(c) depict the three-phase stator currents, rotor speed, and torque responses of BLDC motor with proposed OCDHC. Torque ripple of 12.3% is recorded at half load condition and 11.8% at full load condition Proposed Control has a low differential slew rate. Hence current ripples and torque ripples are greatly reduced.Figure 7
Simulation result for OCDHC control.Table1 compares torque ripple values in Newton meters (Nm) and percentages (%) for the classic commutation technique, torque ripple suppression by SEPIC converter, and proposed OCDHC under variable load torque conditions.Table 1
Torque ripple analysis.
Load torque (Nm)Traditional commutationVDC control by SEPICProposed OCDHCTorque rippleTorque rippleTorque rippleNm%Nm%Nm%0.160.10264.30.03924.70.0212.860.3250.20362.60.07523.20.04112.620.650.39600.1421.50.0812.30.9750.55957.40.19519.960.11411.951.31.16555.30.24218.650.15411.8


## 4. PI, Fuzzy, and ANFIS Controller

Controlling the speed of the BLDCM is a crucial aspect of control applications. Because they are structurally simple while being robust in the application, PI-based control schemes are frequently used in BLDCM speed control [24]. PI schemes dominate the market for closed-loop industrial controllers (95 percent). Reference [22], these systems have also been included in BLDCM [6, 7]. Due to substantial overshoot of reference points, longer delays in reaching steady-state, inability to respond rapidly to a sudden change in torque load, and sensitivity to controller gains, PI-based speed controllers have low efficiency. PICs (PI controllers) fail in BLDCMs due to their nonlinear character, which influences parameter changes or load disturbances.FLCs (fuzzy logic controllers) have effectively managed speeds with fuzzy regulators even in the face of load disturbances and variations. FLCs effectively deal with nonlinear, complicated, or poorly described systems. Because of their ability to learn and adapt, MLTs (Machine Learning Techniques) such as ANNs (Artificial Neural Networks) have transformed various industries [24]. ANNs are trustworthy and can handle any data. As a result, this work suggests a unique controller that combines the advantages of FLCs and ANNs in its design.ANFIS control structures include components seen in Fuzzy Inference Systems due to a NN (Neural Network) block. In NN design, connections (units) are organized as connected network layers (layers 1–5). [24] Fuzzification, knowledge base, NN, and defuzzification are the four major components of the proposed ANFIS controller framework. The NN layers are discussed in further detail as follows:(i)
The first NN layer uses triangular or bell-shaped fuzzy membership function input variables, whereas the second NN layer uses the first layer's inputs. It is a membership layer that verifies the weights of membership functions. It represents a jumbled set of input variables.(ii)
The third layer of the NN is the rule layer, which receives input from the second layer. This layer's NN neurons or nodes match the fuzzy rules and compute the level of each rule. The nodes use calculations to normalize the weights.(iii)
The fourth layer is the defuzzification layer, which generates results based on rule inferences.(iv)
Layer 5 is the final or output layer, which turns the fuzzy classification findings from the previous layers into a single crisp output value.(v)
The ANFIS features based onT–S (Takagi–Sugeno) fuzzification (Sugeno& Kang 1988 [17]); (Takagi and Sugeno1985 [27]) are as follows:(vi)
The outputs of all membership functions must be of the same type and provide a constant or linear value.(vii)
Its order should be zero or first orderT–S systems, with a single output obtained from defuzzified data averaging.(viii)
It should not share any rules, and several rules should not utilize the same output membership function simultaneously.(ix)
The number of output membership functions and rules should be equal, and each rule should have a single weight.Grid partitioning is utilized to cluster the initial membership function generation in this work, while fuzzy rules are used for the input/output training sets are listed in Table2. Grid division chooses rules for each input variable separately. For two inputs, five membership functions are determined. The recommended Hybrid learning technique combines GD (Gradient Descent) with LSE to establish ANFIS premises with consequent parameters. Each learning cycle includes a forward and reverse pass sequence. When a forward pass sequence input is received, the node outputs up to the fourth layer are updated, and this method is repeated for all training data set samples. LSE must determine the following parameters in the next stage. Backward passes transport each node's error signal derivatives from its output to its input, accumulating GD vectors for each training input/output data set sample. GD is used to update the premises parameters after a backward sweep through all training data sets. The Simulated ANFIS Model architecture of the BLDCM is seen in Figure 8. After completing the upgrades, on-premises, and subsequent parameters, FIS calculates a collection of relevant membership functions and rule bases. These established parameters are then followed to deliver the best possible control signal. The T-S-based FIS initial and final rule bases are depicted in Figures 9 and 10.Table 2
Initial input membership function.
Distribution of membership functionωe or A1 (error)Δωe is B1 (change in error)mjnjojujvjwj1−3500−2000−500−525−300−752−2000−5001000−300−751503−50010002500−7515037541000250040001503756005250040005500375600825Figure 8
Simulated ANFIS model structure for BLDCM.Figure 9
T–S based FIS initial rule base.Figure 10
T–S based FIS final rule base.The model provided in this paper was tested using the Simulink/MATLAB environment. The toolboxes required for testing the model in conjunction with the model for controlling the BLDCM drive were chosen. The Simulink model of the OCDH controller with PI/Fuzzy/ANFIS is shown in Figure11. A DC supply, a PWM inverter, a motor measuring system, PI/FUZZY/ANFIS controllers, a switching logic circuit, and BLDCM were all included in the model. The power input of the PWM inverter was a DC source, and the output was fed into BLDCM. Rotor position and speed were measured using a Hall sensor and a tacho generator model. Considering the existing commutation time transfer process from phase A to phase B. During the transfer, Ib, also known as the incoming phase current (IGP), increases from the maximum current, whereas Ia, also known as the out-going phase current (OGP), falls from the maximum current. To eliminate torque ripple, the difference in current slew rates should be zero or minimal. Using hysteresis control, OCDHC regulates the OGP current in relation to the reference current. When the actual current is less than the hysteresis-band current, the duty ratio is controlled by hysteresis, which removes the differential slew rate and torque ripple during commutation. The OGP control period is chosen from a commutation vector corresponding to hysteresis duty ratio controls.Figure 11
OCDH control diagram for BLDCM CTR control with PI/Fuzzy/ANFIS.The BLDCM and simulated controller performances were tested with different loads and speeds and the results of these tests are described in detail below.


### 4.1. Case 1: Under Constant Load and Fixed Speed

Figure12 depicts the simulation performance of the PI, Fuzzy, and ANFIS controllers while maintaining a constant load of 1 Nm at a set speed of 3000 rpm. According to the results, the PI controller's BLDCM achieves the reference speed in 0.36 s with a rising time and settling error of 0.135 s and 14 rpm. When the Fuzzy-based controller is employed, the BLDCM achieves the reference speed in 0.073 s with a rising time and settling inaccuracy of 0.04 s and 8.2 rpm, respectively. However, the ANFIS controller achieves the reference speed in 0.018 s with a rising time and settling error of 0.009 s and 3.97 rpm, respectively. The results reveal that the ANFIS controller outperforms the PI and Fuzzy controllers.Figure 12
Controller performances under the constant load of 1 Nm and fixed speed of 3000 rpm.


### 4.2. Case 2: Under Fixed Speed and Decrement Load Change

The load was decreased from 1.3 Nm to 0.6 Nm at 0.5 seconds and the simulation performance of PI, Fuzzy, and ANFIS controller was attained.Figure13 demonstrates that the PI controller with BLDCM achieves the reference speed in 0.132 s with a peak overshoot and settling error of 75 rpm and 15 rpm, respectively. When the Fuzzy-based controller is employed, the BLDCM achieves the reference speed in 0.02 s with a peak overrun of 31.5 rpm and a settling error of 9.4 rpm. However, the ANFIS controller achieves the reference speed in 0.009 s with a peak overshoot and settling error of 15.6 rpm and 5.3 rpm, respectively.Figure 13
Controller performances at a fixed speed of 3000 rpm with a decrement in load from 1.3  Nm to 0.6 Nm.


### 4.3. Case 3: Under Fixed Speed and Increment Load Change

In simulations, the load was raised from 0.6 Nm to 1.3 Nm at 0.5 s. Figure14 demonstrates that the PI controller with BLDCM achieves the reference speed in 0.19 s with a peak overshoot and settling error of 93.6 rpm and 19.6 rpm, respectively. When the Fuzzy-based controller is employed, the BLDCM achieves the reference speed in 0.026 s with a peak overshoot and settling error of 42.6 rpm and 10.6 rpm, respectively. However, the ANFIS controller achieves the reference speed in 0.011 s with a peak overshoot and settling error of 21 rpm and 5.5 rpm, respectively. The simulation results demonstrate the advantages of the proposed ANFIS controller for BLDCM drives over competing controllers.Figure 14
Controller performances at a fixed speed of 3000 rpm with increment in load from 0.6 Nm to 1.3 Nm.


### 4.4. Case 4: Under Constant Load and Decrement Variable Speed

In the simulations, a constant load of 1 Nm was supplied, and the speed was reduced from 3000 rpm to 1500 rpm in 0.5 s. As shown in Figure15, the PI controller on BLDCM achieves the reference speed in 0.32 s with a settling error of 12 rpm. The BLDCM achieves the reference speed in 0.056 s with a settling error of 7.6 rpm when the Fuzzy-based controller is utilized. However, the ANFIS controller achieves the reference speed in 0.017 seconds with a settling error of 3.15 rpm. The simulation results demonstrate the advantages of the proposed ANFIS controller for BLDCM drives over competing controllers.Figure 15
Controller performances with constant load 1 Nm and variable speed (3000 rpm to 1500 rpm).


### 4.5. Case 5: Under Constant Load and Increment Variable Speed

The simulation results demonstrate the advantages of the proposed ANFIS controller for BLDCM drives over competing controllers. In the simulations, a constant load of 1 Nm was applied, and the speed rose from 1500 rpm to 3000 rpm in 0.5 s. As shown in Figure16, the PI controller of BLDCM achieves the reference speed in 0.36 s with a settling error of 14 rpm. When the Fuzzy-based controller is employed, the BLDCM achieves the reference speed in 0.065 s with an 8.2 rpm settling error. However, the ANFIS controller achieves the reference speed in 0.018 seconds with a settling error of 4.65 rpm. The performance of BLDCM with PI, Fuzzy, and ANFIS controllers is compared for settling time, peak overshoot (Mp), and steady-state error. These values are found and tabulated in Table 3.Figure 16
Controller performances constant load 1 Nm and increment variable speed 1500 rpm to 3000 rpm.Table 3
Performance comparison of different controller parameters.
CasesPIFuzzyANFISSettling time (s)Peak overshoot (%)Steady state error (%)Settling time (s)Peak overshoot (%)Steady state error (%)Settling time (s)Peak overshoot (%)Steady state error (%)10.36—0.470.073—0.280.018—13.220.1322.50.50.021.050.310.0090.520.17630.193.120.650.0261.420.350.0110.70.18340.32—0.80.056—0.50.017—0.2150.36—0.460.065—0.270.018—0.15


## 4.1. Case 1: Under Constant Load and Fixed Speed

Figure12 depicts the simulation performance of the PI, Fuzzy, and ANFIS controllers while maintaining a constant load of 1 Nm at a set speed of 3000 rpm. According to the results, the PI controller's BLDCM achieves the reference speed in 0.36 s with a rising time and settling error of 0.135 s and 14 rpm. When the Fuzzy-based controller is employed, the BLDCM achieves the reference speed in 0.073 s with a rising time and settling inaccuracy of 0.04 s and 8.2 rpm, respectively. However, the ANFIS controller achieves the reference speed in 0.018 s with a rising time and settling error of 0.009 s and 3.97 rpm, respectively. The results reveal that the ANFIS controller outperforms the PI and Fuzzy controllers.Figure 12
Controller performances under the constant load of 1 Nm and fixed speed of 3000 rpm.


## 4.2. Case 2: Under Fixed Speed and Decrement Load Change

The load was decreased from 1.3 Nm to 0.6 Nm at 0.5 seconds and the simulation performance of PI, Fuzzy, and ANFIS controller was attained.Figure13 demonstrates that the PI controller with BLDCM achieves the reference speed in 0.132 s with a peak overshoot and settling error of 75 rpm and 15 rpm, respectively. When the Fuzzy-based controller is employed, the BLDCM achieves the reference speed in 0.02 s with a peak overrun of 31.5 rpm and a settling error of 9.4 rpm. However, the ANFIS controller achieves the reference speed in 0.009 s with a peak overshoot and settling error of 15.6 rpm and 5.3 rpm, respectively.Figure 13
Controller performances at a fixed speed of 3000 rpm with a decrement in load from 1.3  Nm to 0.6 Nm.


## 4.3. Case 3: Under Fixed Speed and Increment Load Change

In simulations, the load was raised from 0.6 Nm to 1.3 Nm at 0.5 s. Figure14 demonstrates that the PI controller with BLDCM achieves the reference speed in 0.19 s with a peak overshoot and settling error of 93.6 rpm and 19.6 rpm, respectively. When the Fuzzy-based controller is employed, the BLDCM achieves the reference speed in 0.026 s with a peak overshoot and settling error of 42.6 rpm and 10.6 rpm, respectively. However, the ANFIS controller achieves the reference speed in 0.011 s with a peak overshoot and settling error of 21 rpm and 5.5 rpm, respectively. The simulation results demonstrate the advantages of the proposed ANFIS controller for BLDCM drives over competing controllers.Figure 14
Controller performances at a fixed speed of 3000 rpm with increment in load from 0.6 Nm to 1.3 Nm.


## 4.4. Case 4: Under Constant Load and Decrement Variable Speed

In the simulations, a constant load of 1 Nm was supplied, and the speed was reduced from 3000 rpm to 1500 rpm in 0.5 s. As shown in Figure15, the PI controller on BLDCM achieves the reference speed in 0.32 s with a settling error of 12 rpm. The BLDCM achieves the reference speed in 0.056 s with a settling error of 7.6 rpm when the Fuzzy-based controller is utilized. However, the ANFIS controller achieves the reference speed in 0.017 seconds with a settling error of 3.15 rpm. The simulation results demonstrate the advantages of the proposed ANFIS controller for BLDCM drives over competing controllers.Figure 15
Controller performances with constant load 1 Nm and variable speed (3000 rpm to 1500 rpm).


## 4.5. Case 5: Under Constant Load and Increment Variable Speed

The simulation results demonstrate the advantages of the proposed ANFIS controller for BLDCM drives over competing controllers. In the simulations, a constant load of 1 Nm was applied, and the speed rose from 1500 rpm to 3000 rpm in 0.5 s. As shown in Figure16, the PI controller of BLDCM achieves the reference speed in 0.36 s with a settling error of 14 rpm. When the Fuzzy-based controller is employed, the BLDCM achieves the reference speed in 0.065 s with an 8.2 rpm settling error. However, the ANFIS controller achieves the reference speed in 0.018 seconds with a settling error of 4.65 rpm. The performance of BLDCM with PI, Fuzzy, and ANFIS controllers is compared for settling time, peak overshoot (Mp), and steady-state error. These values are found and tabulated in Table 3.Figure 16
Controller performances constant load 1 Nm and increment variable speed 1500 rpm to 3000 rpm.Table 3
Performance comparison of different controller parameters.
CasesPIFuzzyANFISSettling time (s)Peak overshoot (%)Steady state error (%)Settling time (s)Peak overshoot (%)Steady state error (%)Settling time (s)Peak overshoot (%)Steady state error (%)10.36—0.470.073—0.280.018—13.220.1322.50.50.021.050.310.0090.520.17630.193.120.650.0261.420.350.0110.70.18340.32—0.80.056—0.50.017—0.2150.36—0.460.065—0.270.018—0.15


## 5. FPGA Experimental Analysis

Xilinx® FPGAs can accelerate the implementation of OCDH-BLDC motor control and ANFIS-based speed control utilizing OCDH due to its parallel processing capacity, rapid computational rate, and connection flexibility. Figure17 shows a block diagram of an experimental setup in which the electrical switching sequence and CTR control are constructed by receiving feedback from the BLDC Motor (ATO-80WDM01330-96V) through the position hall sensor and current sensor (ACS712). The Hall Effect sensor detects motor speed without the use of an external sensor. These signals are sent to the Spartan-6 FPGA, which uses ANFIS OCDH control to limit the speed at a lower CTR. The PWM pulse is sent to the inverter MOSFET through an isolated driver circuit made up of LTV-3120 and NCP51530 (NTP35N15).Figure 17
Experimental setup for proposed BLDCM controller.The torque ripple of a BLDC motor is determined by the stator current ripple. We researched the commutation current ripple at CMP for traditional electronic commutation and suggested OCDH control to regulate the current ripple of the BLDC motor. These FPGA Spartan 6 controllers are constructed using hall sensor feedback and current monitoring (ACS712). We investigate the current ripple of standard electronic commutation and OCDH control at torques of 0.5 Nm and 1 Nm by loading the motor with a DC motor and load resistor in this experiment (see Figure18).Figure 18
Experimental arrangement proposed ANFIS-based OCDH control of BLDC motor.Figure19(a) is the stator voltage that is produced by a three-leg MOSFET inverter to drive the BLDC motor according to the traditional electronic commutation method. Figure 19(b) shows the stator current at half load (0.5 Nm), in which the commutation current ripple is 61.2%, so the commutation torque ripple is also high.Figure 19
Electronic commutation at half load: (a) stator voltage; (b) stator current.
(a)(b)Figure20(a) depicts the OCDH control stator voltage at 0.5 Nm and 3000 rpm. The stator current is almost ripple-free, so an almost trapezoidal current waveform is obtained, as illustrated in Figure 20(b).Figure 20
OCDH control at half load: (a) stator voltage; (b) stator current.
(a)(b)Figure21(a) shows the stator voltage produced by a three-leg MOSFET inverter used to power the BLDC motor using the standard electronic commutation technique, with a peak voltage of 94 V. Figure 21(b) shows a stator current with 5.5 peaks at 1 Nm and 3000 rpm and a commutation current ripple of 52.3 percent, suggesting a high CTR.Figure 21
Electronic commutation at full load: (a) stator voltage; (b) stator current.
(a)(b)Figure22(a) depicts the OCDH control stator voltage at 1 Nm and 5000 rpm. The stator current is adjusted in this method to decrease the commutation current ripple and generate a pure trapezoidal current, as illustrated in Figure 22(b).Figure 22
OCDH Control at full load: (a) stator voltage; (b) stator current.
(a)(b)At a switching frequency of 60 KHz, the performance of the BLDC motor was evaluated using PI, Fuzzy, and ANFIS controllers with OCDH torque ripple reduction using Spartan 6. The study is carried out for two different situations, each with a constant load torque and a variable step speed. The STM32F401RE controller is used to measure the speed variation.


### 5.1. Case 1: Under Constant Load and Decrement Variable Speed

In this case, the load torque is fixed to 1 Nm, and the speed is decreased from 3000 rpm to 1500 rpm at a specified time.Figure23(a) depicts the rotor speed response when the speed decreases from 3000 rpm to 1500 rpm with a settling time of 0.43 s. and Figure 23(b) depicts the speed ripple for the PI controller. The settling error of 22.8 rpm is observed for the PI controller.Figure 23
PI controller performance: (a) speed (rpm); (b) speed ripple (rpm).
(a)(b)Figure24(a) depicts the rotor speed response when the speed decreases from 3000 rpm to 1500 rpm with a settling time of 0.145 s. Figure 24(b) depicts the speed ripple for the Fuzzy controller. The settling error of 14.4 rpm is observed for the fuzzy controller.Figure 24
Fuzzy controller performance: (a) speed (rpm); (b) speed ripple (rpm).
(a)(b)Figure25(a) depicts the rotor speed response when the speed decreases from 3000 rpm to 1500 rpm with a settling time of 0.025 sec. Figure 25(b) depicts the speed ripple for the ANFIS controller. The settling error of 7.2 rpm is observed for the ANFIS controller.Figure 25
ANFIS controller performance: (a) speed (rpm); (b) speed ripple (rpm).
(a)(b)


### 5.2. Case 2: Under Constant Load and Increment Variable Speed

In case 2, the load torque of the motor is fixed at 1 Nm, and the speed of the drive is increased from 1500 rpm to 3000 rpm at a specified time.Figure26(a) depicts the rotor speed response when the speed increases from 1500 rpm to 3000 rpm with a settling time of 0.37 seconds, and Figure 26(b) depicts the speed ripple for the PI controller. The settling error of 22.8 rpm is observed for the PI controller.Figure 26
PI controller performance: (a) speed (rpm); (b) speed ripple (rpm).
(a)(b)Figure27(a) depicts the rotor speed response when the speed increases from 1500 rpm to 3000 rpm with a settling time of 0.11 sec. Figure 27(b) depicts the speed ripple for the fuzzy controller. The settling error of 16.8 rpm is observed for the fuzzy controller.Figure 27
Fuzzy controller performance: (a) speed (rpm); (b) speed ripple (rpm).
(a)(b)In the ANFIS controller, the BLDC motor speed attained to 3000 rpm at a settling time of 0.016 sec is shown in Figure28(a), and its speed ripple is 7.2 rpm shown in Figure 28(b). The experimental waveform under adverse speed circumstances confirms that the ANFIS controller has a shorter settling time and a lower ripple than the PI and fuzzy controllers.Figure 28
ANFIS controller performance: (a) speed (rpm), (b) speed ripple (rpm).
(a)(b)


## 5.1. Case 1: Under Constant Load and Decrement Variable Speed

In this case, the load torque is fixed to 1 Nm, and the speed is decreased from 3000 rpm to 1500 rpm at a specified time.Figure23(a) depicts the rotor speed response when the speed decreases from 3000 rpm to 1500 rpm with a settling time of 0.43 s. and Figure 23(b) depicts the speed ripple for the PI controller. The settling error of 22.8 rpm is observed for the PI controller.Figure 23
PI controller performance: (a) speed (rpm); (b) speed ripple (rpm).
(a)(b)Figure24(a) depicts the rotor speed response when the speed decreases from 3000 rpm to 1500 rpm with a settling time of 0.145 s. Figure 24(b) depicts the speed ripple for the Fuzzy controller. The settling error of 14.4 rpm is observed for the fuzzy controller.Figure 24
Fuzzy controller performance: (a) speed (rpm); (b) speed ripple (rpm).
(a)(b)Figure25(a) depicts the rotor speed response when the speed decreases from 3000 rpm to 1500 rpm with a settling time of 0.025 sec. Figure 25(b) depicts the speed ripple for the ANFIS controller. The settling error of 7.2 rpm is observed for the ANFIS controller.Figure 25
ANFIS controller performance: (a) speed (rpm); (b) speed ripple (rpm).
(a)(b)


## 5.2. Case 2: Under Constant Load and Increment Variable Speed

In case 2, the load torque of the motor is fixed at 1 Nm, and the speed of the drive is increased from 1500 rpm to 3000 rpm at a specified time.Figure26(a) depicts the rotor speed response when the speed increases from 1500 rpm to 3000 rpm with a settling time of 0.37 seconds, and Figure 26(b) depicts the speed ripple for the PI controller. The settling error of 22.8 rpm is observed for the PI controller.Figure 26
PI controller performance: (a) speed (rpm); (b) speed ripple (rpm).
(a)(b)Figure27(a) depicts the rotor speed response when the speed increases from 1500 rpm to 3000 rpm with a settling time of 0.11 sec. Figure 27(b) depicts the speed ripple for the fuzzy controller. The settling error of 16.8 rpm is observed for the fuzzy controller.Figure 27
Fuzzy controller performance: (a) speed (rpm); (b) speed ripple (rpm).
(a)(b)In the ANFIS controller, the BLDC motor speed attained to 3000 rpm at a settling time of 0.016 sec is shown in Figure28(a), and its speed ripple is 7.2 rpm shown in Figure 28(b). The experimental waveform under adverse speed circumstances confirms that the ANFIS controller has a shorter settling time and a lower ripple than the PI and fuzzy controllers.Figure 28
ANFIS controller performance: (a) speed (rpm), (b) speed ripple (rpm).
(a)(b)


## 6. Conclusion

On the control side of BLDC motors, this article examines various control methodologies for decreasing torque ripples. It is either the motor’s design or the power inverter supply that causes the pulse torque movements to deviate from ideal conditions, resulting in nonideal current waveforms. BLDC motor torque pulsations are generated by unnecessary torque pulsations in the drive, which causes oscillations in the motor speed and resonances in the motor, resulting in noise and vibration. There is a ripple in the torque produced by brushless DC motors (BLDCM) when switching-in and switching-out occurs in different phases. It would be possible to reduce ripple in the communication torque if the slew rates were the same.This article examines the issue of torque ripples caused by machine control and drives, which might be reduced using the proposed OCDH control approach. The simulation results clearly contrast the proposed OCDH control approach with classic commutation without CTR control. A wide variety of comparisons are done for the aforementioned torque ripple controller under fixed speed variable torque and variable speed fixed torque situations. This clearly demonstrates that the OCDH controller is far superior at managing the slew rate at commutation moments to decrease the torque ripple in BLDC motors.An efficient controller has been presented for the BLDC speed control drive with OCHD control. Under varied load and set speed circumstances, the suggested controller, ANFIS controller, was compared with existing controllers. Overshoot, undershoot, steady-state error, rising time, settling time, and recovery time have all been measured, evaluated, and compared for all controllers studied. In a MATLAB simulation for ANFIS OCHD controller based on BLDC motors, the fuzzy controller outperforms the PI in terms of dynamic performance and time to steady-state.ANFIS controller operates the BLDC motor more effectively by minimizing the torque ripple oscillation. The current ripple analysis for PI, Fuzzy, and ANFIS with OCDH-BLDC control at various load and speed conditions is verified practically, demonstrating that the ANFIS creates reduced torque ripple at the high switching frequency. However, the proposed OCDH speed control has a delay due to its PWM creation with a selection switch, which influences the torque ripple due to the long recovery time. Therefore, a combined reference signal generation will be used instead of the selective switch in future developments to solve this problem.



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*Source: 3971695-2022-06-25.xml*