Enhanced Generalized Vector Control Strategy for Torque Ripple Mitigation of IPM-type Brushless DC Motors

ABSTRACT:

 Optimal currents with appropriate harmonic components injected into the motor windings can effectively mitigate torque ripple for interior permanent magnet (IPM) type brushless DC motors (BLDCMs). However, existing approaches may fail to accurately inject the optimal currents into motors due to the limited current loop bandwidth. This paper proposes a simple enhanced generalized vector control strategy to mitigate the torque ripple for IPM-type BLDCMs. With the proposed vector control strategy, the control block diagram for IPM-type BLDCMs is as simple as that with traditional vector control for sinusoidal permanent magnet synchronous motors. Firstly, an electromechanical energy conversion voltage (EECV), considering the effects of the non-sinusoidal back-EMF and the rotor salience property, is proposed in -axis. Then, a novel coordinate frame is constructed with the proposed EECV, which is based on the arbitrary reference frame theory. As a result, the currents of IPM-type BLDCMs can be decomposed into two constant components, one being linked to the torque and the other one to the flux linkage. Thus, the bandwidth of current loop with simple proportional integral regulator can be equivalently expanded in the proposed coordinate frame. Finally, comprehensive experiments are conducted in different operation conditions to validate the effectiveness of the proposed vector control strategy. 1

KEYWORDS:

1.      Brushless DC motors (BLDCMs)

2.      Vector control

3.      Optimal currents

4.      Torque ripple mitigation

SOFTWARE: MATLAB/SIMULINK

CONCLUSION:

An enhanced generalized vector control strategy based on the arbitrary reference frame theory is proposed. And a voltage component involving in electromechanical energy conversion, namely EECV, is utilized to establish the novel coordinate frame of the generalized vector control strategy. Therefore, the current components of BLDCMs mapped in the proposed coordinate frame are constant, surmounting the bandwidth limitations of PI current regulator thoroughly. With the proposed strategy, the torque ripple minimization and MTPA operation for BLDCMs can be achieved simultaneously, and the steady and dynamic performance have been verified by experimental results. In addition, the influence of permanent magnet flux and inductance term variations on the torque ripple mitigation has been investigated with experimental tests.

In conclusion, the proposed method has the following advantages:

1) Compared with two phase feeding mode, the proposed method eliminates the switching of control strategy between normal conducting period and commutation period, and between low speed and high speedarea. Thus, the executability of torque ripple mitigation is enhanced.

2) Compared with the traditional vector control with Park transformation [4] and the vector control with GSRF [11], the proposed method can simplify the mathematical model of IPM-type BLDCMs, being similar with that of the surface sinusoidal PMSMs. Then, with simple PI current regulator, the steady state and transient state performance of torque ripple mitigation are improved.

3) Compared with the vector control based on the conventional rotor orientation with the additional resonant controllers[15]-[20]or repetitive controllers[21], or the method based on multiple reference frames[22], all torque ripple harmonic componentscan be mitigatedtheoretically, not only the selective torque harmonic components.Thus, the torque ripple can be mitigated further with the proposed method.

REFERENCES:

 

[1] T. Shi, X. Niu, W. Chen, and C. Xia, “Commutation torque ripple reduction of brushless DC motor in braking operation,”. IEEE Trans. Power Electron., vol.33 no.2, pp.1463-1475, Dec, 2018.

[2] H.S. Seol, J. Lim, D.W. Kang, J. S. Park and J. Lee, “Optimal design strategy for improved operation of IPM BLDC motors with low-resolution hall sensors,” IEEE Trans. Ind. Electro., vol.64, no.12, pp.9758-9766, Dec, 2017.

[3] M. Bertoluzzo, G. Buja, R. K. Keshri, and R. Menis, “Sinusoidal versus square-wave current supply of PM brushless DC drives: a conven-ience analysis,” IEEE Trans. Ind. Electro., vol.62, no.12, pp.7339-7349, Dec, 2015.

[4] G. Buja, M. Bertoluzzo, and R. K. Keshri, “Torque ripple-free operation of PM BLDC drives with petal-wave current supply,” IEEE Trans. Ind. Electro., vol.19, no.2, pp.4034-4043, July, 2015.

[5] J.-H. Song, and I. Choy, “Commutation torque reduction in brushless dc motor drives using a single dc current sensor,” IEEE Trans. Power Electron., vol.33 no.2, pp.312-319, Mar, 2004.

DC Environment for a Refrigerator With Variable Speed Compressor; Power Consumption Profile and Performance Comparison

 ABSTRACT:

 DC power distribution in residential sector has regained interest among researchers and industrial players as new electronics-based appliances became locally available. However, the compatibility of appliances with DC distribution systems still requires much research effort. This work mainly explores on the power consumption profile of an inverter-driven Variable Speed Controller (VSC-based) refrigerator that has not yet been analyzed as one of the most important household loads. This paper compares the power consumption in two scenarios; 1) using three supply configurations for a VSC-based refrigerator, a Battery-Inverter-Load, a Battery-Load and Grid-Load, and 2) using a same AC power source to supply a VSC-based refrigerator and a same-size conventional refrigerator. This analysis helps toward modeling and energy estimation of PV system applications involving storage batteries. A wireless monitoring circuit has been employed to handle temperature, current and voltage measurements with a high sampling rate to cover the potential surge power. The experimental measurements show a better performance on using DC over AC power source and the power rate consumed has a smooth pattern at the starting-on time until approach a rated power. The measured efficiency of the Battery-Load topology approaches 99% compared to that of the Battery-inverter-load topology, which is approximately 78.5%. It is also found that the tested refrigerator with Battery-Load topology consumes an energy amounting to 1.850 kWh daily, while with Battery-inverterload topology consumes 2.466 kWh daily under the same operating conditions. These results can serve as a model for modeling refrigerators and other appliances that adopt speed controller technology to drive their motors.

KEYWORDS:

1.      Compression refrigeration system

2.      Dc microgrid

3.      Total power consumption

4.      Building energy

5.      Modeling

6.      PV-battery systems

SOFTWARE: MATLAB/SIMULINK

CONCLUSION:

In this paper, experimental tests have been conducted to evaluate the performance of a VSC-based refrigerator and the effectiveness of using such refrigerator with the proposed DC level of voltage towards the solar PV applications. Based on the obtained results, the followings can be concluded:

1) Since the power circuit of the new commerciallyavailable inverter-driven refrigerators is already rectifying an AC input, it is possible to efficiently use such refrigerators with the DC voltage level that equivalent to the rectified grid AC without any modification.

2) Using VSC-based refrigerators with the proposed (Battery-Load) has better performance than that with the traditional (Battery-Inverter-Load) configuration of PV systems, which increases system efficiency, prolongs system storage and decreases cost through dispensing the use of inverter.

3) As compared with the traditional, the power consumption pattern of the VSC-based refrigerator does not have any surge power, in which it is possible avoiding the using a very high capacity inverter and batteries even with the traditional configuration Battery- Inverter-Load.

4) The outcome of the conducted experiments for power consumption patterns can serve for further analysis such as; refrigerator consumption modeling, forecasting, and control purposes.

5) It is recommended to use a VSC-based refrigerator for systems that have battery pack within the solar PV scheme as the system would be more efficient and economical.

REFERENCES:

[1] M. J. Al-Dulaimi, F. A. Kareem, and F. A. Hamad, ``Evaluation of thermal performance for natural and forced draft wet cooling tower,'' J. Mech. Eng. Sci., vol. 13, no. 4, pp. 6007_6021, Dec. 2019, doi: 10.15282/jmes.13.4.2019.19.0475.

[2] O. Ekren, S. Celik, B. Noble, and R. Krauss, ``Performance evaluation of a variable speed DC compressor,'' Int. J. Refrig., vol. 36, no. 3, pp. 745_757, May 2013, doi: 10.1016/j.ijrefrig.2012.09.018.

[3] C. L. Xia, Permanent Magnet Brushless DC Motor Drives and Controls. Hoboken, NJ, USA: Wiley, Apr. 2012.

[4] Mathwork. Residential Refrigeration Unit_MATLAB & Simulink. Accessed: Mar. 29, 2020. [Online]. Available: https://www.mathworks. com/help/physmod/hydro/examples/residential-refrigeration-unit.html

[5] F. A. Qayyum, M. Naeem, A. S. Khwaja, A. Anpalagan, L. Guan, and B. Venkatesh, ``Appliance scheduling optimization in smart home networks,'' IEEE Access, vol. 3, pp. 2176_2190, 2015, doi: 10.1109/ACCESS.2015.2496117.

Comprehensive Controller Implementation for Wind-PV-Diesel Based Standalone Microgrid

 ABSTRACT:

  In this paper, a comprehensive controller of a standalone microgrid is implemented, which has three dispersed generation units based on a wind, solar photovoltaic array and a diesel generator. The power ratio variable step perturb and observe method is applied to achieve maximum power point tacking of a solar photovoltaic array and a variable speed wind turbine coupled a permanent magnet brushless DC generator without rotor/wind speed sensors. Moreover, to ensure perfect synchronization of a diesel generator to the point of common coupling (PCC), a control algorithm is developed, which is based on in-phase and quadrature units. An active power control based on proportional-integral controller with anti-windup, is used for voltage and frequency regulation. The LCL filter based on virtual resistor, is used for power quality improvement at PCC. Simulation and test results are presented for the validation of proposed system using a prototype of 2 kW in the laboratory.

KEYWORDS:

1.      Standalone microgrid

2.      Solar photovoltaic array

3.      Wind turbine

4.      Diesel generator

5.      Active damping

6.      LCL filter based virtual resistor

7.      PCC voltage regulation

8.      power quality improvement and PI controller with anti-windup

SOFTWARE: MATLAB/SIMULINK

CONCLUSION:

The proposed microgrid for an isolated water treatment station based on three dispersed generation units; fixed speed DG, variable speed wind turbine and solar photovoltaic array, has been found to operate safely at sever conditions while supplying the load demand continuously at regulated voltage. The power ratio variable step P&O method for MPPT, has easily been implemented in a prototype to achieve high level of performance from wind turbine and solar photovoltaic array without any wind/speed sensors and without oscillations around MPP. The developed active power control based on AWPI controller with virtual resistor based active-damping for voltage regulation at PCC, has been implemented effectively and obtained results have demonstrated desired performance without saturation issue during transitions. The BES is protected from overcharging with utilization of excess power for space heating system as a DC dump load. DG has been used only as a backup energy source and its synchronization with PCC has been achieved safely without destabilizing the system operation. Switching harmonics are perfectly attenuated without losses using LCL filter based virtual resistor. Therefore, it is concluded that the comprehensive control proposed in this work for wind-solar diesel based standalone microgrid, is expected to be an effective alternative for uninterrupted supply in remote and isolated areas.

 REFERENCES:

[1] N. Mendis, K. M. Muttaqi, S. Perera, and M. N. Uddin, “Remote Area Power Supply System: An Integrated Control Approach Based on Active Power Balance,” IEEE Industry Applications Magazine, vol.21, no.2,pp.63-76, Mar. 2015.

[2] M. Rezkallah, S. Sharma, A. Chandra and B. Singh, “Implementation and control of small-scale hybrid standalone power generation system employing wind and solar energy,” in Proc. IEEE IAS Annual Meeting, 2016.

[3] Y. Tan, K. M. Muttaqi, P. Ciufo, and L. Meegahapola, “Enhanced Frequency Response Strategy for a PMSG-Based Wind Energy Conversion System Using Ultracapacitor in Remote Area Power Supply Systems,” IEEE Trans. Industry Applications., vol.53, no.1, pp. 549-558, Feb.2017.

[4] M. Rezkallah, A. Hamadi, A. Chandra, and B. Singh, “Hybrid AC-DC standalone system based on PV array and wind turbine,” in Proc. IECON, 2014, pp. 5533-5539.

[5] M. Rezkallah, A. Hamadi, A. Chandra, and B. Singh, “Real-Time HIL Implementation of Sliding Mode Control for Standalone System Based on PV Array Without Using Dumpload,” IEEE Trans. Sustainable Energy, vol. 6, no.4, pp. 1389-1398, Oct.2015.

 

Analysis of the Three-Phase Inverter Power Efficiency of a BLDC Motor Drive Using Conventional Six-Step and Inverted Pulsewidth Modulation Driving Schemes

ABSTRACT:

 In this paper, the three-phase inverter power efficiency of a brushless DC (BLDC) motor drive

is analyzed theoretically and verified experimentally. An inverted pulsewidth modulation driving scheme has higher power efficiency than a conventional six-step driving scheme, particularly under low rotor speed due to less diode conduction power loss of Sync metal–oxide–semiconductor field-effect transistors (MOSFETs). However, the difference in the power efficiency decreases as the rotor speed increases; for a rotor speed above 1000 r/min, the difference in the power efficiency is negligible. In addition, the power efficiency of the inverted driving scheme drops further than one for the conventional six-step driving scheme with sampling frequency increase. It is due to the additional switching power loss of Sync MOSFET. The theoretical analysis of power loss in a three-phase inverter verifies the experimental results.

KEYWORDS:

1.      Brushless dc (BLDC)

2.      Inverted pulsewidth modulation (PWM)

3.      Power efficiency

4.       Power loss

5.      Three-phase inverter

SOFTWARE: MATLAB/SIMULINK

 CONCLUSION:

In this paper, two different driving schemes for a BLDC motor drive, conventional six-step and inverted PWM, are analyzed in terms of power efficiency and loss to facilitate the understanding of the type and amount of the power loss in a three-phase inverter driving BLDC motor. Besides the conduction and switching power loss of HS and LS MOSFETs, the additional conduction and switching power loss from Sync MOSFET driven by an inverted PWM driving scheme must be compared to the conduction power loss from the diode of Sync MOSFET to select the more power-efficient driving scheme of the two schemes studied. The power efficiency of the three-phase inverter driven by the inverted PWM driving scheme is greater than that driven by the conventional six-step  driving scheme, particularly in the low rotor speed range. This is due to the reduction of the Sync MOSFET diode conduction power loss in the three-phase inverter driven by the inverted PWM driving scheme.

REFERENCES:

[1] J. Shao, D. Nolan, and T. Hopkins, “A novel direct back EMF detection for sensorless brushless DC (BLDC) motor drives,” in Proc. 17th Annu. IEEE Appl. Power Electron. Conf. Expo., Dallas, TX, USA, vol. 1, Mar. 2002, pp. 33–37.

[2] P. Yedamale, “Brushless DC (BLDC) motor fundamentals,” Microchip Technol. Inc., Chandler, AZ, USA, Appl. Note. 20:3-15, 2003.

[3] M. R. Rahman and P. Zhou, “Analysis of brushless permanent magnet synchronous motors,” IEEE Trans. Ind. Electron., vol. 43, no. 2, pp. 256–267, Apr. 1996.

[4] A. Hughes and W. Drury, Electric Motors and Drives: Fundamentals, Types and Applications. Oxford, U.K.: Newnes, 2013.

[5] J. S. Lawler, J. M. Bailey, J. W. McKeever, and J. Pinto, “Limitations of the conventional phase advance method for constant power operation of the brushless DC motor,” in Proc. IEEE Southeast Con, Apr. 2002, pp. 174–180.

An Incorporated Control Strategy of Commutation and Conduction Torque Ripples Mitigation for BLDCM Drives in Household Appliances

 ABSTRACT:

In this paper, an incorporated control strategy of both commutation and conduction torque ripples mitigation for brushless DC machine (BLDCM) with the sinusoidal back electromotive force(EMF) is proposed to reduce the vibration and noise of household appliances for higher comfortable capability. Based on the combined torque ripple analysis with respect to the stator flux linkage trajectory, a three-phase voltage vector injection (TVVI) method is designed and implemented in the commutation interval to compensate the sharp dips of the stator _ux trajectory for the mitigation of the commutation torque ripple, and duty cycle of the injected voltage vector could be regulated automatically. Then, a simple direct power control (DPC) method with TVVI in the PWM modulation is employed as inner-loop for BLDCM to obtain the desired waveforms of currents with the speci_c dc-link current sampling method, and the reduction of both conduction and commutation torque ripples is achieved. The proposed incorporated control strategy is validated through simulation experiment results, and the effect on the torque ripples are compared with the traditional approaches.

KEYWORDS:

1.      Incorporated control strategy

2.      Commutation and conduction torque ripples mitigation

3.      Direct power control

4.      Three-phase voltage vector injection

5.      Stator flux trajectory

 SOFTWARE: MATLAB/SIMULINK

 CONCLUSION:

In this manuscript, an incorporated control strategy of commutation and conduction torque ripples mitigation for BLDCM with the sinusoidal back EMF in household appliances is proposed. Unlike the conventional separated analysis of the commutation and conduction torque ripples, a combined torque ripples analysis depending on the stator flux linkage trajectory is introduced. A three-phase voltage vector injection(TVVI) method is designed and implemented in the commutation interval to compensate the sharp dips of the stator _ux trajectory for the mitigation of the commutation torque ripple, then, a simple DPC is employed as inner-loop with the specific dc-link current sampling method to replace the traditional current-loop, and the desired waveforms of currents could be obtained for the conduction torque ripple mitigation. Moreover, the TVVI and DPC control schemes are combined together to achieve the torque ripples of less than 0.1Nm, which is only 12.5% of that in the traditional current-loop control method. From the results of the comparison tests, the proposed method ensures a signicant reduction of the commutation and conduction torque ripple for BLDCM with the low-cost property, and the effectiveness and feasibility have been extended to the other PWM patterns and wide speed range. Thus, BLDCM with the improved higher torque performance can also be applied to the other applications, where, the cost and torque ripples are of great concern.

 REFERENCES:

[1] R. Carlson, M. Lajoie-Mazenc, and J. C. D. S. Fagundes, ``Analysis of torque ripple due to phase commutation in brushless DC machines,'' IEEE Trans. Ind. Appl., vol. 28, no. 3, pp. 632_638, May 1992.

[2] Y.-K. Lin and Y.-S. Lai, ``Pulsewidth modulation technique for BLDCM drives to reduce commutation torque ripple without calculation of commutation time,'' IEEE Trans. Ind. Appl., vol. 47, no. 4, pp. 1786_1793, Jul./Aug. 2011.

[3] J. Shi and T.-C. Li, ``New method to eliminate commutation torque ripple of brushless DC motor with minimum commutation time,'' IEEE Trans. Ind. Electron., vol. 60, no. 6, pp. 2139_2146, Jun. 2013.

[4] F. Yang, C. Jiang, A. Taylor, H. Bai, A. Kotrba, A. Yetkin, and A. Gundogan, ``Design of a high-ef_ciency minimum-torque-ripple 12-V/1-kW three-phase BLDC motor drive system for diesel engine emis- sion reductions,'' IEEE Trans. Veh. Technol., vol. 63, no. 7, pp. 3107_3115, Sep. 2014.

[5] C. K. Lad and R. Chudaman, ``Simple overlap angle control strategy for commutation torque ripple minimisation in BLDC motor drive,'' IET Electr. Power Appl., vol. 12, no. 6, pp. 797_807, Jul. 2018.

A Single-Stage Sensorless Control of a PV based Bore-Well Submersible BLDC Motor

 ABSTRACT:

 Permanent magnet (PM) brushless dc (BLDC) motor based photovoltaic (PV) water pumps are becoming popular in rural areas due to their higher efficiency, reliability, etc compared to induction motor based pumps. The water table level in these rural areas is typically more than 15 m. Hence, deep borewell submersible motors are used for extracting potable water from the water table. The motor and controller are submerged in the water table, and have more temperature rise due to the poor ambience. Thus, control of a PM BLDC motor with halleffect based position sensor is unreliable in these environments due to the temperature sensitivity of the hall-effect sensors. In this paper, a single-stage sensorless control of a deep borewell submersible ferrite PM BLDC motor drive is presented. A position sensorless control scheme is implemented to eliminate the use of hall-sensors, thus improving reliability of the overall system. Further, the challenges involved in the control of a deep bore-well submersible ferrite PM BLDC motor are elaborated. The prototype of a 1.5 kW submersible BLDC motor drive is fabricated and the experimental results are presented.

KEYWORDS:

1.      Permanent magnet motors

2.      Brushless dc machines

3.      Sensorless control

4.      Photo-voltaic and bore-well

 SOFTWARE: MATLAB/SIMULINK

 CONCLUSION:

A single-stage sensorless control of a deep bore-well PV based submersible ferrite PM BLDC motor is presented. Borewell pumps have poor ambience and thus hall-effect sensor based control is not reliable in these environments. Further, the PV based water pumps are usually installed in remote rural areas where reliability is a critical factor. Hence, a position sensorless control scheme is implemented to eliminate the use of hall-sensors, thus improving reliability of the overall system. Further, unlike in the existing literature a single stage three phase dc-ac converter is used for achieving both MPP operation and motor commutation. The challenges involved in the fabrication of a deep bore-well submersible ferrite PM BLDC motor are elaborated. The prototype of a 1.5 kW submersible BLDC motor sensorless drive is fabricated and the experimental results are presented. The measured efficiencies of the ferrite BLDC motor and the dc-ac inverter at rated power are 87% and 92%, respectively.

REFERENCES:

[1] M. Mahmoud, “Experience results and techno-economic feasibility of using photovoltaic generators instead of diesel motors for water pumping from rural desert wells in Jordan,” IEE Proceedings C - Generation, Transmission and Distribution, vol. 137, no. 6, pp. 391–394, Nov 1990.

[2] J. L. Davies and M. Malengret, “Application of induction motor for solar water pumping,” in Proc. 3rd AFRICON ’92 Conf., Ezulwini Valley, Sep 1992, pp. 209–212.

[3] E. Muljadi, “PV water pumping with a peak-power tracker using a simple six-step square-wave inverter,” IEEE Trans. Ind. Appl., vol. 33, no. 3, pp. 714–721, May 1997.

[4] J. V. M. Caracas, G. d. C. Farias, L. F. M. Teixeira, and L. A. d. S. Ribeiro, “Implementation of a high-efficiency, high-lifetime, and low-cost converter for an autonomous photovoltaic water pumping system,” IEEE Trans. Ind. Appl., vol. 50, no. 1, pp. 631–641, Jan 2014.

[5] T. R. Brinner, R. H. McCoy, and T. Kopecky, “Induction versus permanent-magnet motors for electric submersible pump field and laboratory comparisons,” IEEE Trans. Ind. Appl., vol. 50, no. 1, pp. 174–181, Jan 2014.

A Simple Voltage Modulator Scheme for Torque Ripple Minimization in a Permanent Magnet Brushless DC Motor

 ABSTRACT:

 This paper presents a simple dc-link voltage modulation scheme to minimize the commutation torque ripple in a Permanent Magnet Brushless DC Motor (PMBLDCM). Maintaining a constant current in the non-commutating (NC) phase helps to minimize the torque ripple, which can be achieved by boosting the motor input voltage whenever two phase currents are undergoing commutation. At low speeds, since the required ac voltage at commutation is also less than nominal, the standard PWM operation of inverter with the nominal dc-link voltage suffices. However, at higher speeds, a momentary (only during the commutation interval) boost in the dc-link voltage (above the nominal level) is needed to ensure boost in motor voltage, hence a steady current in the NC phase. In the proposed scheme, the dc voltage boost at higher speeds is obtained by connecting two capacitors in series which are normally connected in parallel across the dc-link. The proposed scheme is verified for a 1hp PMBLDCM drive through simulations and experiments in the laboratory. Results exhibit a notable improvement in reducing the torque ripple.

KEYWORDS:

 

1.      Dc-link voltage modulation

2.      Permanent magnet brushless dc motor

3.      Commutation torque ripple

 SOFTWARE: MATLAB/SIMULINK

 CONCLUSION:

A simple capacitor switching based dc-link voltage modulation scheme to minimize the commutation torque ripple in a PMBLDCM is presented in this paper. Maintaining a steady value of the NC phase current by altering the dc-link voltage can effectively minimize the torque ripple. PWM control of inverter at low speed range and PWM control along with dc-link voltage modulation at high speed range (proposed scheme) ensure a low torque ripple. A simple additional circuitry is employed to momentarily boost the dc voltage to the inverter in the high speed range. The DVM scheme offers a significant diminution in torque ripple and a smooth and noise free operation of the PMBLDC machine.

REFERENCES:

 

[1] R. Krishnan, “Electric Motor Drives Modeling, Analysis and Control”, PHI Learning Private Limited, 2001.

[2] P. Pillay and R. Krishnan, “Modeling, simulation, and analysis of permanent-magnet motor drives, Part II: The permanent magnet synchronous drive,” IEEE Trans. Ind. Appl., vol. IA-25, no. 2, pp.265–273, Mar./Apr. 1989.

[3] R. Carlson, L.-M. Milchel, and J. C. Fagundes, “Analysis of torque ripple due to phase commutation in brushless dc machines,” IEEE Trans. Ind.Appl., vol. 28, no. 3, pp. 632–638, May/Jun. 1992.

[4] H. Lu, L. Zhang, and W. Qu, “A new torque control method for torque ripple minimization of BLDC motors with un-ideal back EMF,” IEEETrans. Power Electron., vol. 23, no. 2, pp. 950–958, Mar. 2008.

[5] J. Shi and T. C. Li, “New method to eliminate commutation torque ripple of brushless DC motor with minimum commutation time,” IEEE Trans.Ind. Electron., vol. 60, no. 6, pp. 2139–2146, Jun. 2013