comparison of trapezoidal and sinusoidal pwm techniques

POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 18 | NUMBER: 4 | 2020 | DECEMBER

Comparison of Trapezoidal and Sinusoidal PWMTechniques for Speed and Position Control

of PMSM

Erdal BEKIROGLU 1, Ahmet DALKIN 2

1Department of Electrical and Electronics Engineering, Faculty of Engineering,Bolu Abant Izzet Baysal University, BAIBU Golkoy Yerleskesi, 14030 Bolu, Turkey

2Department of Electronics and Automation, Yesilyurt Demir Celik Vocational School, Ondokuz MayisUniversity, Organize Sanayi Bolgesi Sosyal Tesisler Alanı, 513. Sk. No:6, 55300 Samsun, Turkey

[email protected], [email protected]

DOI: 10.15598/aeee.v18i4.3842

Abstract. In this article, speed and position controlsof Permanent Magnet Synchronous Motor (PMSM)are performed by using a genetic algorithm-based con-troller. Hall Effect sensors have been used to obtain po-sition data of the motor. Since Hall Effect sensors havebeen mounted, PMSM has been driven as a BrushlessDC (BLDC) motor. Sinusoidal and trapezoidal cur-rent reference models have been used in the control sys-tem. The proposed control system has been operated forspeed control as well as position control of the motor.The developed genetic-based speed and position controlmethod has been tested for both trapezoidal and sinu-soidal PWM commutation techniques. The results ob-tained from these commutation techniques have beencompared. Speed and position results of the motor havebeen obtained under the different load and operatingconditions. The results reveal that the proposed controlsystem is reliable, robust and effective.

Keywords

Permanent Magnet Synchronous Motor, Sinu-soidal Commutation, Speed and Position Con-trol, Trapezoidal Commutation.

1. Introduction

Recently, Permanent Magnet Synchronous Motors(PMSMs) are used in servo systems due to their su-periorities, such as high efficiency, power factor, hightorque/weight ratio, and high torque/inertia ratio.Therefore, PMSM becomes the first research subject

for many industrial variable speed applications that re-quire speed and position control [1] and [2].

However, the performances of the PMSMs arevery sensitive to parameter and load variations.To overcome these problems, several modern con-trol strategies, such as PI (Proportional-Integral) orPID (Proportional-Integral-Derivative) control, FuzzyLogic Control, Neural Network and Genetic AlgorithmControl methods are proposed for speed control [3].

In PMSMs, it is crucial to determine the rotor posi-tion and to perform commutation exactly at the ac-curate time. Hall Effect sensors and encoders areused to receive the information of position and speedthrough the rotor. Position and speed data can bereceived without using sensors; nevertheless, the mi-croprocessor must have both high memory capacityand rapid process time.

1.1. Related Works

Several works have reported speed and position con-trol of the PMSM with different driving and controltechniques. C. Wu controlled the speed and posi-tion of a BLDC with a Hall Effect sensor througha PI Controller by using trapezoidal commutation tech-nique [4]. A. Simpkins used analogous Hall Effect sen-sors in order to be able to perform positional esti-mation in BLDC pancake motor, a quite small typeof motor [5]. J. Park proposed the speed test sys-tem of the motor by applying current reference withPI-based drive system. In addition, a stepwise posi-tion reference was applied to the system and the posi-tion control was performed through Hall Effect sensors.Park corrected the position-error arising from paramet-

c© 2020 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 207


rical errors, impairments of current on commutationpoints and the waveform of back Electromotive Force(EMF) by using a separate PI Controller with the dif-ferent current references [6]. S. Dehghan, unlike tradi-tional approaches to speed control of PMSM, carriedout offline tuning method and reference speed followedthe actual speed smoothly [7]. K. Thangarajan real-ized the speed control of PMSM with Model Predic-tive Control (MPC) investigator. In addition, positionand torque control was carried out using recommendedinvestigators [8]. S. Sakunthala described the perfor-mance and comparisons of BLDC motor and PMSMdrives [9]. H. Li developed a new type of sensorlessdrive with self-correction of commutation points forhigh-speed control of BLDC motor with nonideal backEMF form [10]. S. Murali proposed a new controlscheme for the BLDC motor based on tuning of slid-ing mode surface parameters, and a search algorithmis used to set the parameters of the sliding mode con-troller. In this way, speed comparison is realized withPI and PID controls [11]. I. Vesely designed model ref-erence adaptive current controller for PMSM and usedd-q axis current equations in the rotating referenceframe [12].

In this article, speed and position control of PMSMhas been performed by using Hall Effect sensor. A con-ventional PI Controller has been used for the speedcontrol, while P Controller has been used for the po-sition control. The coefficients of PI and P Con-trollers have been achieved online through a geneticsearch algorithm. In this way, optimum coefficientsare determined so that the actual speed and positioncan get rapidly through the reference speed and posi-tion without exceeding. In the article, current refer-ence has been firstly applied to the motor in the si-nusoidal waveform and then in the trapezoidal wave-form. Speed results and position results of the mo-tor have been obtained for each reference and then,these results have been compared under the differentload conditions. Current control is carried out withthe hysteresis band current controller. The d-q ref-erence frame transformation is not required becausethe proposed controller has a fast response and nostatic error. An encoder is generally used to get speedand position data from a PMSM. However, there isno possibility of utilizing an encoder, and cost-effectiveHall Effect sensors are also used. When Hall Effect sen-sors are used, a PMSM needs to be driven as a BLDC.Variations in the speed and position of PMSM usingHall Effect sensors have been shown in the article.The proposed genetic algorithm-based speed and po-sition control of PMSM has been tested for differentload and operating conditions. Obtained results showthat the control method is precise, effective, available,and applicable for the control of PMSM.

2. PMSM Dynamics

The equivalent circuit of PMSM motor and a PWMinverter are shown in Fig. 1.

Vdc

Sa

Sa

Sb

Sb Sc

Sc

ia

ib

ic

Ra

Rb

Rc

ea

eb

ec

N

PWM Inverter PMSM

Laa

Lbb

Lcc

Fig. 1: PMSM model and inverter.

The stator voltage equations of PMSM are expressedin Eq. (1). va

vbvc

=

Rs 0 00 Rs 00 0 Rs

· iaibic

+

+

Lss −M 0 00 Lss −M 00 0 Lss −M

·· ddt·

iaibic

+

eaebec

,(1)

where va, vb, and vc are the phase voltages, ia, ib,and ic are the phase currents, Rs is the PMSM’s sta-tor resistance, ea, eb, ec are the EMFs of phase wind-ings. In Eq. (1), the expression of Lss −M is equalto the PMSM’s inductance Ls presented by Eq. (2).

Ls = Lss−M = L1 +Lms−(− 1

2Lms

)= L1 +

3

2Lms.

(2)

In Eq. (2), Lms is self-inductance, Lss is the to-tal phase inductance, including leakage L1, and M isthe mutual inductance. Equation (1) is rearranged intostate-space form as in Eq. (3).

d

dt·

iaibic

=1

Ls·

vavbvc

·RsLs

0 0

0RsLs

0

0 0RsLs

·

·

iaibic

− 1

Ls·

eaebec

.(3)

EMFs generated by field flux connections of the per-manent magnet are calculated using the followingEq. (4).



eaebec

= −λfωr ·

sin(θr)

sin(θr − 2π3 )

sin(θr + 2π3 )

, (4)

where θr is the rotor position and the generated elec-trical torque is defined as:

Te = −λf ·p

2·

ia sin (θr) + ib sin

(θr −

2π

3

)+ ic sin

(θr +

2π

3

).

(5)

Finally, the rotor position and rotor speed can bewritten as:

d

dtωr =

p

2

(Te − TL −B

(2

P

)ωr

)J

, (6)

d

dtθr = ωr. (7)

3. PMSM Control Strategy

3.1. P and PI Controller

The speed loop is a dynamic model of motor and in-cludes reference speed, speed feedback, and speed con-troller. In speed loop, measured or estimated motorspeed is approximated to reference speed by using ac-tual speed controller [13].

Artificial intelligent control techniques like fuzzylogic, artificial neural networks or genetic algorithmsare used as speed controllers of the motor, besidesadaptive control techniques, such as sliding mode con-trol and variable structure control [14].

The block diagram on the time scale of PI controlleris demonstrated in Fig. 2. Here, et expresses the er-ror signal, Kp and Ki modulation and integral gain,and yt the output signal. Equation (8) shows the PIequation used for the speed loop and Eq. (9) showsthe P equation used for the position.

Fig. 2: Proportional-Integral controller block diagram.

yt = Kpet +Ki

∫etdt, (8)

yt = Kpet. (9)

3.2. Hysteresis Band CurrentController

All sources fed by 3-phase voltage source inverters gen-erally use current feedback. Therefore, the perfor-mance of the inverter depends largely on the currentcontrol technique used in [15], [16], [17], and [18], re-spectively. The task of the hysteresis band current con-troller is to ensure that the actual current of the motorfollows the reference current generated within a prede-termined band. Hysteresis band’s current controller iseasy to implement and provides effective current con-trol against changes in load and source parameters pre-sented in [19], [20], [21], and [22], respectively.

Hysteresis current controllers switch the powerswitches in the inverter with the appropriate sequenceto keep the error signal obtained by comparing the cur-rent measured from the motor windings with the refer-ence current in a given range. The structure of the hys-teresis current controller is given in Fig. 3. Here i∗a isthe reference current of phase a, ia is measured actualcurrent of phase, ∆ia is hysteresis bandwidth, and Sais switching signal.

The value of the switching frequency in hysteresiscurrent controllers depends on the bandwidth. Reduc-ing the hysteresis bandwidth ensures that the actualcurrent is closer to the reference current, but should notexceed the switching frequency of the power switchesused in the inverter circuit [23].

(a)

(b)

Fig. 3: (a) Block diagram of the hysteresis band currentcontroller, (b) Phase current of current controllerand switching states.



Fig. 4: PMSM drive system.

Furthermore, the switching frequency varies depend-ing on the size and frequency of the reference signal.Besides the advantages of being simple in structureand high accuracy, it has disadvantages like switch-ing frequency is variable, and switching losses are high.When examining Fig. 3, the actual current value is sub-tracted from the reference current for any phase cur-rent. Switch Sa is switched-on if the obtained value isgreater than or equal to the positive value of the hys-teresis band value. Switch Sa is switched-on if the ob-tained value is less than or equal to the negative valueof the hysteresis band value [24].

3.3. PMSM Drive System

The configuration of the PMSM drive and controlsystem used for the simulations is shown in Fig. 4.The model has not required any transformation such asPark and Clark reference frame transformation becauseit is able to estimate nominal operating conditions eas-ily.

The actual speed value of the motor, ωr, is calcu-lated through the use of the signals from the positionsensor. Speed error eω is calculated, which is the dif-ference between the desired speed value ω∗

r and the ac-tual speed value. In the study, PI Controller is usedas a speed controller and P Controller as a positioncontroller. The optimum coefficients of Kp, Ki in PIand P Controllers were produced by the genetic searchalgorithm. Three-phase reference currents are obtainedby using electrical position information with controlsignals passed through the controllers. The resultingreference currents are used in the hysteresis band cur-rent controller. PWM signals are generated by compar-ing the actual current values obtained from the currentsensor with the reference positions [25].

4. Structure of Genetic SearchAlgorithm

In the genetic algorithm search steps, each vari-able/data structure used as a solution candidate iscalled a chromosome (individual). All of these chro-mosomes are called the population, and the chromo-somes in the population at each stage in the programcycle are defined as a generation. In addition, accord-ing to the data structure chosen to be used as a chro-mosome at the beginning of the program, each chromo-some consists of genes that represent bits of the datastructure if it is an integer, and elements of the se-quence if it is a sequence. According to the “strongis survived” rule, the fitness calculated for each chro-mosome is chosen according to the degree of eligibilityof the chromosome in each step in order to surviveother operations that need to be determined.

Each conventional controller coefficient representsa gene. In classical genetic algorithms, the binary cod-ing technique is used. In the present study, integerdecimal numbers were preferred to reduce the geneticalgorithm processing time.

When determining the population, the numberof chromosomes and the selection of initial value areimportant. If the population is large, it takes a longtime for the genetic algorithm to reach the desired solu-tion. Conversely, if the population is selected too small,the diversity of chromosomes within the population willdecrease, and population remains at local minimum.Therefore, it is very important to select as large a pop-ulation as possible, taking into account the algorithmcycle time. In this article, a population of 100 chromo-somes is determined according to the trial and errormethod. The fitness function used in the study is de-fined as follows [25]:



fitness function =1

1 +

N∑k=1

|eω(k)|

. (10)

The fitness function is the basic parameter that in-dicates which chromosome will be present in the nextgeneration. The higher suitability value of a chro-mosome is so important. The PMSM drive systemis run for each chromosome sequence. Fitness valuesare available for all chromosomes in the population.The genetic algorithm is terminated if the previouslydetermined conformity value is captured. The chro-mosome with the highest fitness value is stored sothat the most appropriate activity functions are ob-tained. In order to produce the next generation, fami-lies are determined among the chromosomes in the pop-ulation based on their fitness values. In this study,Rank-based and elitism methods, which are a spe-cial method used in the selection of families, were ap-plied [25], [26], [27], and [28].

First of all, chromosomes in the population wereranked from the highest to the lowest according to theirvalue. The chromosomes with the highest eligibilityvalue were both selected as a family and directly in-volved in the next generation. Thus, the best perfor-mance is maintained until the chromosome algorithmis completed. In addition, the crossing process wascarried out at several points to form the chromosomesrequired for the next generation [25].

The chromosomes crossed were randomly selectedand the optimum value of 0.75 was used as the proba-bility value. The crossing points were again determinedby random selection.

The mutation was applied to increase the diversityof the chromosomes obtained at the end of the crossingand the probability of each chromosome mutation wasselected as the optimum value of 0.25.

The following parameters are used in the geneticalgorithm. Rank-based and elitism methods wereused and 100 chromosomes were determined accord-ing to the trial and error method. The chromosomescrossed were randomly selected and a probability valueof 0.75 was used. The probability of each chromosomemutation was selected as the optimum value of 0.25.

5. Results

Tests for different speed and position references wereperformed using the PMSM drive system and controllerdescribed in Sec. 3. and Sec. 4. . The actualparameters of the PMSM used in the simulations aregiven in Tab. 1.

Tab. 1: PMSM and inverter parameters.

Parameters ValuesRated voltage (V) 300Rated power (kW) 3Rated speed (rpm) 3000

Stator resistance per phase (Ω) 2.0Stator inductance per phase (H) 0.01

Moment of inertia (Kg·m2) 0.0124Friction coefficient (Wb) 0.0012

Pole number 8Switching frequency of inverter (kHz) 1

Using the proposed PMSM drive and control sys-tem described in Sec. 3. , simulations were per-formed for both speed and position references with si-nusoidal reference and trapezoidal reference currents.The performance of the controller is determined bythe actual speed and position of the motor preciselyfollows the reference commands. For this purpose,the reference current was taken as a sinus wave by sinu-soidal commutation technique; at 500 rpm, 1500 rpm,and 3000 rpm. The actual speed changes were investi-gated according to the reference speed. Then the ref-erence current was taken as a trapezoidal wave bytrapezoidal commutation technique; the actual speedfollows the reference speed of 500 rpm, 1500 rpm,and 3000 rpm.

The reference current was taken as sinus by the si-nusoidal commutation technique and it was investi-gated how much the actual position changes accord-ing to the reference position in 2π, π and

π

2radians.

Then the reference current was taken as trapezoidal bytrapezoidal commutation technique and it was inves-tigated how much the actual position changes accord-ing to the reference position in 2π, π, and

π

2radians.

For each value, the variations of the speed and positionsunder the different load conditions were also examined.

Figure 5 shows the sinusoidal reference current ap-plied to the system. The reference current is limitedto 10 A in order to avoid high current at initial stage.Sinusoidal reference current shape for 500 rpm refer-ence speed can be seen in the figure.

Fig. 5: Sinusoidal current reference.



Figure 6 shows the trapezoidal reference current ap-plied to the system. The reference current is limitedto 10 A in order to avoid high current at initial state.Trapezoidal reference current shape for 500 rpm refer-ence speed is shown in the figure.

Fig. 6: Trapezoidal current reference.

In Fig. 7, Fig. 8 and Fig. 9, the results obtainedin both sinusoidal reference current and trapezoidalreference current are given for the reference speedof 500 rpm, 1500 rpm, and 3000 rpm, respectively.The tests were carried out under no-load condition.The coefficients of PI Controller system were deter-mined by Genetic Search Algorithm. Kp = 99.945andKi = 3.0776 coefficients were obtained from the ge-netic algorithm. As can be seen from the figures,the speed in the sinusoidal reference current is muchfaster and ideal for climbing and reaching stability thanthe actual speed in the trapezoidal reference.

Fig. 7: Sinusoidal and trapezoidal PMSM speed for 500 rpm.

In Fig. 10, Fig. 11 and Fig. 12, the results obtainedin both sinusoidal reference current and trapezoidalreference current are given for the reference speedof 500 rpm, 1500 rpm, and 3000 rpm. Tests werecarried out at 3 Nm. The coefficients of the PI Con-troller system were determined by genetic search al-gorithm. Since only the fitness function of the geneticsearch algorithm is determined as in Eq. (10), the valueof the load torque increases and some overshoot occursat PMSM speeds. As can be seen, the actual speed inthe sinusoidal reference current can rise, and reachingstability is much faster and ideal than the trapezoidalreference current.





The following figures show the position controlof the PMSM. A reference position is applied to the mo-tor as shown in the figures and it is observed whetherthe actual position of the motor closely follows the ref-erence position. During the control, the sinusoidal ref-



erence current and then the trapezoidal reference cur-rent were applied to the motor as used in the fastgraphics.

Figure 13, Fig. 14 and Fig. 15 show the results forboth the sinusoidal reference current and the trape-zoidal reference current for the reference position,which is 2π, π and

π

2radians. The tests were carried

out under a no-load condition. The coefficient of P con-trol system is determined by Genetic Search Algorithm.Kp = 72.36 coefficient was obtained from the ge-netic algorithm. As seen, the actual position track-ing and stability in the sinusoidal reference current aremuch faster and ideal than the actual position trackingand stability in the trapezoidal reference current.


Fig. 13: Sinusoidal and trapezoidal PMSM position for 2π rad.

Fig. 14: Sinusoidal and trapezoidal PMSM position for π rad.

Figure 16, Fig. 17 and Fig. 18 show the results forboth the sinusoidal reference current and the trape-

zoidal reference current for the reference position,which is 2π, π and

π

2radians, respectively. Tests

were performed at 3 Nm load torque. The coefficientsof the PI Controller system were determined by GeneticSearch Algorithm. Since only the Genetic Search Algo-rithm is determined as in the fitness function definedin Eq. (10), as the load torque increases, some over-shoots occur at actual speeds. As seen from the figures,the rising and stability of the actual velocity in the si-nusoidal reference current are much faster and idealthan the trapezoidal reference current.

Fig. 15: Sinusoidal and trapezoidal PMSM position forπ

2rad.

Fig. 16: Sinusoidal and trapezoidal PMSM position for 2π rad.

Fig. 17: Sinusoidal and trapezoidal PMSM position for π rad.



Fig. 18: Sinusoidal and trapezoidal PMSM position forπ

2rad.

6. Conclusion

In this article, speed and position control of the PMSMwas performed using a genetic algorithm-based con-troller. In order to get position information of PMSM,Hall Effect sensors are preferred owing to cost-effectivethan the encoder. When using a Hall Effect sen-sor, PMSM should be driven like BLDC. In this case,the reference speed and position tracking of the mo-tor will be slower than the sinusoidal state as de-scribed above. The genetic algorithm-based modelhas been applied both for speed and position controlof the motor successfully. Sinusoidal and trapezoidalreference current models were applied to the systemand simulation studies of the control system were car-ried out at different speeds and positions. As seenfrom the results, when sinusoidal reference current isapplied to the PMSM, where the back EMF shapeis sinusoidal, the reference speed and position appliedto the motor are observed to be much faster and morestable than the trapezoidal reference current.

References

[1] LEE, Y. na J.-I. HA. High efficiency dualinverter drives for a PMSM considering fieldweakening region. In: Proceedings of The 7thInternational Power Electronics and Mo-tion Control Conference. Harbin: IEEE,2012, pp. 1009–1014. ISBN 978-1-4577-2085-7. DOI: 10.1109/IPEMC.2012.6258939.

[2] ELMAS, C., O. USTUN and H. H. SAYAN.A neuro-fuzzy controller for speed controlof a permanent magnet synchronous motordrive. Expert Systems with Applications. 2008,vol. 34, iss. 1, pp. 657–664. ISSN 0957-4174.DOI: 10.1016/j.eswa.2006.10.002.

[3] ELMAS, C. and O. USTUN. A hybrid controllerfor the speed control of a permanent magnet syn-chronous motor drive. Control Engineering Prac-

tice. 2008, vol. 16, iss. 3, pp. 260–270. ISSN 0967-0661. DOI: 10.1016/j.conengprac.2007.04.016.

[4] WU, H.-C., M.-Y. WEN and C.-C. WONG. Speedcontrol of BLDC motors using hall effect sen-sors based on DSP. In: 2016 International Confer-ence on System Science and Engineering (ICSSE).Puli: IEEE, 2016, pp. 1–4. ISBN 978-1-4673-8966-2. DOI: 10.1109/ICSSE.2016.7551633.

[5] SIMPKINS, A. and E. TODOROV. Posi-tion estimation and control of compact BLDCmotors based on analog linear Hall effectsensors. In: Proceedings of the 2010 Amer-ican Control Conference. Baltimore: IEEE,2010, pp. 1948–1955. ISBN 978-1-4244-7427-1.DOI: 10.1109/ACC.2010.5531357.

[6] PARK, J.-W., W.-Y. AHN, J.-M. KIM andB.-M. HAN. Sensorless control algorithmof BLDC motors with current model. In: 2013IEEE International Conference on Indus-trial Technology (ICIT). Cape Town: IEEE,2013, pp. 1648–1652. ISBN 978-1-4673-4569-9.DOI: 10.1109/ICIT.2013.6505920.

[7] DEHGHAN, S. M., A. J. ABIANEHand M. MANSOURIAN. Offline self-tuningalgorithm for speed controllers consider-ing position sensor quantisation error. In-ternational Journal of Electronics. 2020,vol. 107, iss. 12, pp. 1–21. ISSN 1362-3060.DOI: 10.1080/00207217.2020.1819437.

[8] THANGARAJAN, K. and A. SOUNDAR-RAJAN. Performance comparison of perma-nent magnet synchronous motor (PMSM)drive with delay compensated predictive con-trollers. Microprocessors and Microsystems.2020, vol. 75, iss. 1, pp. 1–10. ISSN 0141-9331.DOI: 10.1016/j.micpro.2020.103081.

[9] SAKUNTHALA, S., R. KIRANMAYIand P. N. MANDADI. A study on industrial mo-tor drives: Comparison and applications of PMSMand BLDC motor drives. In: 2017 InternationalConference on Energy, Communication, Data An-alytics and Soft Computing (ICECDS). Chennai:IEEE, 2017, pp. 537–540. ISBN 978-1-5386-1887-5. DOI: 10.1109/ICECDS.2017.8390224.

[10] LI, H., X. NING and W. LI. Implemen-tation of a MFAC based position sensor-less drive for high speed BLDC motors withnonideal back EMF. ISA Transactions. 2017,vol. 67, iss. 1, pp. 348–355. ISSN 0019-0578.DOI: 10.1016/j.isatra.2016.11.014.

[11] MURALI, S. B. and P. M. RAO. Adaptive slidingmode control of BLDC motor using cuckoo search


http://dx.doi.org/10.1109/IPEMC.2012.6258939

http://dx.doi.org/10.1016/j.eswa.2006.10.002

http://dx.doi.org/10.1016/j.conengprac.2007.04.016

http://dx.doi.org/10.1109/ICSSE.2016.7551633

http://dx.doi.org/10.1109/ACC.2010.5531357

http://dx.doi.org/10.1109/ICIT.2013.6505920

http://dx.doi.org/10.1080/00207217.2020.1819437

http://dx.doi.org/10.1016/j.micpro.2020.103081

http://dx.doi.org/10.1109/ICECDS.2017.8390224

http://dx.doi.org/10.1016/j.isatra.2016.11.014


algorithm. In: 2018 2nd International Conferenceon Inventive Systems and Control (ICISC). Coim-batore: IEEE, 2018, pp. 989–993. ISBN 978-1-5386-0807-4. DOI: 10.1109/ICISC.2018.8398950.

[12] VESELY, I., L. VESELY and Z. BRADAC.MRAS identification of permanent magnet syn-chronous motor parameters. IFAC-PapersOnLine.2018, vol. 51, iss. 6, pp. 250–255. ISSN 2405-8963.DOI: 10.1016/j.ifacol.2018.07.162.

[13] AGRAWAL, J. and S. BODKHE. ExperimentalStudy of Low Speed Sensorless Control of PMSMDrive Using High Frequency Signal Injection. Ad-vances in Electrical and Electronic Engineering.2016, vol. 14, iss. 1, pp. 29–39. ISSN 1804-3119.DOI: 10.15598/aeee.v14i1.1564.

[14] DEMIRBAS, S. Control of A Permanent Mag-net Synchronous Motor Without Position Sensor.Ankara, 2001. Dissertation. Gazi University. Su-pervisor: Gungor Bal.

[15] PILLAY, P. and R. KRISHNAN. Control charac-teristics and speed controller design for a high per-formance permanent magnet synchronous motordrive. IEEE Transactions on Power Electronics.1990, vol. 5, iss. 2, pp. 151–159. ISSN 1941-0107.DOI: 10.1109/63.53152.

[16] RAHMAN, M. A., T. S. RADWAN, A. M. OS-HEIBA and A. E. LASHINE. Analysis of cur-rent controllers for voltage-source inverter. IEEETransactions on Industrial Electronics. 1997,vol. 44, iss. 4, pp. 477–485. ISSN 1557-9948.DOI: 10.1109/41.605621.

[17] MALESANI, L. and P. TOMASIN. PWM currentcontrol techniques of voltage source converters-a survey. In: Proceedings of the 19th Inter-national Conference on Industrial Electronics,Control and Instrumentation. Maui: IEEE,1993, pp. 670–675. ISBN 978-0-7803-0891-6.DOI: 10.1109/IECON.1993.339000.

[18] KAZMIERKOWSKI, M. P. and L. MALE-SANI. Current control techniques for three-phase voltage-source PWM converters: A sur-vey. IEEE Transactions on Industrial Electronics.1998, vol. 45, iss. 5, pp. 691–703. ISSN 1557-9948.DOI: 10.1109/41.720325.

[19] KANG, B.-J. and C.-M. LIAW. A robust hys-teresis current-controlled PWM inverter for lin-ear PMSM driven magnetic suspended position-ing system. IEEE Transactions on IndustrialElectronics. 2001, vol. 48, iss. 5, pp. 956–967.ISSN 1557-9948. DOI: 10.1109/41.954560.

[20] LE-HUY, H., K. SLIMANI and P. VIAROUGE.Analysis and implementation of a real-time predic-tive current controller for permanent-magnet syn-chronous servo drives. IEEE Transactions on In-dustrial Electronics. 1994, vol. 41, iss. 1, pp. 110–117. ISSN 1557-9948. DOI: 10.1109/41.281616.

[21] CHUN, T.-W. and M.-K. CHOI. Developmentof adaptive hysteresis band current control strat-egy of PWM inverter with constant switching fre-quency. In: Proceedings of Applied Power Elec-tronics Conference (APEC). San Jose: IEEE,1996, pp. 194–199. ISBN 978-0-7803-3044-3.DOI: 10.1109/APEC.1996.500442.

[22] SINGH, B., C. L. P. SWAMY, B. P. SINGH,A. CHANDRA and K. AL-HADDAD. Per-formance analysis of fuzzy logic controlledpermanent magnet synchronous motor drive.In: Proceedings of the 1995 IEEE 21st Inter-national Conference on Industrial Electronics,Control, and Instrumentation. Orlando: IEEE,1995, pp. 399–405. ISBN 978-0-7803-3026-9.DOI: 10.1109/IECON.1995.483429.

[23] OUNNAS, D., M. RAMDANI, S. CHENIKHERand T. BOUKTIR. A Combined Methodol-ogy of H∞ Fuzzy Tracking Control and Vir-tual Reference Model for a PMSM. Advancesin Electrical and Electronic Engineering. 2015,vol. 13, iss. 3, pp. 212–222. ISSN 1804-3119.DOI: 10.15598/aeee.v13i3.1331.

[24] USTUN, O. Speed Control of The PermanentMagnet Synchronous Motor Using Parallel Asso-ciated Fuzzy Neural and Sliding Mode Controllers.Ankara, 2004. Dissertation. Gazi University. Su-pervisor: Cetin Elmas.

[25] USTUN, O. A Tracking Position Controlof the Switched Reluctance Motor with Geneticbased Conventional Controller. SDU Interna-tional Journal of Technological Sciences. 2016,vol. 8, iss. 1, pp. 66–75. ISSN 1309-1220.

[26] CHAOUI, H., M. KHAYAMY, O. OKOYEand H. GUALOUS. Simplified Speed Con-trol of Permanent Magnet SynchronousMotors Using Genetic Algorithms. IEEETransactions on Power Electronics. 2018,vol. 34, iss. 4, pp. 3563–3574. ISSN 1941-0107.DOI: 10.1109/TPEL.2018.2851923.

[27] WANG, M., W. CHANG, H. YANG and W. YAN.Sensorless Vector Control of Permanent Mag-net Synchronous Motor Based on Improved Hy-brid Genetic Algorithm. In: 2019 4th Interna-tional Conference on Control and Robotics Engi-neering (ICCRE). Nanjing: IEEE, 2019, pp. 21–26. ISBN 978-1-7281-1593-1. DOI: 10.1109/IC-CRE.2019.8724180.


http://dx.doi.org/10.1109/ICISC.2018.8398950

http://dx.doi.org/10.1016/j.ifacol.2018.07.162

http://dx.doi.org/10.15598/aeee.v14i1.1564

http://dx.doi.org/10.1109/63.53152

http://dx.doi.org/10.1109/41.605621

http://dx.doi.org/10.1109/IECON.1993.339000

http://dx.doi.org/10.1109/41.720325

http://dx.doi.org/10.1109/41.954560

http://dx.doi.org/10.1109/41.281616

http://dx.doi.org/10.1109/APEC.1996.500442

http://dx.doi.org/10.1109/IECON.1995.483429

http://dx.doi.org/10.15598/aeee.v13i3.1331

http://dx.doi.org/10.1109/TPEL.2018.2851923

http://dx.doi.org/10.1109/ICCRE.2019.8724180

http://dx.doi.org/10.1109/ICCRE.2019.8724180


[28] DALKIN, A. The Comparison Of Speed And Po-sition Control Of PMSM By Using TrapezoidalAnd Sinusoidal Commutation Techniques. Bolu,2016. Dissertation. Bolu Abant Izzet Baysal Uni-versity. Supervisor: Erdal Bekiroglu.

About Authors

Erdal BEKIROGLU received his B.Sc., M.Sc.,and Ph.D. degrees from the Gazi University inthe field of Electrical Technologies. He workedas a research assistant at Gazi University be-tween 1996 and 2003. He is currently professorat the Department of Electrical and Electronics

Engineering, Faculty of Engineering, Bolu AbantIzzet Baysal University. His research interests aredrive and control of electrical machines, ultrasonic mo-tors, intelligent control, and renewable energy systems.

Ahmet DALKIN was born in Turkey, in 1989.He received B.Sc. degree in Electrical and Electron-ics Engineering from Sivas Cumhuriyet University,in 2012, and received M.Sc. degree in Electricaland Electronics Engineering from Bolu Abant IzzetBaysal University, in 2016. He is currently a Lecturerin Ondokuz Mayis University, Samsun. His currentresearch interest is focused on control of electricalmachines, intelligent control and renewable energyresources.


comparison of trapezoidal and sinusoidal pwm techniques

Documents