The Engineering Journal of Application & Scopes, Volume 1,Issue 1, March 2016

TEJAS © 2016

http://www.ij-tejas.com

Sensorless control & Performance analysis of

PMBLDC motor using back emf detection

Sumit Nema Assistant Professor

Department of Electrical Engineering

College of Engineering Roorkee

Roorkee, India - 247667

sumitnema@live.in

Aadesh Kumar Arya Assistant Professor

Department of Electrical Engineering

College of Engineering Roorkee

Roorkee, India – 247667

adesh_kumararya@rediffmail.com

Abstract—Thispaper presents the implementation of

sensorless PMBLDC motor involving the back emf detection.

Along with the back emf detection respective zero-crossing points

are identified which is based on detecting the instant at which the

back-EMF in the unexcited phase crosses zero. These zcp can be

used for the generation of pulses for electronic commutation of

inverter switches to achieve sensorless operation of

permanentmagnetbrushlessDC(PMBLDC) motor. Performance

analsysis is carried out in comparison with a sensored

machines.The simulation model has been developed in

MATLAB/SIMULINK environment.

Index Terms- PermanentmagnetbrushlessDC(PMBLDC)

motor,electromotiveforce(emf), voltage source inverter (VSI),zero

crossing point (ZCP)

I. INTRODUCTION

BLDC motors from micro to large size are extensively used

for applications in many types of motion control apparatus and

systems as adjustable speed drives.

The BLDC are typically permanent synchronousmotor,they are well driven by dc voltage. They have a commutationthatis done mainly by electronicsapplication.Someofthemanyadvantagesofabrushlessdcmotorover the conventional brushed dc motors are highlightedbelow:

1. Better speed versus torquecharacteristics

2. High dynamicresponse

3. Highefficiency

4. Long operatinglife 5. High speedranges

6. Low maintenance (in terms of brushes

cleaning;whichis peculiar to the brushed dcmotor).

Basically PMBLDC motor drive uses one or more sensors

to have positional information which results in a higher drive

cost so sensorless techniques are keen desire. Fig. 1 shows

basic inverter topology employed:

Vdc

S1 S3 S5

S4 S6S2

PMBLDC

MOTOR

Fig.1Inverter Topology with PMBLDC Motor’s Equivalent Circuit

One of the most common methods used for inverter

switching is pulse width modulation (PWM) techniques..

II. MATHEMATICAL MODELLINGOF PMBLDC MOTOR

For a three phase star connected PMBLDC motor, per phase voltages (Van,Vbn,Vcn) can be given as:

van

vbn

vcn

= Rs 100

010

001

ian

ibn

icn

+ LMM

MLM

MML p

ian

ibn

icn

+

ean

ebn

ecn

(1)

Where Rs is stator phase resistance, L is stator phase inductance, M is mutual inductance between the phases, ian, ibn, icn are stator current and van, vbn, vcn are phase voltage of the stator’s winding and p is derivative operator.

For a three phase star connected PMBLDC motor,

ian + ibn + icn = 0 (2)

van

vbn

vcn

=Rs 100

010

001

ian

ibn

icn

+ L − M

00

0L − M

0

00

L − M p

ian

ibn

icn

+

ean

ebn

ecn

(3)

Using Eq. (3), we can have current derivative as:

p

ian

ibn

icn

= L − M

00

0L − M

0

00

L − M

−1

van

vbn

vcn

−

ean

ebn

ecn

−Rs 100

010

001

ian

ibn

icn

(4)

Theelectromagnetic torques can be given as:

Te = ∑ (exn ixn )/ωr (5)

The Engineering Journal of Application & Scopes, Volume 1,Issue 1, March 2016

TEJAS © 2016

http://www.ij-tejas.com

Where𝛚r, represents the rotor speed, x represent the phase a, b

and c while n represent the neutral terminal. Since back emf is

a function of flux and rotor position, it can be expressed as:

exn = fxn θ λx ωr (6)

Where𝛌x, represents the flux linkage and fxn (𝝷) have the same

shape as of the back emf. Substituting Eq. (6) in Eq. (5), we

have:

Te = λx ∑ fxn θ ixn (7)

The equation of motion for simple system is

Jdω

dt+ Bω = Te − Tl (8)

Where, Te is electromagnetic torque, Tlis load torque, J is

motor inertia and B is damping constant.The relation between

angular position (electrical) and angular mechanical velocity is

given by:

dθe

dt=(P/2)∗ ω (9)

Eq. (1)-(9) represents the dynamic model of the PMBLDC

motor. The trapezoidal back EMF waveform and the phase

current of the PMBLDC motorareshown in the Fig.2. The

graph is presented for one complete cycle of 360 degrees.

InthismethodZCPoftheback

EMFisdetecteddirectly.FortypicaloperationofaBLDCmotor,the

phasecurrentandback-EMFshouldbealignedtogenerate the

constanttorque.ThecommutationpointcanbeestimatedbytheZC

Pofback EMF. The conducting intervalforeach phase is 120

electrical degrees. Therefore, leaving the thirdphasefloating,

only two phases conduct current at any time. The inverter

should be commutated every 60° by detecting

zerocrossingofbackEMFonthefloatingcoilofthemotor in order

to produce maximum torque,

sothatcurrentisinphasewiththebackEMF.

0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚ 210˚ 240˚ 270˚ 300˚ 330˚ 360˚

tea

ia

eb

ib

ic

t

t

t

t

t

ec

Fig.2 Back EMF and Phase current waveforms of PMBLDC motor

III. SIMULATION RESULTS AND ANALYSIS

Simulation for the discussed technique has been carried out in MATLAB/SIMULINK environment and experimental model modelled as shown in Fig. 3. All the respective parameters for techniques are mentioned in appendix, Various wave-form for current, back emf, speed and torque and inverter pulses has been obtained at no load as well as on load condition having load of 3 N-m and the respective wave-form obtained are as follow:

Ref.

Speed

Speed

Controller

3 Phase VSI Inverter

ea+

-

PMBLDC

Motor

ia

te

n

Ref. Current

Pulses

A

B

C

A

B

C

N

S

ZCP DetectorPulse Decoder

m

Fig.3 Back EMF and Phase current waveforms of PMBLDC motor

The Engineering Journal of Application & Scopes, Volume 1,Issue 1, March 2016

TEJAS © 2016

http://www.ij-tejas.com

Fig.4Response for No Load Condition

Fig.5Pulses for No Load Condition

The Engineering Journal of Application & Scopes, Volume 1,Issue 1, March 2016

TEJAS © 2016

http://www.ij-tejas.com

Fig.6Response for Load Condition

Fig.7 Pulses for Load Condition

The Engineering Journal of Application & Scopes, Volume 1,Issue 1, March 2016

TEJAS © 2016

http://www.ij-tejas.com

Based on various results following analysis has been made:

TABLE I. ANALYSIS FOR SPEED RESPONSE

No Load

Method

Settling

Time

(s)

Maximum

transient

Overshoot

(r/min)

Speed Ripple

(Peak to Peak)

under steady

state

(r/min)

Physical

Condition

BEMF ZCD 0.07 3096

3

(2999-

3002)

Excellent

Response

and stable

TABLE II. ANALYSIS FOR SPEED RESPONSE

On Load

Method

Settling

Time

(s)

Maximum

transient

Overshoot

(r/min)

Speed Ripple

(Peak to Peak)

under steady

state

(r/min)

Physical

Condition

BEMF ZCD 0.07 3096

3

(2999-

3002)

Excellent

Response

and stable

IV. CONCLUSION

The aim of the work was to introduce sensorless operation

ofPMBLDC motor. Based on discussed procedure, simulation

model has been developed and response is shown in different

figures along with inverter pulses for no load as well as on

load operation. With respect to various results conclusion can

be drawn that at no load as well as on load condition Back

EMF approch implies excellent and same response as

compared to sensored machine.

APPENDIX

A. PMBLDC Motor Specifications[16]:

Power : 1 Kw

Speed : 3000 rpm

Vdc : 500V

Stator phase resistance Rs : 2.875 ohm

Stator phase inductance Ls : 0.0085 h

Flux linkage : 0.175 V.s

Voltage Constant : 146.6077

Torque Constant : 0.49

Back EMF flat area (degrees) : 120

Inertia, J : 0.00012 kg.m2

Friction factor F : 0.001 N.m.s

Pole Pairs P : 4

Back EMF waveform : Trapezoidal

Mechanical input : Tm

B. PI-Controller parameters:

Proportional gain, Kp : 0.13

Integral gain, Ki : 16.61

C. Three-PhaseInverter:

Input DC Voltage : 500 V

No. of switches : 6

REFERENCES

[1] R. Krishnan, Electric Motor Drives: Modeling,Analysis and Control, Pearson Education, New Delhi,2001.

[2] G. K. Dubey, “Power Semiconductor ControlledDrives”, Prentice Hall, New Jersey,1989.

[3] T. J. E. Miller, Brushless Permanent Magnet andReluctance Motor Drive, Clarendon Press, oxford,1989

[4] R. Somanatham, P. V. N. Prasad and A. D. Rajkumar, “Modeling and Simulation of Sensor less Control of PMBLDC Motor Using Zero-Crossing Back E.M.F Detection”, International Symposium on Power Electronics, Electrical Drives, Automation and Motion (SPEEDAM), pp. 984 – 989,2006.

[5] Yen-Shin Lai and Yong-Kai Lin, “Novel Back-EMF Detection Technique of Brushless DC Motor Drives for Wide Range Control Without Using Current and Position Sensors”, IEEE Trans. Power Electronics, vol. 23, no. 2, pp. 934 – 940, 2008.

[6] K. S. Rama Rao, Nagadeven and Soib Taib,“Sensorless Control of a BLDC Motor with Back EMF Detection Method using DSPIC”, 2ndIEEE International Conf. Power and Energy (PECon 08), pp. 243 – 248, Dec. 2008.

[7] Yen-Shin Lai and Yong-Kai Lin, “Back-EMF Detection Technique of Brushless DC Motor Drives for Wide Range Control”, IEEE Trans. Power Electronics, vol. 23, no. 2, pp. 934 – 940, 2008.

[8] Haifeng Lu, Lei Zhang, and Wenlong Qu,“A New Torque Control Method for Torque Ripple Minimization of BLDC Motors With Un-Ideal Back EMF”, IEEE Trans. Power Electronics, vol. 23, no. 2, pp. 950 – 958, March 2008.

[9] B. Singh and S. Singh, “State of the Art on Permanent Magnet Brushless DC Motor Drives”, Journal of Power Electronics, vol.. 9, no. 1, January 2009

[10] Tae-Hyung Kim and Mehrdad Ehsani, “Sensorless Control of the BLDC Motors From Near-Zero to High Speeds”,IEEE Trans. Power Electronics, vol. 19, no. 6, November 2004.

[11] S. Singh and B. Singh,“Power Quality Improvement of PMBLDCM Driven Air-conditioner usingaSingle-Stage PFC Boost Bridge Converter”, Annual IEEE India Conf. (INDICON), 2009.

[12] Paul P. Acarnley and John F. Watson, “Modeling of BLDC Motor with Ideal Back EMF for Automotive Applications”, IEEE Trans. Industrial Electronics, vol. 53, no. 2, pp. 352-362, April, 2006.

[13] Sha Lin and Du Qifei, “Review of Position-Sensorless Operation of Brushless Permanent-Magnet Machines”, International Conf. Control, Automation and Systems Engineering (CASE), pp. 1–3, 2011.

[14] Sha Lin and Du Qifei, “Sensorless Control Technique for BLDCM”, International Conf. Control, Automation and Systems Engineering (CASE), pp. 1–3, 2011.

[15] B. S. Parihar and S. Sharma, “Performance Analysis of Improved Power Quality Converter Fed PMBLDC Motor Drive”, IEEE Students Conf. Electrical, Electronics and Computer Science (SCEECS), 2014

[16] Matlab 7.10.0 (R2010a) Mathwork Ink.

[17] Microchip AN885 “Brushless DC (BLDC) Motor Fundamentals” Microchip Technology Inc.