Minimization of Torque Ripple for a 4-ø BLDC Motor with Non-Ideal Back Emf by using Phase to Phase Back-Emf Estimation.

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International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 5, Issue 2, February 2015)

299

Minimization of Torque Ripple for a 4-ø BLDC Motor with

Non-Ideal Back Emf by using Phase to Phase Back-Emf

Estimation.

D. Bharath kumar

1

, M. Anka Rao

2 1

M.Tech (Power and Industrial Drives) Scholar, Department of EEE, JNTUA Anantapuramu-515002, India

2

Assistant Professor, Department of EEE, JNTUA Anantapuramu-515002, India

Abstract— Brushless motors are gaining attention from

various Industrial manufactures because of its high efficiency, noise less operation and high speeds. In conventional control methods of Brushless Dc motors, the back electromotive force is assumed to be in ideal form i.e., Trapezoidal form, so that rectangular currents are injected from the inverter. In real time, the back-Emf may not to be trapezoidal due to its magnetic materials, design considerations, limitations in manufacturing, etc., this makes the generation of ripples in torque waveform which is inacceptable in sensitive Industries. In this paper, the ripples generated in torque waveform due to non ideality of back-Emf is compensated by injecting the currents which are proportional to the instantaneous phase to phase back Emf magnitude for a four phase Bldc Motor.

Keywords— Four phase BLDC Motor, Hysterisis

controller, Phase-Phase back-Emf estimation.

I. INTRODUCTION

A motor which has the characteristics of DC Motor but eliminates the commutator and brushes is called Brushless DC Motor. In these motors the windings are connected to the Inverter. The controlling of the Inverter replaces the function of commutator by energizing the proper windings based on the rotor position. So, the Bldc motor employs electronic commutation which makes maintenance free. Hall sensors, position encoders and resolvers are used to determine the rotor position to energize the windings by giving proper signals to the inverter. These Bldc motors have advantages like high efficiency, speeds, noise less operation etc. Performance of Bldc motors is important due to its wide range of applications. It is possible that the back-Emf of a motor is not exactly trapezoidal because of magnetic materials, design considerations, etc. This makes the generated electromagnetic torque contains ripples in its waveform. In sensitive industries where the electromagnetic torque with minimum ripple is required.

In conventional control methods the non uniformity of back-Emf is not taken into account and injecting similar rectangular current commands to stator phases which lead to generation of ripples in torque waveform.

Hence a control strategy is necessary to minimize the ripples in its electromagnetic torque is essential. In this paper a procedure is presented to reduce ripples in torque waveform of a Bldc motor with non-ideal back-Emf is presented and the fft analysis of torque waveform in conventional method and proposed method is compared. The basic concept in the proposed method is phase to phase back-Emf estimation. In this method the controlling is applied in stationary frame and no d-q transformation is applied. The torque ripple is reduced by considering instantaneous phase to phase back-Emf magnitude, when the estimated back-Emf magnitude is increases when it is compared with the previous estimated value, the current injecting in the stator phase currents are reduced and vice versa.

II. MATHEMATICAL MODELLING OF 4-PHASE BLDC MOTOR.

Bldc Motor can be analyzed in abc phase variable and d-q axis model. In Bldc motor the back Emf is trapezoidal, so that the mutual inductance between stator and rotor is non-sinusoidal thus the d-q transformation does not add any particular advantage so that the abc phase variable model is preferred. In the present model the Bldc motor is assumed to be star connected and the following assumptions are made:

i. The motor is star connected and not saturated, stray and iron loses are neglected.

ii.Stator resistances of all the windings are equal, self and mutual inductances are constant.

iii. Power semiconductor devices in the inverter are ideal.

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International Journal of Emerging Technology and Advanced Engineering

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Fig.1 Equivalent Circuit of Four Phase Bldc Motor

From the equivalent circuit the voltage equations are motor are expressed as

a a a a a e dt di L R i

V    ….. (1)

b b b b b e dt di L R i

V   

…. (2) c c c c c e dt di L R i

V   

….. (3) d d d d d e dt di L R i

V   

….. (4)

The matrix form of the above equations is

… (5) Where,

R= Resistance per phase,

L=La=Lb=Lc=Ld=Ls-M, Ls andM are self-inductance and mutual inductance respectively.

ea = back-Emf of phase‟a‟.

The back-Emf is the function of rotor position and speed of the motor and each phase has a 900 phase displacement from the previous phase.

ea = Kbf(



e)



r

... (6)

Where

Kb= back-Emf constant

r



_{= Speed of the Motor in rad/sec.}

The electromagnetic torque of the motor is given as

r r l e B dt d J T

T  







.…. (7) Where r d d c c b b a a e i e i e i e i e T      …... (8)

J = Inertia coefficent

B = Friction coefficent

Neglecting friction factor B, The Speed and torque related as





 1 ( _e _l)

r T T

J



….. (9)

III. PHASE TO PHASE BACKEMF ESTIMATION

In a four-phase BLDC motor, in each 90° of electrical rotation, two phases are conducting. This means that phases „a‟ and „c‟ which have 180 electrical degrees phase difference, conduct in two 90° sections in one electrical rotation(360°).In one of these section, phase „a‟ carries the positive current and phase „c‟ carries the negative current. In the other section, phase „c‟ carries the positive current and phase „a‟ carries the negative current.This is also valid for the other phases „b‟ and „d‟, which conduct in the other two 90° sections.

In two of the 90° sections ia=-ic &

In the other two sections ib=-id

From Eqns (1) & (3)

..… (10)

From Eqns (2) & (4)

..… (11)

The DC bus voltage in first 900section is given as

Vdc= Va-Vc ...… (12)

From (10) …... (13)                                                                            d c b a d c b a d c b a d c b a e e e e i i i i L L L L i i i i R R R R V V V V 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  c a a a

ac

e

dt

di

L

R

i

V



2 



d b b b

bd

e

dt

di

L

R

i

V



2 



dt

di

L

R

i

e

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International Journal of Emerging Technology and Advanced Engineering

301 Using (13), phase to phase back-Emf voltage equation can be estimated. Using the same algorithm the other sections back-Emf is estimated.

IV. CONVENTIONAL CONTROL METHOD

The Block diagram of Conventional control method is shown in Fig.2. In this method the speed controller compares the reference speed with actual speed and the error signal goes through a proportional integral (PI) block to generate torque reference signal. The torque reference signal is divided by a torque coefficient to produce reference current command

) (

*

t e

ref _K

T I  .

Fig.2 Block diagram of Conventional method

The reference current command is given to the Hysteresis Block to generate pulses for four phase Inverter based on the rotor position to achieve the desired speed and Torque. This method is effective when the back-EMFs are trapezoidal.

A. Hysteresis Controller

In this paper Hysteresis current control method is used to obtain fast dynamic response during transient condition. In order to express the phenomenon of current dynamics, the phase current needs to be modeled in four modes as shown in Fig.3.

Mode[1]Ia< Lower Limit (LL)

Mode [2] Ia> Upper Limit (UL)

Mode [3] LL <Ia<UL and

dt

dI

_a

>0

Mode [4] LL <Ia<UL and

dt

dI

_a

<0

Fig.3. Detail current modes in Current dynamics

In order to express Mode [3] & [4] in Matlab/simulink a memory element is used which is shown in Fig.4 and by using the rotor position the entire current dynamics can be realized by using the equation(14).

Fig.4. Hysteresis current control block for phase ‘a’

F (a) =

…… (14)

V. PROPOSED METHOD

To reduce torque ripples generated due to non ideality of back Emf, reference current should be generated considering back-Emfs.

Electromagnetic torque is expressed as a function of phase currents and back Emf as given in equation (8)

Consider an interval such that two phases are conducting

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International Journal of Emerging Technology and Advanced Engineering

302

r c c a a e

i e i e T



 

……… (14)

c

a

i





………. (15)

r

e

a

c

a

e

i

T

e



)





(

_{……… (16)}

Assume, the electromagnetic torque command from speed controller as Te

*

From equation (16), the current reference command generated as

)

/(

*

c

a

r

e

c

a

i

T

e

i











_{…… (17)}

In equation (17) the phase to phase back-Emf estimated in equation (13) is used.

Hence, in every 90° of rotation, reference currents of conducting phases can be calculated.In this method, it is not necessary to know each phase back-EMF individually. This is an advantage, since the neutral point of stator windings is not always accessible.

The Block diagram of the proposed system is shown in Fig.5. The speed controller compares the reference speed with the actual speed and the error signal goes through PI controller to generate the torque command signal. The torque command signal is given to the current reference generator block. On the other hand the DC bus voltage, phase currents are used to estimate the phase to phase back-Emfs and thus it given as input to the current reference generator block to produce reference current command and then it passes to the hysteresis band controller to generate pulses for the four phase inverter.

Fig.5. Block diagram of Proposed method

The main difference between the proposed control method and the conventional control method is their current reference generation blocks.

In conventional method torque reference is divided by a coefficient (torque coefficient) to produce current commands. This is effective when the back-EMFs are trapezoidal. When back-EMF waveforms are not ideal i.e trapezoidal, using conventional method, this non-ideality leads to considerable torque ripples which affects the Performance of the system. In the proposed method, current commands are generated proportional to instantaneous estimated values of back-EMFs. So the non-ideality in the back-EMF waveform is compensated by generating proper controller current commands.

VI. MATLABBASED SIMULATION AND RESULTS

A four pole four phase Bldc motor with phase resistance of 4Ω and self inductance of 2mh and mutual inductance of 1mh with non-ideal Back emf is used to study the performance of the system in Matlab/Simulink. Since the back-Emf is not trapezoidal, so as to create the non-ideality, the back-Emf generated as sinusoidal which is shown in Fig.8. This makes the motor suitable to study under non ideal back-Emf effects. The motor starts up with the reference speed of 800 rpm and the load torque of 0.11N.m

The Matlab/Simulink model for conventional control method and the proposed control method is shown in Fig.6 and Fig 7.

The current and torque waveforms of conventional method is shown in Fig.10 and Fig.12 respectively. As seen in Fig.10 the current has a rectangular shape because of constant current command this makes generation of electromagnetic cups as shown in Fig.12. The estimated phase to phase back-Emf is shown in Fig.9 which is responsible for generation of ripples in electromagnetic torque. The current and torque waveforms of proposed method is shown in Fig.11 and Fig.13. As we can observe the current is not rectangular as in Fig.11 this is due to the non-ideality of waveform which is shown in Fig 9. The controller generates phase current commands to compensate back-Emf curve non ideality. So the convex form of phase to phase back-Emf voltage makes concave shape of the motor current.

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International Journal of Emerging Technology and Advanced Engineering

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Fig.6. Matlab/Simulink model of Conventional Method.

Fig7. Matlab/Simulink model of Proposed Method.

Fig.8. Time vs Non ideal back Emf.

Fig.9. Time vs Estimated phase to phase backEmf.

Fig.10. Time vs Phase ‘a’ current waveform in conventional method.

Fig.11. Time vs Phase a current waveform in proposed method.

Fig.12. Time vs Torque waveform in conventional method.

Fig.13. Time vs Torque waveform in proposed method

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International Journal of Emerging Technology and Advanced Engineering

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Fig.15. FFT analysis of torque in conventional method

Fig.16. FFT analysis of torque in Proposed method

VII. CONCLUSION

This paper presents a new control method for electromagnetic torque ripple reduction for a BLDC motor with non-ideal back-EMF waveform. The concept is based on phase-to-phase back-EMF estimation. In conventional control method, phase current commands are generated by dividing reference torque by a coefficient.

However, in the proposed method, the desired torque is generated by current commands which are proportional to instantaneous back-EMF magnitudes of conducting phases. This means that when the back-EMF value increases, the injected current magnitude decreases and vice versa.

In this paper, the conventional method and proposed method is simulated in Matlab/Simulink environment. From the simulation results the conventional control method results and proposed method results are compared and analysed.

REFERENCES

[1] P. Pillay and R. Krishnan. Modeling, simulation, andanalysis of permanent-magnet motor drives Part II:The brushless dc motor drive. IEEE Trans. on IndustryApplications 1989. p. 274-279. [2] “BLDC motor modeling and control- a MATLAB / SIMULINK

implementation”, Master Thesis in Electrical Power Engineering, May 2005

[3] Sang-Hoon Song., Yong-Ho Yoo., Byoung-Kuk Lee and Chung-Yuen Won:Autonomous underwater vehicles with modeling and analysisof seven phase BLDC motor drives, J Electr Eng Technol Vol. 9, No. 3: 932-941, 2014

[4] Tewari, S.V., Indu Rani, B.: „Torque ripple minimization of BLDC motor with un-ideal back EMF‟. Second Int. Conf. Emerging Trends in Engineering and Technology (ICETET), 2009, pp. 687–690 [5] Fang, J., Li, H., Han, B.: „Torque ripple reduction in BLDC torque