a study on direct torque control of bldc motor in 120 degree

International Journal of Advanced Engineering Research and Technology (IJAERT)

Volume 3 Issue 11, November 2015, ISSN No.: 2348 – 8190 364

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A Study on Direct Torque Control of BLDC Motor in 120 Degree

Conduction Mode

Shiny Sara Jacob*, P Sandhya**

*Department of Electrical & Electronics Engineering

MBCET-Kerala, India-695015

** Department of Electrical & Electronics Engineering

MBCET-Kerala, India-695015

ABSTRACT

In this paper, Direct Torque Control (DTC) of

Brushless DC Motor (BLDC) drive is presented. This

control algorithm is implemented in the constant torque

region of BLDC motor drive. Unlike conventional three

phase DTC drives, the proposed DTC approach

introduces two phase conduction mode. In the proposed

DTC, the quasi-square wave current is obtained by

properly selecting the inverter voltage space vectors of

the two phase conduction mode from a simple look-up

table. This will improve the torque response compared to

other control strategies. The experimental results are

validated in MATLAB/SIMULINK.

Keywords - Direct Torque Control (DTC), Brushless Dc

Motor (BLDC), Constant Torque Region

I. INTRODUCTION Industrial automation is mainly concentrated around

motion control systems in which controlled electric

motors plays an important role as heart of the system.

Therefore the performance of motor and its control

systems enhances the production rate and the quality of

the products. The advancement of control theories,

power electronics equipment in combine with electric

motors led to a new era in industries. The great example

is that Brushless DC Motors (BLDC). BLDC motor is a

type of synchronous motor in which it is differentiated

from other motors by its trapezoidal shaped back emfs,

120 degree rectangular currents and its electronic

commutation. Earlier the use of BLDC motors is limited

due to its material cost. But the emergence of magnetic

materials like Neodynium, Samarium Cobalt and the

alloys of neodymium with its attractive features like high

magnetic density per volume and enables the rotor to

compress further for same torque made them so popular

for BLDC motors with further cost reduction. The

BLDC motors have its own advantages compared to

other motors and include higher efficiency, higher

output, increased armature current loading, absence of

commutator, elimination of radio frequency and

electromagnetic interference, operation from a low dc

voltage is possible, long life, less maintenance, high

speed of operation etc. These advantages of BLDC

motors leads to wide range applications extending from

household appliances to traction purposes and in

aerospace applications when space and weight makes a

crucial factors. For example the cd-rom drive and

cooling fan of laptop or desktop computers are made up

of BLDC motor.

Dealing with control strategies, BLDC motors mostly

employed torque and current control strategies assuming

that torque is proportional to the phase current. But in

real cases, the assumption is nonlinear which results in

torque pulsations. In [1], the electromagnetic torque is

calculated from back emfs and current in the two phase

conduction as well as commutation period. A mid

precision sensor is used to store the back emfs values

which are costly. In [2] ,optimal current excitation

scheme was proposed based on pre-optimized

waveforms for reference current which results in

minimum torque ripple and copper losses. They used

hydraulic dynamometer to characterize the torque-angle

and torque-current characteristic for direct drive which is

costly. In [3-5], an instantaneous torque controller based

on d-q frame was proposed. The scheme was applicable

only for 180 degree conduction mode rather than 120

degree conduction mode.

There are two types of instantaneous electromagnetic

torque controlled AC drives available in industries for

high performance applications, one is Field Oriented

Control (FOC) and other is Direct Torque Control

(DTC). Both techniques works well with the on-off

conditions of inverter switches. Among them DTC made

an important impact in industrial applications for high

performance applications. DTC means we are directly

controlling the electromagnetic torque developed and the

stator flux linkage through the optimal voltage selection

of VSI in an independent manner. The idea of DTC [4]

was originally developed for induction machine drives

by Takahashi and Depenbrock in the mid 1980s.

According to the conditions of torque error, stator flux

error and sector, a switching table is developed and

stored so that faster torque response is obtained as

compared to conventional PWM methods. Since the

beginning the DTC was characterized by simplicity,

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good performance and robustness. Using DTC it is

possible to [3] obtain a good dynamic control of the

torque without any mechanical transducers on the

machine shaft.

The BLDC motor was always operated in 120 degree

conduction mode. In 120 degree conduction or two

phase conduction mode, the two phases are active at any

time except during commutation period. The method is

simple but having disadvantage of torque pulsation

during commutation period.

II. MODELLING OF BLDC MOTOR The mathematical modelling of BLDC can be done

using the following equations. The assumptions [9]

made for the modelling of BLDC motor are

The three-phase stator windings are Y connected

The mutual torque produced by the motor is linearly

proportional to the phase current

The cogging torque does not exist

The mutual inductance between phases is negligible

DC source voltage is infinite and is capable of

delivering infinite di/dt.

The motor is not saturated.

The resistance and inductance of all phases are

identical.

All three phases have an identical back-EMF shape.

Power semiconductor devices in the inverter are

ideal.

Iron losses are negligible.

Eddy current and hysteresis effects are neglected.

The modeling of a BLDC motor consisting of three

phases is explained by the following series of equations.

Since there is no neutral used, the system is wye

connected, thus the sum of the three phase currents must

add up to zero, i.e.

Isa+ Isb + Isc = 0 (1)

Isa+ Isb = - Isc (2)

Under the above assumptions a three phase BLDC motor

mathematical model can be represented by the following

equation in matrix form

𝑉𝑠𝑎𝑉𝑠𝑏

𝑉𝑠𝑐

=

𝑟𝑎 0 00 𝑟𝑏 00 0 𝑟𝑐

𝐼𝑠𝑎𝐼𝑠𝑏𝐼𝑠𝑐

+

𝑑

𝑑𝑡

𝐿𝑎𝑎 𝐿𝑏𝑎 𝐿𝑐𝑎

𝐿𝑎𝑏 𝐿𝑏𝑏 𝐿𝑐𝑏

𝐿𝑎𝑐 𝐿𝑏𝑐 𝐿𝑐𝑐


+

𝑒𝑎

𝑒𝑏

𝑒𝑐

(3)

If the rotor has a surface-mounted design, which is

generally the case for today’s BLDC motors, there is no

saliency such that the stator self-inductances are

independent of the rotor position, hence

Laa = Lbb = Lcc = L (4)

Again with no saliency all mutual inductances will have

the same form such that,

Lab = Lba = Lcb = M (5)

Also, under balanced three-phase condition all the phase

resistances are equal, such that

ra = rb = rc = r (6)

𝑉𝑠𝑎𝑉𝑠𝑏

𝑉𝑠𝑐

=

𝑟𝑎 0 00 𝑟𝑏 00 0 𝑟𝑐


+𝑑

𝑑𝑡 𝐿 𝑀 𝑀𝑀 𝐿 𝑀𝑀 𝑀 𝐿


+

𝑒𝑎

𝑒𝑏

𝑒𝑐

(7)

The electromechanical torque is expressed as

𝑇𝑒𝑚 =𝑒𝑎 𝐼𝑠𝑎 + 𝑒𝑏 𝐼𝑠𝑏 +𝑒𝑐𝐼𝑠𝑐

𝑤𝑚 (8)

Where ea, eb and ec are the back emfs of phases A, B and

C respectively

Isa, Isb, Isc are the stator phase currents of A, B and C

phase respectively.

The mechanical equation is

𝑇𝑒𝑚 = 𝑇𝐿 + J𝑑 𝜔𝑚

𝑑𝑡 + B 𝜔𝑚 (9)

Where TL is the load torque, J is the moment of inertia

and B is the friction coefficient.

III. DIRECT TORQUE CONTROL OF

BLDC MOTOR

Fig.1 Basic block diagram of DTC




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The idea of DTC is, we directly controls the

electromagnetic torque developed by the machine and the

stator flux linkage directly and independently by the help

of voltage source inverter switching table [7]. The typical

DTC includes two hysteresis controllers, one for torque

error correction and other for flux linkage error

correction. The hysteresis stator flux controller makes the

stator flux rotate along the reference trajectory. The

hysteresis torque controller makes the motor torque in a

predefined hysteresis band. The three signals requires for

generation of voltage space vectors are electromagnetic

torque error, stator flux linkage error and the sector of the

stator flux linkage.

3.1 Generation of voltage space vector

The operation of BLDC is always in 120 degree

conduction mode. In two phase or 120 degree

conduction mode, two phases are always conducting at

any time, while the third phase remains off [6]. At every

60 degree commutation occurs and the next two phases

conduct. Since the upper and lower switches in a phase

leg may be simultaneously off, irrespective of the state

of the associated freewheel diodes, six digits are required

for each switch. Thus the voltage space vector V1,

V2……V6 are represented as switching signals

(100001),(001001),(011000),(010010),(000110),(10010

0),Respectively, where, from left to right, the logical

values express states of the upper and lower switch

signals of phases A,B, and C respectively. The switching

table for DTC of BLDC motor in 120 degree conduction

mode is shown in table 1.

Table 1. Switching table for DTC of BLDC motor in 120

degree conduction mode

3.2. Torque and Flux control strategy in DTC of BLDC

motor

The basic torque equation for a surface mounted

permanent magnet motor [8] is

Te = 3 𝑃

2 𝐿𝑠𝜆s 𝜆r sinδ (10)

Where p is the no of poles, Ls is the stator

inductance, s is the stator flux , r is the rotor flux

and δ is the load angle or angle between stator and rotor

flux.

As it can be seen from equation if the load angle is

increased then torque variation is increased. To increase

the load angle, the stator flux vector should turn faster

than rotor flux vector. The rotor flux rotation depends on

the mechanical speed of the rotor, so as to decrease load

angle, stator flux should turn slower than rotor flux.

Since the rotor flux is remaining constant,

electromagnetic torque is controlled by changing the

amplitude and rotation of stator flux.

The stator flux of a motor is obtained through dc link

voltage and given by

s = s -Rs I) dt. (11)

Where Vs is the stator voltage, Rs is the stator resistance

and I is the stator current. Hence by effectively

controlling the voltage vectors, stator flux is controlled

thereby torque is controlled. During the sampling

interval time, one out of the six voltage vectors is

applied. The goal of controlling the flux in DTC is to

keep its amplitude within a pre-defined hysteresis band.

By applying a required voltage vector stator flux linkage

amplitude can be controlled. To select the voltage

vectors for controlling the amplitude of the stator flux

linkage the voltage plane is divided into six regions. In

each region two adjacent voltage vectors, which give the

minimum switching frequency, are selected to increase

or decrease the amplitude of stator flux linkage,

respectively.

IV. MODELLING OF DTC OF BLDC MOTOR

IN TWO PHASE CONDUCTION MODE

The modeling of DTC of BLDC requires

Torque estimation

Stator flux estimation and it’s sector

Rotor position

Voltage vector selection table switching table

Voltage, current, backemf transformation

includes Clarkes and Park transformation

The electromagnetic torque equation for a non-salient

pole brushless dc motor in the stationary reference frame

or in the α-β reference frame is given as [6]

𝑇𝑒 = 3

4𝑃 𝑑𝜑 𝑟𝛼

𝑑𝜃𝑒 𝑖𝑠𝛼 +

𝑑𝜑 𝑟𝛽

𝑑𝜃𝑒 𝑖𝑠𝛽

= 3

4𝑃 𝑒𝛼 𝑖𝑠𝛼 + 𝑒𝛽 𝑖𝑠𝛽 (12)

Where p is the no of poles, ϴe is the electrical rotor

angle, φrα, φrβ ,isα, isβ,eα, eβ are the α-and β- axis rotor flux

linkages, stator currents, motor back emfs respectively.

Ϯ

(torque)

Φ

(flux)

sector

1 2 3 4 5 6

1 1 V1 V2 V3 V4 V5 V6

0 V2 V3 V4 V5 V6 V1

-1 V3 V4 V5 V6 V1 V2

0 1 V1 V2 V3 V4 V5 V6

0 V0 V0 V0 V0 V0 V0

-1 V3 V4 V5 V6 V1 V2




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The stator flux linkage vectors can be obtained from the

measured stator voltages and stator currents and given

by

𝜑𝑆𝛼 = (𝑉𝑠𝛼 − 𝑅 𝐼𝑠𝛼 )𝑑𝑡 (13)

𝜑𝑆𝛽 = (𝑉𝑠𝛽 − 𝑅 𝐼𝑠𝛽 )𝑑𝑡 (14)

Fig 2.Simulation diagram of DTC of BLDC under two

phase conduction mode

The magnitude of the stator flux linkage is given by

𝝋= 𝝋𝑺𝜶 𝟐 + 𝝋𝑺𝜷

𝟐 (15)

Since the neutral point of the BLDC motor is not accessible

in real cases, we cannot use the original Clarke’s

transformation. Since the system is balanced we can

neglect the zero sequence term so instead of using 3*3

Clarke’s transformation we used 2*2 Clarke’s

transformation and given by

(16)

Where X represents back emfs, currents, voltages etc.

Table 2 BLDC motor specifications

Back emf Trapezoidal

No of poles 4

Dc link voltage(V) 310

Rated speed(rpm) 3000

Stator phase resistance 3.52ohm

Stator phase inductance 3.285mH

Flux linkage established by

magnets

0.12175Wb

V. SIMULATION RESULTS The validity of DTC of BLDC motor under two phase

conduction mode has been validated by

MATLAB/SIMULINK. The BLDC parameters for the

simulation have shown in table 2. The sampling time

interval is 20µs. The magnitudes of the torque and flux

hysteresis bands are 0.001Nm and 0.1Wb, respectively.

The dc link voltage equals 310V. The BLDC motor runs

under load torque of 2Nm up to 1sec and changed to

4Nm at the speed of 314 elect.rad/sec is shown in fig 3.

There are some torque pulsations seen in the torque

waveform due to commutation torque ripple. Back emf

waveform of amplitude of about 80V is shown in fig 4.

According to load torque of 2Nm corresponding current

of about 10A and for 4 Nm, and amplitude of about 20A

is produced in the machine and shown in fig 5. The stator

flux in alpha and beta axis is shown in fig 6 and we can

observe that there is a phase difference of 90 degree

between alpha and beta stator flux .The stator flux sector

and rotor angle is shown in fig7. The phase voltage of

machine is shown in fig 8. The stator flux is plotted in

XY graph is shown in fig 9 and 10. In fig10 we can

observed that stator flux undergoes commutation at every

60 degree.

Fig 3.Electromagnetic torque and speed developed

when load torque is changed after 1sec

Fig 4.Backemf waveform at a rated speed 3000

rpm




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Fig 5. Current waveform

Fig 6.waveforms of stator flux in alpha and beta axis

respectively

Fig 7 .Waveforms of stator flux sector and rotor angle

Fig 8.Wavefroms of phase voltages of A, B C phase

respectively

Fig 9.stator flux linkage at load

Fig 10 .Stator flux linkage at no load




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VI. CONCLUSION The paper describes the study of direct torque control of

BLDC motor in two phase conduction mode. It has been

shown that DTC has been capable of instantaneous

torque control. The simulated works showed that there

are torque pulsations during commutation period. The

idea of DTC in two phase conduction mode can be

extended to three phase conduction mode so that

commutation torque ripple can be eliminated.

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brushless dc motor with nonideal trapezoidal back-

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[2].P. J. Sung, W. P. Han, L. H. Man, F. Harashima, “A

new approach for minimum-torque-ripple maximum-

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[3].T. S. Low, K. J. Tseng, K. S. Lock and K. W. Lim,

“Instantaneous torque control,” Fourth International

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[4].T. S. Low, K. J. Tseng, T. H. Lee, K. W. Lim and K.

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[6].Y. Liu, Z. Q. Zhu and D. Howe, "Direct torque

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[7].S. K. Chung, H. S. Kim, C. G. Kim, and M. J. Youn,

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a study on direct torque control of bldc motor in 120 degree

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