International Journal of Engineering Trends and Technology (IJETT) – Volume 28 Number 2 - October 2015
Four Quadrant Operation of BLDC Motor with Current
Controller
1
Sreesha A.S, 2Vandana P
1
Mar Baselios College of Engineering, Electrical & Electronics Engineering 2Assistant Professor, Electrical &
Electronics Engineering, Mar Baselios College of Engineering
Kerala University
Abstract- BLDC motors are conquering more
popularity in aerospace, automation, computers,
military, household appliances and traction
applications for the reason that of its high
competency and low maintenance cost. This makes
the four quadrant operation of BLDC motor very
crucial and important. BLDC motor control requires
rotor position and speed measurements. In this
paper, the modelling of BLDC motor drive system
along with its control systems have been presented
using MATLAB/SIMULINK. The four quadrant
operation of BLDC motor was also presented.
motor and thus all the drawbacksconnected with the
flashing of brushes are eliminated. This motor is
denoted to as a dc motor because its coils are driven
by dc power source. The dc power is given to the
windings on the stator.
Keywords- BLDC motor, PI controller, Hysteresis
controller, Four quadrant operation.
I.INTRODUCTION
Energy saving is the main aim behind all the
development and control of motors. Conventional dc
motors have good control characteristics but their
performances are reduced due to commutation
problems. This commutation problems are
completely absent in induction motors, butthey have
limitations such as stumpy power factor and
deviating speed torque features. As a result of
focussing on energy saving, the demand for variable
speed permanent magnet motor drives has increased.
The usage of motor drives in the field of automation
also resulted in the increased demand for high
efficiency PM motor drives. This give rise to the
emergence of BLDC motors. New energy efficient
electric drives using PMBLDC motor have been
introduced to overcome the above mentioned
limitations. The permanent magnet machines have
better power factor and very good dynamic
characteristics and low inertia. Compared to
induction motor and other brushed dc motors, BLDC
motors have many advantages such as higher
efficiency, long operating life, higher speed ranges,
noiseless operation etc. These qualities of permanent
magnet
BLDC
motor results in widespread
applications like aerospace, automation, computers
robotics, electric vehicles etc.
Fig. 1 Block diagram of BLDC motor
Here the controller we used is hysteresis current
controller. The required reference current of the
controller is obtained from PI speed controller.The
PI controller eliminates delay and provides faster
control. This method of control scheme is quite
pleasing and robust.
III. FOUR QUADRANT OPERATION
For a BLDC motor, four modes of operations
namely forward motoring, forward braking, reverse
motoring and reverse braking are possible. The
operating modes are as shown in fig 2. In the first
quadrant, both speed and torque is positive so motor
rotates in forward direction. In second quadrant
speed remains in positive direction but torque is in
reverse direction. Reverse torque is used to brake the
motor.
II. BLDC MOTOR AND CONTROLLER
BLDC motor can be projected as a brushed dc motor
twisted inside out, where the permanent magnets are
fixed onthe rotor and windings onthe stator.As a
result, there are no brushes and commutator in this
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International Journal of Engineering Trends and Technology (IJETT) – Volume 28 Number 2 - October 2015
Fig.4 Equivalent circuit of BLDC motor.
The voltage equations of BLDC motor are:
Fig. 2. Operating modes
Third quadrant is just opposite of the first
quadrant.ie, both speed and torque is negative so
rotating in reverse direction. Exactly opposite of
second quadrant is fourth where power is being
produced. The supplied voltage is greater than back
EMF during the motoring modes and is less than
back EMF during generating modes.
The above equations in state space form:
Where,
La= Lb= Lc=L.
L is the self-inductances.
Ϸ inside the matrix represent
Va, Vb,Vc are the per phase stator voltages.
R is the per phase stator resistance.
Fig. 3 Closed loop drive
ia,i b,i c are the per phase stator currents.
Ea,Eb, Ec are the induced back EMF.
IV. MODELING OF BLDC MOTOR
There are two possible methods to model a BLDC
motor, one is abc phase variable model and the other
is d-q axis model. BLDC motor is a permanent
magnet motor with trapezoidal back EMF whereas
synchronous motor has sinusoidal back EMF. Since
trapezoidal the mutual inductance sandwiched
between stator and rotor is non sinusoidal. So
transforming to d-q axis does not provide any
addedbenefit, thus abc phase variable model is
chosen. Here we assume that all windings have
equal stator resistance and self and mutual
inductances are constant. The equivalent circuit
diagram of the BLDC motor is as shown in the fig.4.
ISSN: 2231-5381
The generated back EMF is trapezoidal in shape due
to permanent magnet straddling on the rotor and its
expression is as given below:
Where Ke is the back EMF constant and W is the
mechanical speed of rotor.
The electromagnetic torque equation is
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International Journal of Engineering Trends and Technology (IJETT) – Volume 28 Number 2 - October 2015
Where
is the speed of rotor and
electromagnetic torque.
is the
The equation of motion is:
increase of integral gain will allow the motor speed
to catch up with the reference speed. The
proportional and integral gain must be varied within
the limits otherwise it cause instability and the
controller become insensitive. Too high gains may
also result in saturation of the system. The Kp and
Ki values of the controller are resoluted by trial and
error method.
Where,
B. CURRENT CONTROLLER
B = damping constant.
Hysteresis current controller is used to limits the
phase currents within the hysteresis band. It
generates the switching signals to the inverter. This
method is adirect current feedback control, in which
the actual current is continuously tracks the
command current within hysteresis band. When
current exceeds upper limit, the upper switch is
turned off and lower switch is turned on. Similarly
when current exceed lower limit, upper switch is
turned on and lower switch is turned off. The limits
of hysteresis band is normally selected by
considering 10 to 15 percentage of the actual motor
current. Thus the lower limit is taken as 10 % of
actual motor current and upper limit is 15% of the
motor current.
J = moment of inertia of the drive.
= load torque.
Fig.5.Simulink model of BLDC Motor.
A. SPEED CONTROLLER
The speed controller used to accomplish speed
regulation is conventional PI controller. The predetermined speed and restrained speed are the
feedback signals to the controller. PI controller
compares the motor speed with reference speed and
the speed error is processed to control the motor.
Fig.7.Modelling block of Hysteresis controller
The switching pattern is as given below:
If
If
If
If
If
If
Fig.6 Simulink model of PI Controller.
accordingly. It involves two separate modes –
proportional mode and integral mode. The reaction
to the current error is determined by proportional
mode while integral mode determine the reaction
based recent error.
Where
and UL, LL are the
higher and lower bounds of hysteresis band.
The sensitivity of controller and speed overshoot is
controlled by varying proportional gain and the
The input voltage to be fed to three phase BLDC
motor is supplied by voltage source inverter. The
inverter is implemented by the following equations:
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C. VOLTAGE SOURCE INVERTER
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International Journal of Engineering Trends and Technology (IJETT) – Volume 28 Number 2 - October 2015
[S1* Sau + S4*Sal] *|E| = Van.
TABLE 1
[S3* Sbu + S6* Sbl]*|E| = Vbn.
MOTOR PARAMETERS
[S5* Scu + S2* Scl]*|E| = Vcn.
No. of poles
4
Where Van, Vbn and Vcn are line neutral voltages.
No. of phases
3
Rated speed
1000 rpm
Rated voltage
130 V
|E| = Vd /2, Vd is the dc link voltage.
Sau& Sal are the upper & lower pulses of phase A.
Rated current
12 A
Sbu&Sbl are the upper &lower pulses of phase B.
Resistance/phase
0.7ohm
Scu&Scl are the upper & lower pulses of phase C.
Rated power
0.42 hp
Self
&
Mutual
inductance
Back EMF constant
0.0052H/ph
Torque constant
0.057 N-m/A
Moment of inertia
0.0005Kg/m2
Maximum torque
3 Nm
0.057V/rad/s
VI. SIMULATION RESULTS
The simulation results of the BLDC motor with
speed and current controller is as shown below.
Fig.8 Simulink model of inverter
V. DRIVE SYSTEM
The voltage required to drive the BLDC motor is fed
by three phase inverter. The gating pulses of the
inverter are injected by a hysteresis current
controller. This controller produce the required
pulses by comparing the actual motor currents with
reference current. The reference current is generated
by speed controller.Here the speed controller is
conventional PI controller which compares the
actual motor speed with a designed reference speed
to give an eroor signal.
Fig.10 Output waveform of speed of the motor.
The output speed waveform of the motor is as shown
above. The reference speed is taken as 1000 RPM.
From the figure it is clear that the actual motor speed
catches up with the reference speed.
Fig.11 Output waveform of torque of the motor.
Fig.9 Simulink model of Drive System
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The electromagnetic torque of the motor is as shown
in fig.11. In the beginning the torque is high when
the speed is increasing to its steady value. Once
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International Journal of Engineering Trends and Technology (IJETT) – Volume 28 Number 2 - October 2015
speed attain its stable value, torque will also settle to
its steady value.
Fig.15 Phase voltage of inverter
Fig.12 Back EMF waveform of BLDC motor
The above figure shows the trapezoidal back EMF
waveform of BLDC motor and it has 120 degree
mode of operation.The phase currents of the motor is
as shown in fig.13. At the outset the phase current is
high, later it is reduced to reference value when
speed reaches steady value. Here the reference
current is 12 A. The actual motor current in the
simulation result is nearly 12 A.
The simulation results of four quadrant operation of
three phase BLDC motor is given below. The
transition of quadrant from one to another is easily
visible from the following graphs. The output speed
and torque of four quadrant BLDC motor is as
shown below. The reference speed is set as 1000
rpm and load torque is given as 3 Nm.
Fig.16 Output speed waveform of four quadrant
operation of BLDC motor.
Fig.13 Output waveforms of Phase current
Fig.17 Output torque waveform of four quadrant
operation of BLDC motor.
Fig.14 Rotor position of BLDC motor
The phase voltage of three phase inverter is as
shown in fig.15. This voltage is used to fed the
BLDC motor.In this modelling the inverter is
operated according to the sector. So the selection of
sector is very important.
Fig.18 Generated back EMF waveform of four
quadrant operation of BLDC motor.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 28 Number 2 - October 2015
Fig.19Variation of rotor angle during forward
braking to reverse motoring.
Fig.20Variation of rotor angle during reverse
braking to forward motoring.
VII. CONCLUSION
The simulation model of BLDC motor drive system
with PI control and hysteresis current control based
on MATLAB/Simulink is presented. The modelling
of BLDC motor is also presented, which is very
useful in studying the drive system. Closed loop
simulation is carried out and the simulation results
are presented. The speed oscillations are reduced by
closed loop system. The four quadrant operation of
BLDC motor is also presented with the required
waveforms.
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