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Speed Control of Brushless DC Motor Using Conventional Controllers

Article  in  International Journal of Pure and Applied Mathematics · December 2018

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International Journal of Pure and Applied Mathematics
Volume 119 No. 16 2018, 3955-3961
ISSN: 1314-3395 (on-line version)
url: http://www.acadpubl.eu/hub/
Special Issue
http://www.acadpubl.eu/hub/

Speed Control of Brushless DC Motor Using Conventional Controllers

Lokesh Kumar Agrawal 1,*, Bhavesh Kumar Chauhan 2, G. K. Banerjee 1

1
Department of Electrical Engineering, IFTM University, Moradabad (U.P.), India
2
Department of Electrical Engineering, ABESIT, Ghaziabad (U.P.), India
*Corresponding author: lokesh_7575@rediffmail.com

Abstract- DC motors find a considerable relatively simple [2, 3]. DC motors have principle
application where controlling a system is a disadvantages that are: lifetime of brushes is the
primary objective. A motor which exhibits the limited and due to use of brushes, reliability is
characteristics of a dc motor but does not have
lower. Moreover, the need of replacement in
the commutator and the brushes is a Brushless
DC motor (BLDC) These motors are popular operation is also required for time to time
for many industrial applications due to their maintenance [4].
reliability, high efficiency, high starting torque, In practice, the design of BLDC motor drive
and reduced electrical noise. For BLDC motor involves a complex process such as modeling,
speed control, different controllers are control scheme selection, simulation and parameters
employed. In this work, the behavior of BLDC tuning etc [5,6]. PI controller offers the simplest and
motor has been determined without controller
yet most efficient solution to many real-world
and with conventional controllers using PI &
PID. The results have been compared to each control problems [7]. PI controller offers the
other; among conventional controllers, PID simplest structure and robust performance in a wide
controller provides better response with range of operating conditions [8]. With the help of
changing load. MATLAB/SIMULINK software PI controlling parameters the speed and armature
is used to carry out the above investigation. current of BLDC motor is controlled and regulated.
Keywords- BLDC motor, PI controller, PID However, conventional PID controller algorithm is
Controller simple, stable, easy adjustment and high reliability,
conventional speed control system used in
I. INTRODUCTION
conventional PID control [9, 10].
There are two types of motors used in This paper discusses about modeling and speed
industries; firstly dc motors where the flux is control techniques of BLDC motor using open loop
created by the current through the field coil of the and closed loop with conventional controllers-PI and
stationary pole structure, secondly, permanent PID controller. The performance of speed control of
magnet brushless dc motors in which the BLDC motor is verified through simulation analysis
permanent magnet provides the necessary air gap on MATLAB Simulink platform.
flux instead of wire wound field poles. As the II. BLDC MOTOR OPERATIONAL
brushless DC motors do not have brushes, the PRINCIPLE
commutation takes place electronically. BLDC
motor is actually a permanent magnet synchronous The working principle of a BLDC motor is
motor (PMSM) with trapezoidal back EMF [1]. same as for a brushed DC motor; i.e. based on
BLDC motors have properties such as internal shaft position feedback. In case of a brushed
DC motor, feedback is maintained using a
torque- speed characteristics and smooth speed
mechanical commutator and brushes. With BLDC
control [1]. In this case, the control of DC motor motor, it is attained using multiple feedback
does not require complex Hardware and also sensors. The most commonly used sensors are hall

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International Journal of Pure and Applied Mathematics Special Issue

sensors and optical encoders. Hall sensors work on is the self inductance of each phase and M is the
the hall-effect principle that when a current- mutual inductance between two phases.
carrying conductor is exposed to the magnetic
field, charge carriers experience a force based on Hence, electromagnetic torque can be obtained as:
the voltage developed across the two sides of the
conductor. If the direction of the magnetic field is 1
Te  (ea ia  ebib  ec ic )
reversed, the voltage developed will reverse as r (2)
well. For Hall-effect sensors used in BLDC
motors, whenever rotor magnetic poles (N or S) Where ωr is the mechanical speed of the rotor. The
pass near the hall sensor, they generate a HIGH or
equation of motion is:
LOW level signal, which can be used to determine
the position of the shaft.
d
For the three phases BLDC motors, the back- r  (Te  TL  Br ) / J (3)
EMF and phase current waveforms with 120° dt
conduction mode are shown in Figs. 1.1, 1.2, [11]-
The electrical speed ωe is related to the mechanical
[12].
speed for a motor with P numbers of poles as
following:

e  ( P / 2)r (4)

Where P is the number of poles, ωr is the rotor speed

in rad/sec.

IV. SPEED CONTROL OF BLDC

MOTOR

Fig. 1.1 Circuit diagram of BLDC motor drive system The speed control of BLDC motor with conventional
controller and fuzzy controller has been investigated.

a) PI Controller

P-I Controller is mainly used to eliminate the steady

state error. Since P-I controller has no ability to
predict the future errors of the system it cannot
decrease the rise time and eliminate the oscillations.
The output of the PI controller in time domain is
defined by the following equation:

t
output  K p e(t )  K i  e(t )dt
0 (5)
Fig. 1.2 Trapezoidal back emf pattern and reference current generation

III. MATHEMATICAL MODELING OF where Kp is the proportional gain, Ki is the integral

BLDC MOTOR gain and e(t) is the instantaneous error in the signal.
Dynamic equations BLDC motor is
b) PID Controller
represented as following:

v a   R 0 0  ia   L  M 0 0  ia  ea  P-I-D controller has the optimum control

v    0 R 0  ib    0 LM 0  d i   e  dynamics including zero steady state error, fast
 b   dt  b   b 
vc   0 0 R  ic   0 0 L  M  ic  ec 
(1) response (short rise time), no oscillations and higher
stability. The necessity of using a derivative gain
Where va, vb, vc are the phase voltages, ia,ib, component in addition to the PI controller is to
ic are the phase currents, ea, eb, ec are the phase eliminate the overshoot and the oscillations
back-EMF waveforms, R is the phase resistance, L occurring in the output response of the system. Its

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International Journal of Pure and Applied Mathematics Special Issue

output sum of three terms, proportional, integral

and derivative term. Each of these terms is
dependent on the error value e(t) between the
input and the output:

t
de(t )
output  K p e(t )  K i  e(t )dt  K d
dt
0 (6)
Where Kd is the proportional gain.

The BLDC motor has been simulated in the

MATLAB/SIMULINK environment. Fig.1.3
shows the Simulation model of BLDC motor
Fig. 1.4 Stator Current and back EMF of phase A
wihout controller. The motor is fed by a PWM
inverter. The inverter gates signals are created by
decoding the Hall Effect signals. Various
parameters used for simulation shown in TABLE
I.

TABLE I PARAMETERS USED FOR SIMULATION OF BLDC MOTOR

Stator phase resistance 2.8750 ohm

Stator phase inductance 8.5 mH

Torque Constant 1.4 N-m/A

Fig. 1.5 Speed of BLDC motor

Voltage constant 40 V/Krpm

Inertia Constant 0.8 X 10-3 Kg- m2

Number of poles 16

Number of phases 3

Voltage Input 24 V
Fig. 1.6 Electromagnetic Torque of BLDC motor

Proportional Constant 0.0015

From speed time waveform it can be seen that speed
Integral Constant 0.25 of motor is directly proportional input voltage.
Speed is a function of voltage. Speed of BLDC
motor can be controlled by applied voltage.
Fig.1.7 shows the Simulation model of BLDC
o
motor with PI controller.

Fig. 1.7 Simulation model of BLDC motor with PI controller

Fig. 1.3 Simulation model of BLDC motor wihout controller

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Fig. 1.8 Stator Current and back EMF of Phase A

Fig. 1.12 Stator Current and back EMF of Phase A

Fig. 1.9 Speed of BLDC motor with PI controller

Fig. 1.13 Speed of BLDC motor with PID controller

Fig. 1.10 Electromagnetic Torque of BLDC motor

Fig. 1.14 Electromagnetic Torque of BLDC motor

V. CONCLUSION

In this paper closed loop speed control of BLDC

motor drive with PID controller loop is carried out
and it is compared with PI controller fed BLDC
drive. Simulation results show that current ripple
and torque ripple are minimized which enhance the
Fig. 1.11 Simulation model of BLDC motor with PID controller performance of the drive. By comparing the
performances of Permanent-magnet brushless dc
motor with PI and PID controller, it is concluded
that applying the load torque to the motor with
conventional controller, motor speed will be
decreased and it should regain its speed quickly.
When load torque of 3 N-m is applied at 0.1 sec to

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International Journal of Pure and Applied Mathematics Special Issue

the motor with PID controller, motor drop its [11] Grasblum P., “3-phase BLDC motor contents control with
Hall sensors using DSP56F80x,”, Motorola App Note
speed and recovers speed in very less time as AN1916/D, 2004.
compared to PI controller. Rise time of PID
controller is better than PI controller. With PID [12] Ji Hua, Li Zhiyong, “Simulation of Sensorless Permanent
Magnetic Brushless DC Motor Control System,”, Proc. of the
controller, BLDC motor has no steady state error IEEE International Conference on Automation and Logistics,
while with PI controller, there is some steady state Qingdao, China, pp. 2847-2851, September 2008.
error. PID response gives high efficiency. The
results show that the dynamic performance of the
motor is quite satisfactory for various loading
conditions.

VI. REFERENCES
[1] Balogh Tibor,Viliam Fedak, Frantisek Durovsky.,
“Modeling and Simulation of the BLDC Motor in MATLAB
GUI”, Proceedings of the IEEE Fifth International
Conference on Fuzzy Systems and Knowledge Discovery,
US, pp. 1403- 1407, 2011.

[2] J.R.Hendershot and T.J.E.Miller, Design of brushless

Permanent-magnet Motors; Oxford, UK: Oxford Science,
1994.

[3] P.Pillay and R.Krishnan, Modeling, Simulation and

Analysis of Permanent-magnet Motor Drives, part II: The
brushless DC Motor Drive, IEEE Transactions on Industry
applications, vol.25,no.2,march/April 1989.

[4] A.K.Wallace and R.Spee, The effects of motor

parameters on the performance of brushless DC drive, IEEE
Transactions on Power Electronics, vol.5, no.1, pp.2-8,
January 1990.

[5] J.E Miler,” Brushless permanent-magnet motor drives,”

Power Engineering Journal, Vol. 2, No. 1, Jan. 1998.

[6] Uzair Ansari, Saqib Alam, Syed Minhaj Un Nabi Jafri,”

Modeling and Control of Three Phase BLDC Motor using
PID with Genetic Algorithm,” 2011 UKSim 13 th
International Conference on modeling and Simulation, PP.
189-194.

[7] Zwe-Lee Gaing,” A Particle Swarm Optimization

Approach forOptimum Design of PID Controller in AVR
System”, IEEE Transactions On Energy Conversion, VOL.
19, NO. 2, JUNE 2004

[8] Joyce Jacob, Surya Susan Alex, Asha Elizabeth Daniel,”

Speed Control of Brushless DC Motor Implementing
Extended KalmanFilter”,Certified International Journal of
Engineering and Innovative Technology (IJEIT) Volume 3,
Issue 1, July 2013.

[9] K. Ang, G. Chong and Y. Li, “ PID control system

analysis, design and technology,” IEEE Trans. Control
System Technology, Vol. 13, PP. 559-576, July 2005.

[10] Atef Saleh Othman Al-Mashakbeh, “ Proportional

Integral and Derivative Control of Brushless DC Motor,”
Eutopean Journal of Scientific Research 26-28 July 2009,
Vol. 35, PP. 198-203.

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