Open Access Library Journal 
2018, Volume 5, e4267 
ISSN Online: 2333-9721 
ISSN Print: 2333-9705 
 
 
 
Design of Drive System for Sensorless 
Brushless DC Motor Based on Model Reference 
Adaptive Control and Its Application in 
Horizontal Well Tractor 
Zhou He, Yongjun Chen*, Bo Ruan, Shuhan Yu, Junwen Zhou 
College of Electronics and Information, Yangtze University, Jingzhou, China 
 
 
 
How to cite this paper: He, Z., Chen, Y.J., 
Ruan,  B.,  Yu,  S.H.  and  Zhou,  J.W.  (2018) 
Design  of  Drive  System  for  Sensorless 
Brushless  DC  Motor  Based  on  Model  Re- 
ference  Adaptive  Control  and  Its  Appli- 
cation  in  Horizontal  Well  Tractor.  Open 
Access Library Journal, 5: e4267. 
https://doi.org/10.4236/oalib.1104267   
 
Received: December 18, 2017 
Accepted: February 6, 2018 
Published: February 9, 2018 
 
Copyright © 2018 by authors and Open 
Access Library Inc. 
This work is licensed under the Creative 
Commons Attribution International   
License (CC BY 4.0). 
http://creativecommons.org/licenses/by/4.0/ 
Open Access
 
 
Abstract 
The actual working environment temperature of the horizontal well tractor is 
too  high,  which  leads  to  position  sensor  of  general  brushless  DC  motor 
(BLDCM)  cannot  work  normally.  Therefore,  the  position  sensorless  drive 
system is designed to overcome the problems caused by the position sensor in 
the  actual  working  conditions.  The  principle  of  sensorless  BLDCM  work  is 
introduced in detail, And drive system of Sensorless BLDCM was established 
by using simulation software. The use of three stage start make motor smoothly 
start,  the  motor  speed  detection  based  on  model  reference  adaptive  control 
(MRAC), ensures accurate commutation. Finally, the hardware and software 
design of the BLDCM system based on digital signal controller (DSC) is in-
troduced and tested. The experimental results show that the drive system can 
start  the  BLDCM  smoothly  in  the  high  temperature  environment,  and  can 
quickly track the given speed, which meet the actual work demand of the ho-
rizontal well tractor. 
 
Subject Areas 
Electric Engineering 
 
Keywords 
Horizontal Well Tractor, Brushless DC Motor (BLDCM), Position Sensorless, 
Model Reference Adaptive Control (MRAC) 
 
1. Introduction 
As horizontal well technology is increasingly used in oil and gas development, 
 
DOI: 10.4236/oalib.1104267    Feb. 9, 2018 
 
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Z. He et al. 
 
horizontal well tractors have been proposed as a new type of downhole motion 
device. It can meet the delivery of logging tools and auxiliary work such as per-
foration and fishing to solve the problem  that the instrument is difficult to be 
transported to a predetermined position in the downhole and horizontal wells by 
gravity. 
Brushless DC Motor (BLDCM) is a new mechatronic product with many ad-
vantages such as stable structure, high power density, high efficiency, easy main-
tenance, long life and easy driving. It has been widely used in the fields of aero-
space,  automotive,  robotics,  household  appliances  and  medical  devices.  There-
fore,  BLDCM  has  been  chosen  as  drive  motor  of  horizontal  well  tractor.  The 
overall structure of the horizontal well tractor is shown in Figure 1. 
However, due to the too high actual working environment temperature of the 
horizontal  well  tractor,  the  position  sensor  of  general  BLDCM  cannot  work 
normally  [1]  [2]  [3]  [4].  As  a  result,  the  general  BLDCM  will  generate  wrong 
commutation signals in this working environment, which may cause the motor 
lost step or even block turn. Therefore, the BLDCM used as drive motor of hori-
zontal well tractor needs to adopt a positionless driving manner to overcome the 
problem caused by the position sensor in the actual working condition. 
Based on the analysis principle of sensorless BLDCM work, the simulation of 
drive system  for sensorless BLDCM was established by using PSIM simulation 
software [5] [6]. The use of three stage start make motor smoothly start, the mo-
tor speed detection based on model reference adaptive control (MRAC) [7], en-
sures accurate commutation. Finally, the drive system for sensorless BLDCM was 
established based on digital signal controller (DSC) and tested. The experimental 
results show that the drive system can make BLDCM run stably in the high tem-
perature environment and  meet the actual  working conditions  of  the horizontal 
well tractor. 
Monitoring 
system on well
PC
Main 
Control
485 bus
RX
TX
TX
RX
SCM
TX
RX
power line 
carrier 
communication
power line 
carrier 
communication
single-core cable
BLDC_DRIVE_1
BLDC_DRIVE_2
BLDC_DRIVE_3
BLDC_DRIVE_4
BLDC_DRIVE_5
Figure 1. The overall structure of the horizontal well tractor. 
 
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DOI: 10.4236/oalib.1104267 
 
Z. He et al. 
 
2. The Principle of Sensorless BLDCM Work 
2.1. The Mathematical Model of BLDCM 
BLDCM  selected  by  horizontal  well  tractor  is  star  connection  and  the  central 
node is not led out, its equivalent circuit shown in Figure 2. 
According to Kirchhoff’s voltage law, the equation of phase voltage can be ob-
tained as follows:
+
=
L
0
0
 
0
R
0
R
0
0
V
a
V
b
V
c
i
0
 
a
 
i
0
 
b
 
R i
 
c
i
 
a
 
i
 
b
 
i
 
c
V V V —Voltage of each phase to the ground; 
in type: 
a
i —Phase current; 
i
,
c
b
k ω=
—Back EMF, 
e m
i
,
a
E
0
L
0
0
0
L
d
t
d
,
,
b
c
×
+
E
a
E
b
E
c
+
V
n
V
n
V
n
              (1) 
x
k ω   are back EMF coefficient and rotor mechani-
,e
m
cal speed; 
R —Phase resistance; 
L L
s
L
m
=
− —Equivalent inductance of stator winding, 
L L   are self induc-
,s
m
tance of stator winding and mutual inductance between stator winding; 
nV —Central node voltage of motor armature winding. 
 
2.2. Principle of Back EMF Zero Crossing Detection 
The back EMF of BLDCM is a trapezoidal wave, the current is a square wave, 
and the phase current of each phase winding must be consistent with the back 
EMF in order for the BLDCM to output the maximum torque. Therefore, Com-
mutation is required for every 60°electric angle in one electric period. Relation of 
back EMF  and current in BLDCM as shown in Figure  3. It can be seen from 
Figure  3  that  back  EMF  zero  crossing  point  leading  the  current  commutation 
signal 30˚ in each phase winding, So, The commutation time can be got accord-
ing to the back-EMF zero crossing point. The motor back EMF can not be meas-
ured directly, so, It is necessary to calculate the equivalent voltage by phase vol-
tage. 
Set x phase is the non-conducting phase, the phase current is 0, according to 
Equation (1) can be got:   
                                                    (2) 
It can be seen from Equation (2) that the commutation signal can be obtained   
V V
x
n
E
=
−
x
aV
bV
cV
L
L
L
ai
bi
ci
R
R
R
+
aE
bE
cE
+
+
-
-
nV
 
 
Figure 2. Equivalent circuit of a star connection BLDCM. 
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DOI: 10.4236/oalib.1104267 
 
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aE
ai
30
90
150
210
270
330 360
BEMF zero crossing 
point
bE
bi
Current commutation signal
cE
ci
a phase
0
b phase
c phase
Z. He et al. 
 
)
/(°θ
)
/(°θ
)
/(°θ
 
 
Figure 3. Relation diagram of back EMF and current. 
indirectly by comparing the relationship between the phase voltage and the cen-
tral node voltage. 
Since the center node of the motor selected by the drive system is not led out, 
it is necessary to fabricate the motor central node voltage. 
As a BLDCM, there are only two phases which have current at the same time, 
Due to conducting two-phase current equal to the opposite direction, the other a 
phase current is 0, from Equation (1) can be got: 
E
+
c
                                    (3) 
It can be seen from Figure 2 that the sum of the three phase back EMF is zero 
when the back-EMF zero crossing, so, the central node voltage at this time can 
be got as:   
V
3
n
E
a
E
b
+
V
a
+
V V
b
c
+
=
+
V
n
=
V
a
+
+
V V
b
c
3
                                                (4) 
3. Simulation and Analysis of Sensorless BLDCM Drive   
System Based on PSIM 
According  to  the  above  analysis,  Block  diagram  of  drive  system  for  sensorless 
BLDCM shown in Figure 4, the drive system uses speed, current double closed- 
loop control. 
PSIM  is  a  computer  simulation  software  specially  designed  for  power  elec-
tronics and motor control. It provides a powerful simulation environment for the 
research of power electronics analysis and digital control motor drive, and uses   
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Z. He et al. 
 
I _
act
DC
source
Spd_
ref
I _
ref
PI
U
PI
PWM 
controller 
Three phase
inverter
BLDCM
Spd_
act
Commutation
signal 
Speed 
calculation and 
positionless 
commutation
Figure 4. Sensorless BLDCM drive system block diagram. 
PSIM to establish drive system of sensorless BLDCM according to Figure 3. The 
parameters of the motor are as follows: The stator resistance is 11.9 Ω, the stator 
inductance is 2.07 mH, the stator mutual inductance is 0.69 mH, the number of 
motor pole pairs is 2, the back EMF coefficient is 16.15 V·krpm−1, the moment of 
inertia is 0.007 g·m2, the friction coefficient is 1.167 g·m2·s−1, the inverter input 
voltage is 300 V, the given speed is 6000 rpm. 
3.1. Three Stage Start of Sensorless BLDCM 
Since  the  back  EMF  increases  with  the  increase  of  speed,  the  back  EMF  zero- 
crossing  detection  is  not  suitable  for  motor  starting.  The  drive  system  adopts 
three  stage  start  algorithm  when  the  motor  is  starting,  namely,  the  rotor 
pre-positioning, external synchronous acceleration, self-synchronization. Figure 
5 and Figure 6 are diagrams of rotor position using a three stage start algorithm. 
From Figure 5 and Figure 6 shows, the use of three stage start algorithm can 
be  achieved  smooth  start  of  the  motor.  Figure  7  is  the  motor  speed  response 
curve. 
It can be seen from Figure 7, the use of three stage start algorithm to start, the 
speed  can  be  in  a  relatively  short  period  of  time  to  track  the  given  speed  to 
achieve the desired start effect. Figure 8 is the a phase voltage, PWM and current 
after switch to self-synchronizing. 
Visible, the simulation results consistent with the previous theoretical analysis, 
the  back-EMF  zero-crossing  lead  the  phase  commutation  signal  30˚  electrical 
angle. 
3.2. BLDCM Speed Detection Based on Model   
Reference Adaptive Control 
Based on the above analysis, Commutation of sensorless BLDCM based on the 
back-EMF zero-crossing detection needs to delay 30˚ electric angle time accord-
ing to speed, therefore, the accuracy of speed detection is crucial for commuta-
tion of sensorless BLDCM. The traditional speed detection is calculated by the 
time difference between two commutation signals. The obtained speed is the av-
erage speed between two commutation signals, which is not accurate enough, so 
commutation can not be performed at the optimum commutation time, So it is   
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Figure 5. Diagrams of rotor position with an initial electric angle of 0 degrees. 
 
Figure 6. Diagrams of rotor position with an initial electric angle of 200 degrees. 
 
Z. He et al. 
 
 
 
 
Figure 7. Motor speed response curve. 
 
DOI: 10.4236/oalib.1104267 
 
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Z. He et al. 
 
 
Figure 8. The a phase voltage, PWM and current after switch to self-synchronizing. 
 
necessary to find a more accurate method of speed detection. 
For BLDCM, when the current from phase a to phase b is considered. There 
are following equations: 
i
i
= −
a
b
 =
i
0
c
E
= −
a
E
b
                                                   
(5) 
According to the formula (1) the line voltage between phase a and phase b can 
be obtained: 
V
ab
=
V V
a
b
−
=
2
Ri
a
+
2
L
i
d
a
t
d
+
2
E
a
                                 
In stable condition, 
i
d
t
d
≈ . Then, (6) can be rewritten as: 
0
ω
m
=
V
ab
Ri
a
2
−
k
2
e
                                               
(6) 
(7) 
According to Equation (7), the motor speed can be calculated according to the 
line voltage and phase current, but the motor windings resistance could change 
with  the  change  of  temperature.  Therefore,  BLDCM  speed  detection  based  on 
model reference adaptive control (MRAC) is proposed. As shown in Figure 9. 
As can be seen from Figure 9, the main module of speed detection is a model 
reference  adaptive  regulator, 
Spe est   is  speed  estimated  by  line  voltage  and 
phase current, 
Spe ce   is speed calculated by the commutation signal, The in-
put of regulator is the deviation of the two speed, the output of the regulator is a 
correction variable quantity 
ck   to estimate the speed. 
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DOI: 10.4236/oalib.1104267 
 
When the motor stator winding resistance increases from 11.9 Ω to 15.9 Ω, the 
actual motor speed, the speed calculated based on the fixed resistor value, the   
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Z. He et al. 
 
ck
abV
ai
=ω
m
V
ab
Ri
a
c
k
2−
k
2
e
Spd_
est
PI
Spd _
ce
 
Figure 9. BLDCM speed detection based on model reference adaptive. 
 
Figure 10. Comparison of several speed detection methods. 
 
 
speed detected based on the commutation signal and the estimated speed based 
on the MRAC are shown in Figure 10. 
It can be seen from Figure 10 that after the change of the resistance of the sta-
tor winding of the motor, the estimated speed based on the MRAC is the closest 
to the actual speed. 
4. Actual Test and Result Analysis of Drive System   
for Sensorless BLDCM 
4.1. DSC Based Drive System of Sensorless BLDCM   
Drive system of sensorless BLDCM includes two parts: software and hardware, 
the software part includes the main program and several subroutines and inter-
rupt service functions, the main function is to achieve BLDCM without position 
start, commutation, PWM duty cycle setting and communicate with the upper 
computer. The hardware part includes the controller, drive circuit, three  phase 
inverter,  voltage  and  current  sampling  circuit.  and  the  overall  structure  of  the 
drive system is shown in Figure 11. 
As the actual working environment temperature of the horizontal well tractor 
is too high, there are high requirements on the controller. Therefore, the control-
ler of the drive system adopts the dsPIC series chip of the MICROCHIP company.   
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DOI: 10.4236/oalib.1104267