Modeling and Simulation of BLDC motor in
Electric Power Steering
Congzhao Cai, Hui Zhang, Jinhong Liu
Yongjun Gao
Xian University of Technology
710048 Xian, Shaanxi, China
esneg01@163.com
Xian Yongdian Electric Co. Ltd
710015 Xian, Shaanxi, China
esneg02@163.com
AbstractThis paper briefly describes the composition of electric
power steering (EPS) system and the development advantages of
brushless DC (BLDC) motor. Based on the mathematical model
of the BLDC motor and the requirements of the EPS system for
assist motor, a control strategy of the BLDC motor used in EPS
system is proposed, then a simulation model of control system
using in BLDC motor is set up, and its simulation analysis is
made. The feasibility, high reliability of the system and the
validity of the control method are proved by the fruitful
simulation results which serve a design method for a further
research of BLDC motor in EPS.
based on the mathematical analysis, and the validity of this
method has been proved by the simulation result.
Index Terms: Electric Power Steering (EPS); Brushless DC
(BLDC) motor; simulation analysis; control method
I.
INTRODUCTION
Electric power steering (EPS) is an advanced steering
system that uses an electric motor to provide steering assist.
EPS has many advantages compared with hydraulic power
steering system, such as saving energy, protecting environment,
and be easy to rectify by changing the design of controller
software to adjust the system's characteristic of power
assistance in any condition. As a new technology, EPS
undoubtedly represents the development direction of steering
system in the future.
The power source of EPS is electric motor, which is the
major factor affecting the EPS performance. In recent years,
the previous brush DC motor used in EPS has been gradually
replaced by the brushless DC (BLDC) motor. The BLDC
motor is a new type of DC motor which uses the electronic
commutation technology instead of mechanical commutation,
with operation high efficiency, high starting torque, wide speed
range, simple structure, reliable operation, etc. With the advent
of high-performance magnetic materials, BLDC motor
performance is greatly increased [1]. Its application in the
power system will be more widespread, especially in the
automotive industry. In practice, in order to shorten design
cycles, reduce cost and risk, the BLDC motor system can first
use modeling and simulation technology to establish its model.
By analyzing the motor speed, torque and other parameters and
imposing different control algorithms on the system, a best
control strategy can be found. In this way, a lot of actual design
time is effectively saved. Finally, in this paper, a simulation
model of BLDC motor for EPS control system is built, which
The authors gratefully acknowledge the financial support of
the Provincial Foundation for the Construction of Key Disciplines of Shaanxi
the National Natural Science Foundation of China (50977078)
the Provincial Education Department Foundation of Shaanxi (09JK676)
the Provincial Natural Science Foundation of Shaanxi(2009JM7001)
the Key Technology R&D Program of Xian (CXY08005)
II.
COMPOSITION OF ELECTRIC POWER STEERING AND ITS
REQUIREMENTS FOR ASSIST MOTOR
A. Composition of Electric Power Steering
The schematic diagram of an EPS system is shown in Fig.
1. The EPS system adopts a so-called column-type EPS system
in which the assist motor connected to the steering shaft
through spur gears delivers assist torque to the shaft. In this
system, EPS is consists of three main components: the signal
transducer (including the torque sensor and speed sensor),
power steering bodies (motor, clutch, retarding mechanism)
and the electronic control unit (ECU).
Fig. 1 The schematic diagram of an EPS system
B. Requirements for Assist Motor
In the EPS system, assist motor is a key component of the
EPS system. It is also the power source of EPS and its function
is in accordance with the instruction output of appropriate
auxiliary torque by electronic control unit. Therefore, the motor
of EPS has the following requirements [2]:
Start quickly, good servo performance, low speed with
large torque, moment of inertia is small.
Low noise, good mechanical properties.
978-1-4244-4813-5/10/$25.00 2010 IEEE
Easy to control, reliability and high security,
convenient maintenance.
Small size, light weight, as much as possible to save
space and reduce weight. In this paper, a 12 V DC
vehicle power supply is used.
III.
Ignore the magnetic circuit saturation, excluding the
eddy current and hysteretic loss.
Ignore alveolar effect, winding evenly distributed,
three-phase stator windings are symmetrical and
concentrated.
Not consider the armature reaction, air-gap magnetic
field distribution is similar to trapezoidal wave.
Fig. 2 shows the circuit topology of a three-phase inverter
for the brushless motor. Based on the above-mentioned
assumptions, the equivalent circuit of BLDC motor is shown in
Fig. 3.
i
Q3
Q1
c
1 c
( u i - ei )
3 i= a
i= a
Te =
IV.
1
(ea ia + eb ib + ec ic )
T - T - B
= e L
J
(2)
(3)
THE ESTABLISHMENT OF SIMULATION MODEL AND
SIMULATION RESULTS
For the BLDC motor of EPS, current control strategy is
adopted. This control strategy only needs wheel torque signal
and vehicle speed signal. Depending on these two signals and
pre-established assistant torque curves, the required current is
acquired (expressed as iref). The control scheme of the system is
shown in Fig. 4 [2].
In this paper, one outer speed loop and one inner current
loop as the double-loop control system is introduced, shown in
Fig. 5. In the double-loop control system, a discrete PID
controller is adopted in the speed loop and a hysteretic current
controller is adopted in the current loop on the principle of
hysteretic current track PWM inverter.
A ,B ,C
Q5
Udc =12V +
un =
The equation of BLDC motor electromagnetic torque can
be written as (2) and its motion equation can be depicted by (3)
MATHEMATICAL MODEL OF PERMANENT MAGNET
BLDC MOTOR
Modeling the entire system is the key to motor modelbuilding. In order to simplify the model and analysis, the
following assumptions are made [3]:
Where
ea
ia
B
Cdc
eb
ec
ib ic
Q2
Q4
Q6
Fig. 2 Circuit topology of a three-phase inverter for BLDC motor
Fig. 4 The control scheme of BLDC motor system in EPS
A ,B ,C
Fig. 3 The equivalent circuit of BLDC motor
Based on the above-mentioned equivalent circuit, the
voltage equation of the employed BLDC motor can be
expressed as (1):
0
0 ia
ua L- M
L- M
0 p ib
ub = 0
uc 0
0
L- M ic
R 0 0 ia ea un
+0 R 0 ib +eb +un
0 0 Ric ec un
(1)
Fig. 5 The double-loop control diagram of BLDC motor
With the help of Matlab/Simulink, the simulation model (as
shown in Fig. 6 [4]) can be set up to verify the control
strategies. The subsystem blocks of BLDC motor, IGBT
inverter, reference current and speed controller are created
respectively based on their own characteristics.
ia_ref
Out1
n_ref
Reference
speed (RPM )
In1
ia
Is
n
Speed Controller
pos
MATLAB
Function
MATLAB Fcn
i(A )
ua0
Ia
In2
ib_ref
In3
ic_ref
pos
Out3
ic
Ua
K-
ub0
Out2
ib
Ib
Gain
uc0
Ic
Ub
IGBT Inverter
Hysteretic current
Ea
e(V)
Eb
Uc
Ec
TL
Theta
Timer
-K -
Gain 1
Pos
n(rpm )
Te
BLDC
Te (N.m)
-KGain 2
pos
Theta
Fig. 6 The simulation model of BLDC motor
The BLDC motor parameters used in the simulation are
shown in TABLE I.
1.8
1.6
1.4
NOMENCLATURES
Symbol
Description
Value
Unit
ne
Rated speed
1000
r/min
Stator phase winding resistance
0.1
Self-inductance of stator winding
mH
Mutual inductance
0.5
mH
Motor inertia
0.002
kg.m2
np
Number of pole pairs of the motor
Supply voltage by the battery
12
Ke
Back-EMF coefficient
0.025
V/(rad.s-1)
Viscous damping coefficient
0.0002
N.m/(rad.s-1)
Simulation time
0.5
TL
Sudden load
0.5
N.m
Torque (N.m)
1.2
0.8
0.6
0.4
0.2
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Time (s)
Fig. 7 The torque response waveform
40
30
20
ia (A)
TABLE I.
10
According to the motor parameters mentioned above, the
simulation experiments of control system are conducted.
Waiting until the system enters its steady-state, the sudden load
is increased from 0.1Nm to 0.6Nm at 0.25s and returned to the
previous at 0.4s and the simulation waveforms have been
shown in Fig. 7~10. Fig. 7 and Fig. 8 respectively show the
simulation waveforms of the torque and the phase A current. In
the start-up stage, the system maintain a constant torque, which
does not result in greater torque and phase current impact as
shown in Fig. 7 and Fig. 8. The Fig. 7 indicates that with the
sudden increase of the load, the torque has a greater pulse,
which is mainly caused by the current commutation and
frequent switching of the current hysteretic controller.
-10
-20
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Time (s)
Fig. 8 The phase A current waveform
The role of the reference current in amplitude limiting is
very effective as shown in Fig. 8. Fig. 9 shows the phase A
back-EMF simulation waveform. Fig. 10 shows the speed
simulation waveform which shows the system has quick and
smooth response in the reference speed n=1000 r/min. Whether
the time at 0.25s or 0.4s, when the load suddenly increases or
reduced, the speed response reached steady-state is fast.
V. CONCLUSIONS
In this paper, a feasible simulation model of the BLDC
motor is established in Matlab/Simulink on the basis of the
motor performance of the requirements in the columntype
EPS system and the electromagnetic equations of BLDC motor.
The fruitful simulation results show that the proposed control
strategy of the BLDC motor is valid. Based on the study above,
according to the specific characteristics of EPS, changing the
part of the functional modules or control strategies is
convenient, so a more precise current control strategy of BLDC
motor for EPS will be further researched.
Ea (V)
-1
-2
-3
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
REFERENCES
0.5
Time (s)
[1]
Fig. 9 The phase A back-EMF waveform
1200
[2]
1000
800
S peed (r/min)
[3]
600
400
[4]
200
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Time (s)
Fig. 10 The speed response waveform
0.4
0.45
0.5
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