Modeling and Characteristic Curves of Electric Power Steering System
Hui Zhang, Yuzhi Zhang, Jinhong Liu, Jing Ren
Xi’an University of Technology 710048 Xi’an, Shaanxi, China
esneg01@163.com
Yongjun Gao
Xi’an Yongdian Electric Co.,Ltd 710015 Xi’an, Shaanxi, China
esneg02@163.com Abstract—Electric Power Steering (EPS) has important
significance in improving the auto’s dynamic and static performances. This paper deals with the mathematical model and characteristic curves of EPS System. First, the principle and structure of EPS are discussed. Then the characteristics of EPS system are analyzed, including the typical power curves which deal the relationship of the assist torque and the steering wheel torque. At last the EPS system’s dynamic model and the computerized simulation model have been established in MATLAB/Simulink in teams of three aspects which are the mechanical steering without power system, EPS system and EPS system with PID control. The simulation result that the actual current of the motor follows precisely the target current validates the designed assist characteristic.
Index Terms--EPS; mathematical model; PID; characteristic curves; simulation
I. EPSSYSTEM OVERVIEW
Compared with mechanical steering systems or hydraulic assist systems, EPS has attracted much attention for its advantages by improving fault-tolerant, disturbance rejection, fuel economy, start-up on low temperature, safety and environment friendliness. EPS is becoming an important spot of the research and development in automobile industry.
For these reasons, the EPS is on the trend of expansionary demand trend in recent years as shown in Fig. 1[1].
Fig. 1. Assist characteristic curves of EPS
The difference between manual steering configuration and EPS system is shown in Fig. 2. In the manual steering, the input steering angle and torque are transferred to rack and
pinion shaft via universal joint. The rotational torque of pinion rod is transformed to propelling power of rack shaft axial force. And the rack shaft axial force will be converted to swing motion of tires via the Tie Rod and Knuckle. On the other hand, in EPS the vehicle speed signal from vehicle speed sensor, steering toque signal from the torque sensor of the Torsion Bar and the power net voltage etc. are processed in the Electronic Controller Unit(ECU) to get the optimized steering characteristic[2].1
(a) manual steering configuration
(b) Configuration of the EPS system Fig. 2. Two different steering model
There are four different types of EPS, column, pinion, rack-assisted and a fully steer by wire type. In this paper, The configuration of column-type EPS is shown in Fig. 2(b) is used as an example. It consists of a torque sensor, which senses the driver’s movements of the steering wheel as well as the movement of the vehicle; an ECU, which performs calculations of assisting force based on signals from the
The authors gratefully acknowledge the financial support of the National Natural Science Foundation of China (50977078) the Provincial Natural Science Foundation of Shaanxi (2009JM7001) the Provincial Education Department Foundation of Shaanxi (09JK676) the Key Technology R&D Program of Xi’an (CXY08005)
PEDS2009
1390
torque sensor and vehicle sensor; a motor, which produces turning force according to the output from the ECU; and a reduction gear, which increases the force from the motor and transfers it to the steering mechanism [3]. In a word, the whole torque required for pure mechanical steering is provided by the driver, but in the EPS system, the motor provides assisted power to the driver, so it reduces the steering torque and provide various steering feel.
II. ASSIST CHARACTERISTIC CURVES
The target motor current which is determined by the assist characteristic based on the input of torque sensor and vehicle speed sensor. The relationship of the real-time vehicle speed is derived from vehicle speed sensor and the steering wheel torque is expressed by the following function IT = f(V,Ts). By using the Lookup Table (2-D) block in MATLAB/simulink, the assist characteristic can be realized as shown in Fig. 3[3] and Fig. 4.
-8 -6 -4 -2 0 2 4 6 8
0 10 20 30 40 50 60 70 -20 -15 -10 -5 0 5 10 15 20
←0Km/h Assist characteristic camber
←10Km/h
←20Km/h
←30Km/h
←40Km/h
←50Km/h
←60Km/h
←70Km/h
the target motor current IT[A]
Fig. 3. Assist characteristic curves of EPS
-8 -6 -4 -2 0 2 4 6 8
0 20 10 30 40 50 60 -2070 -15 -10 -5 0 5 10 15 20
←0Km/h Assist characteristic camber
←10Km/h
←20Km/h
←30Km/h
←40Km/h
←50Km/h
←60Km/h
←70Km/h
the target motor current IT
Needn’t assist power
[A]
Fig. 4. Explanation of Assist characteristic curves
III. EQUATION
Fig. 2(b) shows the model of steering mechanism equipped with EPS. According to Newton’s laws of motion, the mechanical equation and Motor Model of EPS system can be described as (1)~(4).
p s r h s s s s s
s r
K X T K
B
J θ + θ + θ = + (1)
( )
p m r
m m m m m
m r
G X K
T B
J θ + θ = − θ − (2)
Ua=LmIm+RIm+Em (3)
) ( ) (
p s r p
s p m r p d m r r r r r
r r
X r
K r GX r
F GK X K X B X
M + + = + θ − + θ − (4)
Where
m v
m K
E = θ , Tm = KtIm
The corresponding relationship of EPS model’s dynamic equations and the different parts of EPS is shown in Fig. 5.
Where X and r θm stand for the rack position (m) and motor shaft angle (rad), respectively. Besides, θs, F , d T m are the steering wheel angle (rad), disturbance from road condition changes (N), and electromagnetic torque provided by electric motor (Nm), respectively.
) ( ) (
p r s p
s p
r m p
m d r r r r r
r r
x r K r Gx r F GK x K x B x
M + + = + θ− + θ−
m t m p r m m m m m m
m whereT KI
r Gx K T B
Jθ+ θ = − (θ− ) =
m v m m m m m
a LI RI E where E K U= + + = θ
p r s h s s s s s
s r
Kx T K B
Jθ+ θ+ θ= +
Fig. 5. The equations of EPS
IV. EPSCONTROLLER
The control system of EPS is shown in the block diagram of Fig. 6. There are two primary inputs, the driver torque signal detected by a torque sensor on the steering wheel and the vehicle speed signal, along with other system variables are continuously fed into an electric control module which determines the reference current based on the torque map. Normally, the classical proportional–integral–derivative (PID) controller is employed.
Th
V
Fig. 6. Block diagram of EPS control strategy
PEDS2009
1391
Assist Curve
Motor
steering system Controller
Voltage limiter Tsen
thetamp Fd inputed torque
phase compensation
Vehicle speed V
x' = Ax+Bu y = Cx+Du 1
Lm .s+Rm PWM
1 Ts.s+1
PID Gm
0.02 *as+1 0.02 s+1
Kt
Ke
Fig. 7. The model of EPS system
V. SIMULATION MODELS
The EPS system’s model can also be described in MATLAB/Simulink as shown in Fig. 7[4].
VI. RESULTS AND Conclusions
In the simulation, as shown in Fig. 8, the steering wheel is unit step input. Without power assist, the driver must provide the whole torque required for steering. However, with power assist, the amount of driver's torque is significantly reduced based on the reference steering torque from torque map. Fig.8 also shows that PID control used in EPS control strategy works well.
0.5 1 1.5 2 2.5
0 0.2 0.4 0.6 0.8 1 1.2 1.4
Fig. 8. Time responses of three types of steering
The next simulation, Fig. 9 shows the comparison of the steering wheel input force(the blue line) and the electron motor output force(the pink line) when vehicle speed is 30km/h.
VII.
0 0.5 1 1.5 2 2.5 3
-15 -10 -5 0 5 10 15
Fig. 9. Assist torque and driver's torque
From Fig. 10, it shows that the current of the motor’s armature and the driver's input torque nearly superposed, validating the mathematical model and control strategy.
0 0.5 1 1.5 2 2.5 3
-20 -15 -10 -5 0 5 10 15 20
Fig. 10. Target current and motor’s armature current
In this paper, EPS model is set up, and the simulation results of mechanical steering without power system, EPS system and the EPS system with PID control are compared.
At last, the actual current of the motor following the target current precisely shows that the designed assistance characteristic works effectively.
PEDS2009
1392
REFERENCES
[1] W. Ijiri, T. and Tsutsui, “Extension of EPS”, Koyo Engineering Journal No.162, 28, 2002.
[2] Kimitoshi Tsuji, Kenji Kataoka, Yasushi Kusaka, etc. EPS system analysis using multi domain simulation for conventional 12V power network design in a vehicle, Power Electronics and Applications, European Conference, pp. 1 - 10, Sept. 2007.
[3] Haobin Jiang, Jingbo Zhao,Haimei Liu, Long Chen, Low-pass filter based automotive EPS controller and comparative full-vehicle tests.
2008.
[4] Guobiao Shi, Rongwei Shen, Yi Lin, The modeling and simulation technology of electric power steering, Jilin university journals(ENGINEERING SCIENCE) vol.37, No.1, Jan 2007.
PEDS2009
1393
