The SBW model can simulate the mechanical model equivalent. The SBW model without steer column can decrease the vehicle weight and the cost of cars.
The tire model can simulate the external torque of vehicle on different road.
Future we can use the tire model and steering wheel system of SBW model to simulate the steering wheel reactive torque of the vehicle on different road.
33
Reference
[1] 賴耿陽，“車輛驅動及控制＂，台南，復漢，1998。
[2] Hans B. Pacejka, “ Tyre and Vehicle Dynamics”, Butterworth-Heinemann, 2002.
[3] Bakker, E., Pacejka, H.B. and Lidner, L.,”A new tire model with an application in vehicle dynamics studies”, SAE Technical Paper Series, 890087, 1989.
[4] E Bakker, L Nyborg, H Pacejka, “Tyre modelling for use in vehicle dynamics studies”, Society of Automotive Engineers Paper, No.870421, 1987.
[5] M.米奇克，“汽車動力學 C 卷＂，北京，人民交通出版社，1997。
[6] Konghui Guo, Dang Lu, Shih-ken Chen, William C. Lin, Xiao-pei Lu,” The UniTire model: a nonlinear and non-steady-state tyre model for vehicle dynamics simulation”, Vehicle System Dynamics, Jan, 2005.
[7] 郭孔輝，袁忠誠，盧蕩，“UniTire 輪胎穩態模型的聯合工況預測能力 研究＂，汽車工程，6，NO.28，2006。
[8] Gillespie, T.D., “Fundamentals of Vehicle Dynamics”, Society of Automotive Engineers, 1992.
[9] Durstine, J.W., “The Truck Steering System from Hand Wheel to Road Wheel”, SAE SP-374, January 1974.
[10] Gillespie, T.D., “Front Brake Interaction with Heavy Vehicle Steering and Handling during Braking”, SAE Paper No. 760025, 1976.
[11] Dwiggins, B.H., “Automotive Steering Systems”, Delmar Publisher, Albany,
34
NY, 1968.
[12] Taborek, J.J., “Mechanics of Vehicles”, Towmotor Corporation, Cleveland, OH, 957.
[13] Ned Mohan, Tore M. Undeland , William P. Robbins , ” Power Electronics:
Converters, Applications, and Design”, John Wiley & Sons, Inc., 2003.
[14] Reza N Jazar, “Vehicle Dynamics- Theory and Application”, Springer, 2008.
[15] William F. Milliken , Douglas L. Milliken “Race Car Vehicle Dynamics”, Society of Automotive Engineers, 1995.
[16] 吳秉霖，“力回饋方向盤於虛擬實境之發展＂，機械工程系所碩士論文，
國立交通大學，2003.
[17] 王柏堯，“車輛轉向系統方向盤力回饋控制技術研究＂，車輛工程研究 所碩士論文，大葉大學，2006.
[18] 林立璿，“車輛線控轉向系統研究與實作＂，車輛工程研究所碩士論文，
大葉大學，2008.
[19] 張碩編著，“自動控制系統＂，台北，全華，1998.
[20] 清水 浩，李添財 編譯，“電動汽車全集＂，台北，全華，1997.
[21] Bimal K. Bose, Modern Power Electronic and AC Drives, Printice-Hall, 2002.
[22] Ji-Hoon Kim and Jae-Bok Song, “Control logic for an electric power steering system using assist motor,” Science Direct journal, Mechatronics, pp.447-459, April 2002.
[23] Dugoff, H., Fancher, P.S., Segel, L., "An Analysis of Tire Traction Properties and Their Influence on Vehicle dynamic Performance," SAE Paper, No.700377, 1977
35
[24] R.W. Rivers, Technical traffic accident investigators' handbook: a level 3 reference, training, and investigation manual, Thomas, 1997.
[25] Yu Lei-yan, “Research on control strategy and bench test of automobile Steer-by-Wire system”, IEEE Vehicle Power and Propulsion Conference (VPPC), September 3-5, 2008.
[26] CJ Kim, , J-H Jang, S-N Yu, S-H Lee, C-S Han, J K Hedrick,” Development of a control algorithm for a tie-rod-actuating steer-by-wire system”, Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, Volume 222, Number 9 / 2008.
36
Figures
Figure1.1 The physical model of a tire
Figure1.2 Schematic diagram of the system
37
Figure1.3 Schematic block diagram of the system
Figure2.1 Illustration of typical steering systems
38
Figure2.2 Steer rotation geometry at the road wheel
Figure2.3 Front view of a tire and measurement of the camber angle
39
Figure2.4 Front view of a tire and measurement of the kingpin incline angle
Figure2.5 Toe-in and toe-out configuration on the front wheels of a car
40
Figure2.6 A positive and negative caster configuration on front wheel of a car
Figure2.7 Top view of a tire and measurement of the side slip angle
41
Figure2.8 SAE tire force and moment axis system
Figure2.9 Forces and moments acting on a right-hand road wheel
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Figure2.10 Moment produced by vertical force acting on K.P.I. angle
Figure2.11 Moment produced by vertical force acting on caster angle
43
Figure2.12 Steering moment produced by traction force
Figure2.13 Steering moment produced by lateral force
44
Figure2.14 Steering linkages model
Figure2.15 Equivalent dynamic model of steering system
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Figure3.1 Mechanism diagram of mechanical steering system
Figure3.2 Math model of the mechanical steering system K2
B K
B2
J2
J1 θ1
θ2
B1 ≅ 0 K1 ≅ 0
Thum
Text
Text Thum
46
Figure3.3 Steering wheel system and front wheel system
Figure3.4 Math model of steering system K2
B2
J2 J1
θ2 θ1
B1 ≅ 0 K1 ≅ 0
Thum
Text T1 T2
Text T2
Thum
T1 Steering
wheel system
Front wheel system
47
Figure3.5 Steer by wire system Text T2
Thum
T1
M
M
48
Figure3.6 Control block diagram of SBW 1
49
Figure3.7 SAE vehicle axis systems. [8]
Figure3.8 2DOF of bicycle model [8]
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Figure3.9 Simplified model of steering system [22]
Figure3.10 Reaction torque on different road
0 5 10 15 20 25 30
0 2 4 6 8 10 12 14 16 18 20
Torque-ext, V=20 Km/h
front wheel angle (degree)
Torque (N-m)
0 = 0.8
0 = 0.6
0 = 0.4
0 = 0.2
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Figure3.11 Reaction torque of different vehicle velocity
Figure3.12 LQG control structure
0 5 10 15 20 25 30
52
Figure4.1 Pole/Zero map of mechanical model
Figure4.2 Red frame on mechanical model
Pole-Zero Map
53
Figure4.3 Pole/Zero map of steer-by-wire models
Figure4.4 Red frame on steer-by-wire models
-1 -0.5 0 0.5 1
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Figure4.5 Pole/Zero map of SBW model with LQG control
Figure4.6 Red frame on SBW model with LQG control
-1 -0.5 0 0.5 1
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Figure4.7 SBW model root locus
Figure4.8 SBW model with LQG root locus
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
56
Figure4.9 Simulation with LQG, when input is torque human
0 10 20 30 40 50 60 70 80 90 100
1+v(n):without LQG
1+v(n):with LQG
1 estimation
2+v(n):without LQG
2+v(n):with LQG
2 estimation
57
Figure4.10 Simulation with LQG, when input is external torque
0 10 20 30 40 50 60 70 80 90 100
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Figure4.11 Case 1: simulation on different road
Figure4.12 Case1: vehicle locus on different road
0 10 20 30 40 50
Treaction, V=20km/h
time (s)
Vehicle locus, V = 20 km/h
X (m)
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Figure4.13 Case 1: simulation of different vehicle velocity
Figure4.14 Case1: vehicle locus of different vehicle velocity
0 10 20 30 40 50
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Figure4.15 Case 1: simulation with and without LQG control
Figure4.16 Case 1: vehicle locus with and without LQG control
0 10 20 30 40 50
Treaction, V=20km/h
time (s)
Vehicle locus, V = 20 km/h
X (m)
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Figure4.17 Case 1: Simulation with and without LQG control
Figure4.18 Case 1: vehicle locus with and without LQG control
0 10 20 30 40 50
Vehicle locus, 0=0.8
X (m)
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Figure4.19 Case 2: simulation on different road
Figure4.20 Case 2: vehicle locus on different road
0 5 10 15 20 25
2 angle (degree)
Time (sec)
Vehicle locus, V = 20 km/h
X (m)
Y (m)
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Figure4.21 Case 2: simulation of different vehicle velocity
Figure4.22 Case 2: vehicle locus of different vehicle velocity
0 5 10 15 20 25
2 angle (degree)
Time (sec)
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Figure4.23 Case 2: simulation with and without LQG control
Figure4.24 Case 2: vehicle locus with and without LQG control
0 5 10 15 20 25
2 angle (degree)
Time (sec)
Vehicle locus, V = 20 km/h
X (m)
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Figure4.25 Case 2: simulation with and without LQG control
Figure4.26 Case 2: vehicle locus with and without LQG control
0 5 10 15 20 25
2 angle (degree)
Time (sec)
Vehicle locus, 0=0.8
X (m)
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Figure4.27 Case 3: simulation with and without LQG
Figure4.28 Case 3: vehicle locus with and without LQG
0 5 10 15 20
reaction, V=20 km/h,
0=0.8
2 angle (degree)
Time (sec)
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Tables
Parameter Symbol Values Units
Steering wheel moment of inertia
J1 0.04 kg-m2
Steering wheel motor inductance
L1 9.06
× 10−5
Henry
Steering wheel motor resistances
R1 0.0345 Ohm
Steering wheel motor voltage constant
KΦ1 0.0345 V/(rad/s)
Steering wheel motor torque constant
Front wheel motor voltage constant
KΦ2 0.0345 V/(rad/s)
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Front wheel motor torque constant
Kτ2 0.0345 Nm/A
Steering column torsion stiffness
K 172 Nm/rad
Steering column damping B 2.25 Nm/(rad/s)
Steering angle ratio n 20
Steering torque ratio Q 10
Table4.1 Parameter of steer-by-wire model
Parameter Symbol Values Units
Vehicle mass M 1573 kg
Longitudinal distance from front axle to center of gravity
Lf 0.96 m
Longitudinal distance from center of gravity to rear axle
Lr 1.225 m
Longitudinal distance from rear axle to front axle
L 2.185 m
Vehicle yaw moment of inertia IZ 2868 kg-m2
adhesion reduction coefficient AS 0.00353
longitudinal stiffness of tire CS 45837 Nm/rad Front wheel cornering stiffness Cαf 58000 Nm/rad Rear wheel cornering stiffness Cαr 62812 Nm/rad
Pinion radius Rp 0.008 m
Table4.2 Vehicle parameter
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Table4.3 The road friction coefficient [24]
PORTLAND CEMENT
Polished or Glazed Well-traveled New, Coarse
Dry 0.5~0.75 0.6~0.75 0.7~1.0
Wet 0.35~0.6 0.45~0.7 0.5~0.8
ASPHALT or TAR Excess Tar, Bleeding
Polished or Glazed
Well-travele d, Smooth
New, Coarse Dry 0.35~0.6 0.45~0.75 0.55~0.8 0.65~1.0 Wet 0.25~0.55 0.4~0.65 0.4~0.65 0.45~0.8 GRAVEL
Loose Packed, Well-traveled
0.4~0.7 0.5~0.85
SNOW ICE
Cold, Loose Cold, Packed Cold, Frosted Warm Dry 0.1~0.25 0.25~0.55 0.1~0.25
Wet 0.3~0.5 0.3~0.6 0.05~0.1