improving the dynamic performance of multiply-articulated vehicles

184 Pages·2009·6.32 MB·English

IMPROVING T HE DYNAMIC PERFORMANCE
OF MULTIPLY-ARTICULATED VEHICLES
by
Michael R. Rempel
B. A. Sc. (Mechanical Engineering), The University of British Columbia, 1999
A thesis submitted in partial fulfillment of the requirements for the degree of
Master of Applied Science
in
The Faculty of Graduate Studies
Department of Mechanical Engineering
We accept this mesj^^aj^onfomiing tojhe required standard:
The University of British Columbia
November 2001
© Michael R. RempeL 2001
In presenting this thesis in partial fulfillment of the requirements of an advanced degree at the
University of British Columbia, I agree that the Library shall make it freely available for
reference and study. I further agree the permission for extensive copying of this thesis for
scholarly purposes may be granted by the head of my department or by his or her
representatives. It is understood the copying or publication of this thesis for financial gain
shall not be allowed without my written permission.
Department of Mechanical Engineering
The University of British Columbia
2324 Main Mall
Vancouver, BC Canada
V6T 1Z9
Date:
Abstract
Current heavy vehicles having two or more trailers suffer from unique dynamic characteristics
which limit both their stability and maneuverability at speed. The control of these
characteristics in A-train vehicles is the objective of this work; specifically, the attenuation of
rearward amplification and high-speed offtracking. Control is attained is through automatic
steering of the A-dolly axle; the control system is localized entirely on the A-dolly, creating a
modular and easily-implemented unit.
The equations of motion were derived for a reference A-train vehicle, and the results simulated
and compared to literature. A nonlinear two-dimensional yaw plane model with semi-static
load transfer in the pitch and roll modes was found to adequately display the intended system
characteristics.
To apply control, a second linear state space model was created, based on the behavior of the
A-dolly and the second semitrailer only. For high-speed, low amplitude maneuvers under
feasible input frequencies, the results corresponded to the nonlinear simulation. Control was
achieved using a state variable feedback controller to steer the dolly wheels; the gains were
determined by moving the plant eigenvalues via Ackermann's method to the critically-damped
locations of the "faster" mode. The controller was shown as to be robust to parameter
estimation errors and to balance performance and required control inputs well. An Extended
Kalman Filter (EKF) was employed to estimate the unknown tire cornering properties and
states not measurable direcdy from the A-dolly.
Through simulation, it was found that the controller was effective in reducing both the
observed rearward amplification and the dynamic offtracking, although the effectiveness
decreased with increasing forward velocity. At the nominal velocity for interstate highways in
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the United States (24.6 m/s), the peak improvement in rearward amplification under control
was reduced to a minimum of 25 percent of the uncontrolled value; the peak value of
offtxacking was reduced up to 50 percent.
Key Words: rearward amplification, ojftracking, A-train, nonlinear simulation, state space, state variable
feedback, Extended Kalman Filter
Table of Contents
Abstract ii
Table of Contents iv
List of Figures ix
List of Tables xii
Acknowledgements xiii
Introduction and Objectives 1
1.1 Benefits of Twin Operations 2
1.2 Problems Associated With The Operation of Twins 3
1.2.1 Rearward Amplification 3
1.2.2 Rollover 4
1.2.3 Offtracking 5
1.3 Introduction to Equipment Used 7
1.3.1 The Fifth Wheel 7
1.3.2 The Pintle Hook 8
1.3.3 TheA-Dolly 9
1.4 Heavy Vehicle Configuration in the United States 10
1.5 Heavy Vehicle Operation in the United States 12
1.6 The Safety of Combination Vehicles 14
1.7 Conclusion - Subjects for Study 19
Review of Prior Research 22
2.1 Modeling Overview 22
2.2Reference Frames 23
2.3Tire Modeling 25
2.3.1.Slip Angle and Cornering Force 25
2.3.2.Linear Tire Modeling 29
iv
2.3.3 Tire Modeling Using A Look-Up Table 29
2.3.4 Tire Modeling Using Dedicated Functions 30
2.3.5 Combination of Braking and Tractive Force 32
2.4 Vehicle Modeling - Linear Two-Dimension 34
2.5 Vehicle Modeling - Non-Linear Two-Dimensional 34
2.6 Vehicle Modeling - Three Dimensional 36
2.7 Analysis Methods 38
2.7.1 Solution Using an Analog Computer 38
2.7.2 Solution Using Control Theory 39
2.7.3 Solution of Non-Linear Stability Using Lyapunov's Method 40
2.7.4 Simulation of a System of Non-Linear Equations of Motion 41
2.8 Results of Dynamic Modeling 41
2.9 Dedicated Offtracking Models 43
2.10 Methods of Reducing Rearward Amplification 44
2.10.1 C-Dollies and B-Trains 44
2.10.2 Shifted Instant Center Dollies 46
2.10.3 Forced-Steer and Skid-Steer Dollies 47
2.10.4 Liked Articulation Dollies 48
2.10.5 Roll Stiffened Pintle Hook Assembly 48
2.10.6 Locking A-Dolly 48
2.10.7 Steerable C-Dollies 50
2.10.8 Reduction of Rearward Amplification Through Active Yaw Control 50
2.10.9 Reduction of Rearward Amplification using Externally-Mounted Dampers 52
Modeling Multiply-Articulated Vehicles 53
3.1 Modeling Assumptions 53
3.2 Coordinate Systems 55
3.3 System of Equations 56
3.3.1 Yaw Equations of Motion 58
v
3.3.1.1 Tractor Yaw Equations 58
3.3.1.2 Lead Trailer Yaw Equations 59
3.3.1.3 Dolly Yaw Equations 59
3.3.1.4 Second Trailer Yaw Equations 60
3.3.1.5 Articulation Angles and Force Constraints 61
3.3.1.6 Velocity and Acceleration Constraints 63
3.3.1.7 Tire Forces and Aligning Moments 64
3.3.1.8 Manipulation into State Space Form 65
3.4 Load Transfer 66
3.4.1 Static Loading 66
3.4.2 Dynamic Loading Due to Roll 68
3.4.3 Dynamic Loading Due to Pitch 72
3.5 Tire Model Implementation 75
3.6 Driver Model 79
3.7 Simulation Protocols 81
3.8 Method Of Solution 84
3.9 Simulation Results 87
3.9.1 Verification of Results 87
3.9.2 Rearward Amplification Sensitivity Factors 91
- 3.9.3 Offtracking Results 95
3.10 Discussion 97
Control System Design 99
4.1 Linear Model Derivation 99
4.1.1 Preface to Modeling 100
4.1.2 Derivation of the Linear Equations of Motion.. 101
4.1.3 Constraint Equations 102
4.1.4 Slip Angles and Tire Modeling 104
4.2 State Space Formulation of the Equation of Motion 104
4.2.1 Controllability and Observability 106
4.3 Comparison of Linear and Non-Linear Models 107
4.4 System Eigenvalues 110
vi
4.5 State Variable Feedback Control 112
4.5.1 State Feedback and Ackerman's Formula 113
4.5.2 Screening of Candidate Control Strategies 114
4.5.3 The Linear Quadratic Regulator 116
4.5.4 Prototype Control 117
4.5.5 Critical Damping Control of the A-Dolly 118
4.5.6 Critical Damping of Each Mode 120
4.6 Discussion 122
State And Parameter Estimation 124
5.1 State Augmentation and the EKF 124
5.2 Discretization of the Equations of Motion 126
5.3 Formulation of the Extended Kalman Filter 128
5.4 Estimating Performance of the EKF 130
5.4 Convergence of the EKF Algorithm 133
5.5 Evaluation of Miscellaneous Parameters 134
5.6 Discussion 135
Results 136
6.1 Tire Property Identification 136
6.2 Dynamic Performance Improvement 137
6.2.1 Testing Under SAE J2179 138
6.2.2 Testing Using the Frequency Response Method 144
6.3 Comparison of Proposed Controller With UMTRI Results 148
6.4 Steady-State Offtracking Performance 150
6.5 Parameter Sensitivity 151
6.6 A-Dolly Sensor and Actuator Requirements 152
6.7 Discussion 154
Conclusions and Recommendations 155
7.1 Contributions of the Present Work 156
vii
7.2 Recommendations for Future Work 157
References 160
Appendix A: Reference A-train Data 165
Appendix B: Tire Data v 168
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List of Figures
Figure 1-1 — Typical Twin Trailer Truck 2
Figure 1-2 - Schematic of Rearward Amplification 4
Figure 1-3 — Low Speed Offtracking [5] 6
Figure 1-4 - Fifth Wheel Connection 7
Figure 1-5 - Pintle Hook Connection (a) Pintle Hook, (b) Locking Eye 8
Figure 1-6 - Typical A-Dolly 9
Figure 1-7 — Representative Heavy Vehicle Types 11
Figure 1-8 - National Average of Heavy Vehicle Usage, United States (1995) 12
Figure 1-9 - Regions for Analysis 13
Figure 1-10 — Combination Vehicle Usage By Region (Percentage of Total Ton-Miles) 14
Figure 1-11 — Fatal Crashes by Vehicle Class [9] 15
Figure 1-12 — Fatal Crash Rates on Various Highway Classes [9] 16
Figure 1-13 Accident Locations for Singles and Doubles [10] 17
—
Figure 1-14 - Accident Involvement for Singles 18
Figure 1-15 - Accident Involvement for Doubles 18
Figure 2-1 - ISO Standard Vehicle Reference Frame 24
Figure 2-2 Pneumatic Tire Under Lateral Loading [11] 26
—
Figure 2-3 - Slip Angle Versus Lateral Force, Michelin 10.00x20 27
Figure 2-4 - Slip Angle Versus Self-Aligning Torque, Michelin 10.00x20 28
Figure 2-5 — Friction Ellipse Concept 32
Figure 2-6 — C-Dolly Configuration 45
Figure 2-7 - Trapezoidal Dolly Configuration 46
Figure 2-8 - Locking A-Dolly (a) Locked, (b) Unlocked 49
Figure 3-1 - Inertia Reference Frames (black) and Tire Forces (red) and Hitch Forces (blue)
for A-Train 55
Figure 3-2 - Tractor FBD 58
Figure 3-3 - Lead Semitrailer FBD 59
Figure 3-4 - A-Dolly FBD 60
Figure 3-5 - Second Semitrailer FBD 61
Figure 3-6 - Static Loading, Standard A-Train 67
Figure 3-7 - Load Transfer Due to Roll for the A-Dolly Second Semitrailer Unit
(a) A-Dolly, (b) Second Semitrailer 69
Figure 3-8 - Load Transfer Due to Roll for the Tractor-Lead Semitrailer Unit (a) Tractor,
(b) Lead Semitrailer 71
Figure 3-9 Load Transfer Due to Pitch (a) Second Semitrailer, (b) A-Dolly, (c) Lead
—
Semitrailer, (d) Tractor 74
Figure 3-10 - Comparison of Tire Properties: (a) Lateral Force vs. Slip Angle, (b) Aligning
Moment vs. Slip Angle 77
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