Design and Evaluation of a 3D Road Geometry Based Heavy Truck Fuel
Optimization System
by
Wei Huang
A dissertation submitted to the Graduate Faculty of
Auburn University
in partial fulfillment of the
requirements for the Degree of
Doctor of Philosophy
Auburn, Alabama
August 9, 2010
Keywords: truck fuel optimization, nonlinear programming, 3D road geometry, terrain,
map-matching system
Copyright 2010 by Wei Huang
Approved by
David M. Bevly, Chair, Associate Professor of Mechanical Engineering
David Beale, Professor of Mechanical Engineering
Song-yul Choe, Associate Professor of Mechanical Engineering
Andrew Sinclair, Assistant Professor of Aerospace Engineering
Abstract
This dissertation develops a 3D road geometry based optimal powertrain control system
in reducing the fuel consumption of heavy trucks. The real-time optimal control (OC)
system, solving a constrained nonlinear programming problem, is designed to predict and
command the optimal throttle, brake torque (generated from the engine retarder), gear
shifting, and velocity trajectory to minimize the fuel consumption and travel time. Throttle
and gear shifting are continuous and discrete control inputs respectively, which is a mixed-
discrete nonlinear programming problem (MDNLP). The optimization solver developed is
an interior-point algorithm plus a rounding-off method, where all discrete gear ratios are
handled as continuous variables and optimized, and then the optimal discrete gear ratios are
obtained by rounding up each continuous gear ratio to the nearest discrete value.
Simulation and experimental tests of a Class 8 truck are conducted with GIS 3D road
geometries. Test results show that the optimal control system is able to reduce fuel consump-
tion up to 3.0% with small travel time increases on level and rolling terrains when compared
to the defined baseline. When on the highly mountainous terrain with steep crest slope and
long slope length, the OC could only save a small amount of fuel. Thus, it is found that the
gain in fuel economy is directly effected by the change in terrain type.
Additionally, sensitivity analyses for the terrain and road geometry are conducted to
investigate how the change of the terrain and the errors in the terrain data effect the gain
in fuel economy and the system performance. For the terrain sensitivity, it is found that the
gain in fuel economy is directly related to the change of road grade (both the magnitude and
frequency) and slope length. For the terrain error sensitivity, the road error largely effects
both the fuel economy and the system performance. This research reveals that the impact
from the absolute error (a shift in the slope position) on the fuel savings is not as evident
ii
as that from the relative error (a different slope value). The impact from both absolute
and relative errors on the system performance is significant, which shows the requirement to
apply a high accuracy road map in real road tests as well as in production uses.
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Acknowledgments
First and foremost, I would like to thank all of people who encouraged and supported
me during the undertaking of this research.
I would present my deep appreciation to my supervisor Prof. David Bevly, for giving
me the precious opportunity to join in the GPS and Vehicle Dynamics Lab and conduct such
an interesting Ph.D. dissertation project. He, with his strong scientific personality, guided
and discussed with me in many aspects.
I would like to express my sincere gratitude to my Ph.D. program committee members,
Prof. David Beale, Song-yul Choe, Andrew Sinclair, and Prof. John Y. Hung, for their
guidance and advice. They have been a constant source of inspiration, encouragement and
assistance during this dissertation work, both in my academic studies and more.
Special thanks to my parents, relatives and all my friends for their continuous support
and stimulation of my perseverance in my research activities. Without them this work would
have been monumentally harder to carry out.
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Table of Contents
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Motivation and objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Background and literature survey . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2.1 Road profile based fuel economy research . . . . . . . . . . . . . . . . 2
1.2.2 Solving of hybrid optimal control problems . . . . . . . . . . . . . . . 5
1.2.3 Real-time optimal control system design . . . . . . . . . . . . . . . . 14
1.3 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.4 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2 Road Geometry and Baseline . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.1 Road Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.1.1 Basic road definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.1.2 Parameter based highway simulation . . . . . . . . . . . . . . . . . . 23
2.1.3 Calculation of real road grade . . . . . . . . . . . . . . . . . . . . . . 26
2.1.4 Real road geometries and terrain type analysis . . . . . . . . . . . . . 26
2.2 Driver Cycle and Baseline . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3 Heavy Truck Model and Terrain Based Fuel Consumption . . . . . . . . . . . . 32
3.1 Heavy Truck Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.1.1 Longitudinal dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 32
v
3.1.2 Engine map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.1.3 Engine efficiency and fuel consumption map . . . . . . . . . . . . . . 34
3.1.4 Driveline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.1.5 Tire slip and gradeability . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2 Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2.1 Using test data from R5 . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2.2 Using test data from R6 . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.3 Terrain Based Fuel Consumption . . . . . . . . . . . . . . . . . . . . . . . . 46
3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4 Optimal Control System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.1 NLP solver operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.1.1 Direction collocation method . . . . . . . . . . . . . . . . . . . . . . . 50
4.1.2 Evaluation of objective and constraint functions and their gradients . 51
4.1.3 Discrete gear ratio calculation . . . . . . . . . . . . . . . . . . . . . . 53
4.1.4 MDNLP solution module . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.1.5 Global and local optimization analysis . . . . . . . . . . . . . . . . . 57
4.1.6 Series NLP solver operation . . . . . . . . . . . . . . . . . . . . . . . 61
4.2 Real-time optimal control system . . . . . . . . . . . . . . . . . . . . . . . . 64
4.3 Complete real time system structure . . . . . . . . . . . . . . . . . . . . . . 65
4.3.1 CAN interface and Electronic Horizon . . . . . . . . . . . . . . . . . 65
4.3.2 Software Modules 1 and 2 . . . . . . . . . . . . . . . . . . . . . . . 67
4.4 Real time system operation . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.4.1 OC prediction update and initialization . . . . . . . . . . . . . . . . . 69
4.4.2 Optimization time . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5 Road Tests and Result Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.1 Experimental system setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
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5.1.1 Simulation system setup . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.1.2 Real-time experimental system setup . . . . . . . . . . . . . . . . . . 74
5.2 Simulation tests with simulated roads . . . . . . . . . . . . . . . . . . . . . . 76
5.2.1 Single sag and crest . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.2.2 Different road grade and slope length . . . . . . . . . . . . . . . . . . 79
5.3 Simulation tests with real road geometries . . . . . . . . . . . . . . . . . . . 81
5.3.1 Real road geometries tests and results analyses . . . . . . . . . . . . . 81
5.3.2 Analyses of different set speeds for fuel savings . . . . . . . . . . . . . 86
5.4 Real road test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
6 Sensitivity Analysis of Road Map Errors . . . . . . . . . . . . . . . . . . . . . . 92
6.1 Terrain Error Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
6.1.1 Different road maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6.1.2 Simulation setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6.1.3 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6.2 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
7.1 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
7.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
7.2.1 Modification of the optimal control system . . . . . . . . . . . . . . . 103
7.2.2 Design of an optimal power management system for a hybrid electric
truck . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
A Abbreviations and frequently used symbols . . . . . . . . . . . . . . . . . . . . . 110
A.1 List of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
A.2 List of frequently used symbols . . . . . . . . . . . . . . . . . . . . . . . . . 111
B Implementation of optimal control system for real road test . . . . . . . . . . . . 112
vii
B.1 Software module 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
B.1.1 Optimal control system scheme . . . . . . . . . . . . . . . . . . . . . 115
B.1.2 Supervisor system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
B.1.3 CAN and EH data processing . . . . . . . . . . . . . . . . . . . . . . 121
B.1.4 Map-matching lookup table . . . . . . . . . . . . . . . . . . . . . . . 122
B.2 Software module 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
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List of Figures
1.1 The basic structure of the PCC system [5] . . . . . . . . . . . . . . . . . . . 4
1.2 The basic structure of the MPCC system [8] . . . . . . . . . . . . . . . . . . 5
1.3 Method structure of solving dynamic optimization problem . . . . . . . . . . 8
1.4 Complete SQP algorithm flow chart . . . . . . . . . . . . . . . . . . . . . . . 10
1.5 Basic model predictive control loop [36] . . . . . . . . . . . . . . . . . . . . . 15
1.6 Real-time optimal feedback control through an inner-outer loop structure [39] 17
2.1 Road grade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2 Vertical curves and tangents . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3 Generated highway, comparison of simulations 1/2/3 . . . . . . . . . . . . . 25
2.4 Generated highway, comparison of simulations 4/5/6 . . . . . . . . . . . . . 25
2.5 Overview of Intermap?s road geometries in California . . . . . . . . . . . . . 27
2.6 Road elevation and grade maps for R1 and R2 . . . . . . . . . . . . . . . . . 28
2.7 Road elevation and grade maps for R3 and R4 . . . . . . . . . . . . . . . . . 29
2.8 Road elevation and grade maps for R5 and R6 . . . . . . . . . . . . . . . . . 29
3.1 Longitudinal Free Body Diagram (FBD) . . . . . . . . . . . . . . . . . . . . 33
3.2 Comparison of real and approximated engine map . . . . . . . . . . . . . . . 34
3.3 Comparison of real and approximated BSFC time rate map . . . . . . . . . . 36
3.4 BSFC map approximation error: real minus approximated map . . . . . . . 37
3.5 Longitudinal FBD and powertrain model . . . . . . . . . . . . . . . . . . . . 37
3.6 Block diagram for the cruise controlled truck (CC) . . . . . . . . . . . . . . 41
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3.7 Block diagram for model validation . . . . . . . . . . . . . . . . . . . . . . . 41
3.8 Measured data: road grade, CC torque, and gear, R5 . . . . . . . . . . . . . 42
3.9 Comparison of CC and simulation model speeds, R5 . . . . . . . . . . . . . . 42
3.10 Comparison of CC and simulation model fuel use, R5 . . . . . . . . . . . . . 43
3.11 Measured data: road grade, CC torque, and gear, R6 . . . . . . . . . . . . . 44
3.12 Comparison of CC and simulation model speed, R6 . . . . . . . . . . . . . . 44
3.13 Comparison of CC and simulation model fuel use, R6 . . . . . . . . . . . . . 45
3.14 Fuel consumption and terrain conditions, 90 km/h . . . . . . . . . . . . . . . 47
3.15 Fuel consumption and terrain condition, comparing 90 and 110 km/h . . . . 47
4.1 Complete NLP solver algorithm flow chart . . . . . . . . . . . . . . . . . . . 55
4.2 Convex set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.3 Convex function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.4 Zoomed-in BSFC time rate map . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.5 Optimal velocity, engine/brake torque, and gear shifting, on a 4% crest . . . 61
4.6 Series NLP optimizer operation for brake calculation . . . . . . . . . . . . . 63
4.7 Optimal velocity, engine/brake torque, and gear shifting, on a -4% sag . . . . 63
4.8 Real-time fuel optimal feedback control through two DOF structure . . . . . 64
4.9 Real time experimental system setup . . . . . . . . . . . . . . . . . . . . . . 66
4.10 Electronic Horizon system information update . . . . . . . . . . . . . . . . . 67
4.11 Recursive implementation of the optimal control system . . . . . . . . . . . . 69
5.1 Simulation system setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.2 Real time experimental system setup . . . . . . . . . . . . . . . . . . . . . . 75
5.3 Comparison of velocity, engine/brake torque, and gear: CC & OC, on a -4%
sag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.4 Comparison of fuel consumption and rate: CC & OC, on a -4% sag . . . . . 78
x
5.5 Comparison of velocity, engine/brake torque, and gear: CC & OC, on a 4%
crest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.6 Comparison of fuel consumption and rate: CC & OC, on a 4% crest . . . . . 79
5.7 Fuel savings on different road grades and slope lengths, OC vs. CC . . . . . 80
5.8 Travel time increases on different road grades and lengths, OC vs. CC . . . . 80
5.9 Comparison of velocity, torque, and gear on R3 with 25 m/s set speed, OC
vs. CC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.10 Comparison of fuel consumption and rate on R3 with 25 m/s set speed, OC
vs. CC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.11 Zoomed-in comparison of velocity, torque, and gear on R3 with 25 m/s set
speed, OC vs.CC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.12 Fuel saving and travel time change with different set speeds, OC vs CC . . . 86
5.13 Comparison of velocity, torque, and gear on R4 with 31.1 m/s set speed, OC
vs. CC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.14 Comparison of fuel consumption and rate on R4 with 31.1 m/s set speed, OC
vs. CC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.15 Comparison of velocity, engine torque, and gear position on a section of R5 . 89
5.16 Comparison of fuel consumption w.r.t.road geometry on R5, CC vs.OC . . . 89
5.17 Elevation map of R6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
6.1 Comparison of vertical error distribution density, R3.1 to R3.5 . . . . . . . . 95
6.2 Comparison of road maps with different accuracies, R3 vs. R3.2 and R3.5 . . 95
6.3 Block diagram of simulation setup for terrain error sensitivity analysis . . . . 97
6.4 Fuel saving using different road maps: R3 and R3.1-R3.5 . . . . . . . . . . . 98
6.5 Zoomed-in comparison of the OC performances by using maps, R3, R3.2, and
R3.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
B.1 Real time experimental system setup . . . . . . . . . . . . . . . . . . . . . . 112
B.2 Complete system scheme of S1, and CAN receive/transmit blocks . . . . . . 113
B.3 System scheme of S1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
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B.4 Optimal control system scheme . . . . . . . . . . . . . . . . . . . . . . . . . 115
B.5 Electronic Horizon system information update . . . . . . . . . . . . . . . . . 116
B.6 Optimal control system flow chart . . . . . . . . . . . . . . . . . . . . . . . . 117
B.7 Supervisor system scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
B.8 Supervisor system Stateflow chart . . . . . . . . . . . . . . . . . . . . . . . . 120
B.9 Fork road condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
B.10 Nonlinear programming solver system scheme in S2 . . . . . . . . . . . . . . 123
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List of Tables
2.1 Maximum road grade relative to design speed and terrain type . . . . . . . . 23
2.2 Fixed parameters for the parameter based highway simulation . . . . . . . . 24
2.3 Parameter based highway simulation examples . . . . . . . . . . . . . . . . . 24
2.4 Intermap road profiles analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.1 Simulated highways for fuel consumption analysis . . . . . . . . . . . . . . . 46
5.1 Intermap road profiles analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.2 Comparison of fuel consumption and travel time, R1 to R4 . . . . . . . . . . 82
5.3 Comparison of fuel consumption with same travel time, R1 to R4 . . . . . . 83
5.4 Comparison of fuel consumption and travel time for R5, and its sections . . . 88
5.5 Comparison of fuel consumption and travel time for R6 . . . . . . . . . . . . 90
6.1 Analysis of vertical errors in maps R3.1 to R3.5 . . . . . . . . . . . . . . . . 94
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Chapter 1
Introduction
1.1 Motivation and objective
Nowadays, heavy trucks account for a high percentage of the US?s highway fuel usage.
In the 2006, US motor vehicles used 535,809,195,978 liters of petroleum-based motor fuel, 15-
20% of which was used by heavy trucks. Manufacturers, therefore, are interested in making
trucks more fuel efficient. The major fuel losses of moving trucks are from air drag, rolling
resistance, and road slope. The fuel losses resulting from the road slope can be significant
in heavy vehicles such as long haul trucks.
The research was performedin collaborationwith EatonandIntermap Corp., to quantify
the fuel savings for heavy trucks using Eaton?s test truck and Intermap?s 3D road geometry.
The initial research objectives were:
? Design a 3D road geometry based optimal powertrain control system to predict and
command the optimal throttle, brake torque, gear shifting, and velocity trajectory in
reducing the fuel consumption and travel time of heavy trucks.
? Investigate how the change of the terrain and the errors in the terrain road geometry
effect the gain in fuel economy and the system performance.
1.2 Background and literature survey
Several related research directions are surveyed in this section. Prior work focusing on
the relation between the road profile and vehicle fuel economy is introduced first, which is
followed by the theoretical study of solving the trajectory optimization problem and the
design of the real-time optimal control system.
1
1.2.1 Road profile based fuel economy research
The interaction between terrain variation and vehicle fuel consumption has gained more
and more research interest since the 1970s. The conducted work is generally within two
areas: fuel optimal vehicle trajectory optimization and real-time fuel optimal control system
design.
Fuel optimal vehicle trajectory optimization
The original trend of this research was to find the optimal speed profile that minimizes
vehicle fuel consumption in traversing different paths or routes. The results were then used
to support general practice in guideway design for long distance transportation to achieve
the best fuel efficiency, e.g., setting speed limit, training new drivers, and generating advice
to regulate driving style.
Some work, stemming from [1], formulated an optimal control problem for a vehicle
model to minimize fuel consumption and the results suggested that fuel consumption is
minimized by operation at a constant speed [2], [3]. In the early work [1], authors developed
a feedback algorithm for driving a highway vehicle for minimum fuel consumption. The
problem was derived from the Pontryagin maximum principle to provide a mathematically
optimal performance subject to the driver?s choice of a trip time limit. Authors concluded
that the optimal velocity for a level road is a constant velocity. However, they considered
the speed limit only at 55 mph and their analytical solution technique obligated them to
model the car?s fuel consumption rate with a highly simplified function, which may cause a
loss of generality.
Authors in [2] addressed the question of what speed profile will minimize fuel consump-
tion of a land transport vehicle based on the general analysis of various vehicle models and
driving conditions. Their derivation relied on some assumptions such as the inherent re-
sistance of a vehicle having the usual quadratic form and the approximate proportionality
between fuel consumption and propulsive work. However, most engine fuel maps are highly
2
nonlinear related to both engine speed and power, and therefore fuel consumption can not
be simply represented as an affine function of the produced work. Authors in [3] used a
nonlinear fuel map and conducted tests on short road sections with small road grades.
Given these analyses, driving under the constant speed limit may only be fuel optimal
on level roads with small but not significant road grades. In [4], the author found that
optimal varied speed driving could gain substantial fuel saving compared to the constant
speed driving based on the analysis of a wide range of vehicle models and large road grades.
This study used fuel consumption simulators for 15 late-model automobiles to determine how
one ought to drive to maximize fuel economy. Dynamic programming was used to determine
the optimal way to accelerate from rest to cruising speed, to drive a block between stop signs,
and to cruise on hilly terrain while maintaining a given average speed. The dependence of
fuel economy on a constant speed was also characterized for various road grades. However
in this paper only the single crest, sag, and hills were considered, and therefore the result
can not be applied generally to long road sections with combinations of different hills.
Real-time fuel optimal control system design
With the rapid growth of computational power, the 3D road map database, and global
positioning system (GPS) technology, the new research trend, starting from [5], is to design
real-time predictive powertrain controllers to reduce fuel consumption by using road map
data in combination with GPS. Different from the solving of the optimization problem to
find the fuel optimal speed trajectory as described in Section 1.2.1, the fast growing research
has been aimed to design real-time look ahead control systems which command truck be-
havior on-line based on the road map and current truck states to minimize the truck fuel
consumption and travel time.
In [5], DaimlerChrysler researchers developed a Predictive Cruise Control (PCC) system
to reduce fuel consumption of heavy trucks. The PCC basic structure is shown in Figure 1.1,
3
where the position estimation system determines the current vehicle position, the optimiza-
tion algorithm calculates the optimal engine speed, the 3D road map finds the predictive
road grade, and a look-up table stores the map-matched optimal solution. Based on 3D
elevation information and a predictive algorithm, the PCC outputs the requested engine
speed to ECU and controls the vehicle speed to vary within the bounds of the set speed to
reduce fuel consumption. For a designated road profile, the PCC could achieve up to 4%
fuel reduction for a selected vehicle.
Position
Estimator
3DDigital
RoadMap
Optimization
Algorithm
Look-up
Table
Vehicle
MassEst
GPS
Velocity
PCC
Requested
EngineSpeed
Figure 1.1: The basic structure of the PCC system [5]
Scania Inc., as stated in [6], developed an Expert Cruise Controller (ECC) using look-
ahead road information. The ECC is a sort of rule-based control strategy which relies on
logical reasoning of how a driver should control the vehicle in order to solve the optimization
problem. The main idea in the ECC is dividing the road into several sections, describing
uphill and downhill slopes along the road. Different control strategies are implemented
for different section types. Up to 3.4% lower fuel consumption was obtained in simulations.
However, as a rule-based controller, the ECC sometimes totally lacks feedback, and therefore
relies heavily on the accuracy of the road map.
In [7], the author designed the Model Predictive Cruise Control (MPCC) in heavy trucks
by using road topography. In this work, a model predictive control (MPC) scheme was used
4
to control the longitudinal behavior of the vehicle, which entailed determining acceleration
and brake levels and also which gear to engage. The optimization was accomplished through
discrete dynamic programming. A cost function was used to define the optimization criterion
to minimize fuel consumption. Computer simulations with a load of 40 metric tons showed
that the fuel consumption could be reduced by 2.5% with a negligible change in travel time.
As the continuation of work [7], authors in [8] further devised a look-ahead control
system which uses a dynamic programming algorithm in a predictive control scheme by
constantly feeding the conventional CC with new set points, as shown in Figure 1.2. The
algorithm was evaluated in a real truck on a highway, and the fuel consumption was shown
to be reduced by up to 3.5%. Generally speaking, prior work focused mainly on the design
of road map based optimal cruise controllers to minimize fuel consumption on designated
level terrains. In these cases the road information was generated from GPS measurements.
TruckRoaddatabase
CA
Nb
us
Setspeed
DP algorithm
Road
slope
GPS
Position
Currentvelocity
andgear
Figure 1.2: The basic structure of the MPCC system [8]
1.2.2 Solving of hybrid optimal control problems
In this dissertation, a 3D geographic information system (GIS) road geometry based
optimal powertrain control system is designed to reduce the heavy truck fuel consumption
and travel time. The optimizer of the real-time optimal control system (OC) attempts to
5
solve an optimal control problem. Optimal control deals with the problem of finding a
control law for a given system such that a certain optimality criterion is achieved. A control
problem includes a cost function that is a function of state and control variables. An optimal
control is a set of solutions describing the paths of the control variables that minimize the
cost function subject to constraints, which can be expressed using the relatively general
formulation:
minimize F[x(tf),u(tf),tf] (1.1)
subject to dxdt = f(x,u,t) (1.2)
h(x,u,t) = 0 (1.3)
g(x,u,t) ? 0 (1.4)
where tf is the final time, and x(tf) and u(tf) are the final states and controls, respectively.
Additionally, Equation (1.1) is the objective function to be minimized, Equations (1.2) are
the differential equations of system dynamics, and Equations (1.3) and (1.4) are a set of
system equality and inequality constraints.
Optimal control problem solution
Due to the curse of dimensionality, many optimal control problem cannot be solved
analytically. The curse of dimensionality, a term coined by Richard Bellman, is the problem
caused by the exponential increase in volume associated with adding extra dimensions to a
mathematical space. There are mainly three classes of approaches on finding the numerical
solution of the optimal control problem as depicted in Equations (1.1) to (1.4): dynamic
programming (DP) based approaches, indirect methods, and direct methods [9].
The DP approach was first described in [10] and was extended to include constraints on
the state and control variables in [11]. In [1] and [4], DP was used to find the optimal speed
trajectory that minimizes vehicle fuel consumption. In [12] and [8], authors developed a DP
6
based real-time predictive powertrain controller to reduce fuel consumption based on road
information. Generally, the use of DP is limited to small problems since the dimensionality
increases rapidly with problem size. An advantage of DP is the high probability of finding
the global optimum.
Indirect methods [13] focus on obtaining a numerical solution to the classical necessary
conditions for optimality according to the Pontryagins maximum principle. The result is
a two-point boundary value problem (TPBVP) which can be solved in various ways [9].
Indirect methods have been applied in [2] and [3] to solve the fuel minimization problem
with road grade variation, and in [5] to develop a real-time PCC system to reduce fuel
consumption of heavy trucks. Some disadvantages of these methods are that they are very
sensitive to the initial guess and inequality constraints are difficult to handle.
Direct methods transform the infinite dimensional optimal control problem into a fi-
nite dimensional nonlinear programming (NLP) problem and then solve the resulting NLP
problem of the following form by using of the optimizer:
minimize f(x) (1.5)
subject to cj(x) = 0, j = 1,...,k
cj(x) ? 0, j = k + 1,...,m
xiL ? xi ?xiU, i = 1,...,n
where f and cj are the objective and constraint functions respectively, xiL and xiU are
lower and upper bounds for the variable xi, and k, m, and n are the number of equality
constraints, total constraints, and design variables, respectively. The functions f and cj are
usually assumed twice continuously differentiable. Reversely, the optimal control problem
may be interpreted as an extension of the NLP problem to an infinite number of variables
[14]. A structure of methods for solving the optimal control problem is depicted in Figure
1.3.
7
Optimalcontrol
problem
Dynamic
programming
Indirect
method
Direct
method
solvedby
solvedby
transformedto
Nonlinear
programming
problem
SQP,IP
orothers
Stochastic
method
Extended
SQP orIP
Deterministic
method
solvedby
Mixeddiscrete
NLP
solvedby
Figure 1.3: Method structure of solving dynamic optimization problem
There are two general strategies of the direct method: the control parametrization
method [15] where only the controls u are discretized, and the collocation method [16] in
which both the controls u and state trajectories x are discretized using polynomials on
finite elements, and the coefficients of these polynomials and element sizes become decision
variables in a large-scale NLP. The collocation approach can be quickly used to solve a
number of practical trajectory optimization problems.
In the collocation method, the discretization is achieved by first dividing the time in-
terval into a prescribed number of subintervals whose endpoints are called nodes [17]. The
unknowns are the values of the controls and the states at these nodes and the state and
control parameters. The cost function and the state equations can be expressed in terms of
these parameters and can be solved by a standard gradient based nonlinear programming
method, or a heuristic method such as simulated annealing. The time trajectories of both the
control and the state variables can be obtained by using an interpolation scheme. In most
collocation schemes, linear or cubic splines are used as the interpolating polynomials [18].
8
In [14], [19] and [20], instead of using piecewise continuous polynomials as the interpolation
between prescribed subintervals, orthogonal polynomials such as Legendre and Chebyshev
polynomials were used as pseudospectral methods for approximating the control and state
variables.
The sequential quadratic programming (SQP) algorithm has been one of the most suc-
cessful gradient based methods for solving NLP problems especially where a significant degree
of nonlinearity is present. The SQP method is a procedure that generates iterative converg-
ing to a solution of the problem by solving the quadratic approximations to NLP [21]. The
SQP method has been widely applied to solve NLP problems in the area of ground and
space vehicle path planning, obstacle avoidance, and trajectory optimization [22], [23]. Here
the direct collocation method transforms the optimal control problem into a NLP prob-
lem by discretizing the vehicle trajectory into a number of segments and approximating the
equations of motion along those segments with cubic polynomials.
The SQP algorithm consists of four main steps and its flow chart is illustrated in Figure
1.4 [24]:
a. Compute the gradient of the Lagrange function L: Lagrange function, with the Lagrange
multipliers ?, can be written as:
L(x,?) = f(x) +?c(x), x ={u,v} (1.6)
where x is the parameter vector that needs to be optimized, which may include the
control u and state v. The second order approximation of Equation (1.6) is:
L(x,?) = L(xi,?)+?L(xi,?)?(x?xi) +
1
2(x?xi)
T ?HL(xi,?)?(x?xi) (1.7)
9
System
dynamicsmodel
InitialguessofControland
Statevectors, andu v
Objectivefunction:
f(v,u)
Constraints:
c(v,u)
SQP
solution
module
Reachtheterminalcondition:
tolerancesfor f( )&c( )v ,u v ,ui+1 i+1 i+1 i+1
yes
Optimalcontrol&state:
uO and vO
no
Outputsfromcurrentiteration,
,uandv areusedasinitial
valuesfornextQP iteration
gen. Lagrangefunction
&computeitsgradient
L,
SolveapproximatedQP problem
tofindthesearchdirection di
Definethenewestimate:
vi+1 =v +di i,
InputstotheSQP module
Figure 1.4: Complete SQP algorithm flow chart
where H is the approximated Hessian matrix of the Lagrange function, and the linear
approximation of the equality constraint by its gradient?c(x) is:
c(x) = c(xi) +?c(xi)?(x?xi) (1.8)
b. Find the optimum search direction d = x?xi, by solving the quadratic programming
(QP) problem, and formulate a QP subproblem by Equation (1.7):
mind 12dT ?HL?d+?f(xi)?d
10
subject to : c(xi) +?c(xi)?d = 0
c. Define the new estimate: the calculated optimum di can be used as a new search direction
to perform a line search, and find a new estimate xi+1.
d. Evaluate whether f(xi+1) and c(xi+1) have reached terminal conditions.
On the other hand, the interior point (IP) method provides an alternative method to
solve the nonlinear NLP problem. The algorithm is essentially a barrier method in which the
subproblems are solved by using a SQP iteration with trust regions. The SQP idea is used
to efficiently handle nonlinearities in the constraints. The trust region method allows the
algorithm to treat convex and non-convex problems uniformly, permitting the direct use of
second derivative information [25], [26]. This method has been successfully applied to solve
the trajectory optimization NLP problems in space and manned aircraft [27], but has only
seen limited use in ground vehicle applications.
Mixed-discrete NLP solution
The throttle and gear shifting in this work are continuous and discrete control inputs,
respectively. When some variables are discrete and others are continuous, the NLP prob-
lem is called a mixed discrete-continuous nonlinear programming (MDNLP), which has the
following form [28]:
minimize f(x) (1.9)
subject to cj(x) = 0 j = 1,...,k
cj(x) ? 0, j = k + 1,...,m
xi ? Di, Di = (di1,di2,...,diqi), i = 1,...,nd
xiL ? xi?xiU, i = nd + 1,...,n
11
where nd is the number of discrete variables, Di is the set of discrete values for the ith
variable, qi is the number of the discrete values for the ith variable, and dik is the kth
discrete value for the ith variable.
In general, a MDNLP problem can be solved by optimization methods which can be
classified into two groups: stochastic and deterministic methods. Some of the stochastic
methods for global optimizations include the sequential random search and various evolu-
tionary programming methods such as simulated annealing and genetic algorithms. Most of
these stochastic methods do not need a priori knowledge about the objective function. These
methods, however, usually require a large number of function evaluations, which makes these
methods impractical to the real-time optimal control problem involving computationally in-
tensive processes in this research.
When the objective and constraint functions are explicitly expressed, deterministic
methods can be applied. These methods include the branch and bound, sequential linear pro-
gramming, cutting plane techniques, outer approximation, Lagrange relaxation approaches,
and so on. Another group of methods are called the rounding methods, which use simple
dynamic rounding-off techniques. Most of these methods such as branch and bound either
use the closely related NLP to reach to the main MDNLP, or rely on the successive solutions
of the related mixed integer programming such as outer approximation [29].
The branch and bound is basically an implicit enumeration method in which one sys-
tematically tries to reduce the number of trials to reach the minimum point [28]. The penalty
function approach is to treat discrete requirements as explicit constraints and construct an
objective function penalizing deviations from discrete values. The Lagrangian relaxation
method replaces the original MDNLP problem with a sequence of convex and separable
approximate subproblems that are solved using Lagrangian relaxation and minimizing the
dual function with a subgradient method [30]. For optimization problems with nonlin-
ear constraints, linearly constrained Lagrangian methods solve a sequence of subproblems
that minimize an augmented Lagrangian function subject to the linearization of constraints.
12
These deterministic approaches are based on explicitly expressed objective and constraint
functions.
In [31], authors generated time-optimal velocity profiles for a group of path-constrained
vehicles with fixed and known initial and goal locations. Each vehicle robot must follow a
fixed path, arrive at its goal as quickly as possible, and stay in communication with other
robots in the arena throughout its journey. Authors sought to solve this multi-objective
optimization problem by generating optimal velocities along the paths. The problem was
formulated as a NLP with constraints on the kinematics, dynamics, collision avoidance, and
communication, where the discrete requirements were approximated as continuous value
constraints by using sequential linear approximation.
Additionally, a lot of research has been conducted to find the extension of the well-
known continuous nonlinear NLP solvers such as SQP and IP to solve the MDNLP problem.
Authors in [32] presented a new trust region SQP method for the MDNLP problem, where
convexity and relaxation are not required. However, the authors assumed that the model
functions are smooth in the sense that an increment of an integer variable by one leads to
a small change of function values. The author in [33] introduced an extension of the SQP
method to solve the mixed-integer programming problem (MINLP). The general idea is to
combine a SQP step with a direct search cycle in the integer space. Hessian information is
updated based on difference formulae at neighbored grid points.
A simple approach for the MDNLP problems is to first obtain an optimum solution using
a continuous approach, e.g., SQP or IP. Then using heuristics, the variables are rounded-
up to the nearest available discrete values to obtain a discrete solution. However, it is not
necessary to round-up all variables to their nearest discrete neighbours. Some of them could
be decreased while others could be increased. The main concern of a rounding-off approach
is the selection of variables to be increased and the variables to be decreased [28]. This is a
simple idea, but it often results in an infeasible design for problems having a large number
of variables.
13
For the MDNLP problem at hand, this research couples a direct collocation method
with a deterministic discrete variable search strategy with the following steps:
1. Apply the direction collocation method to transform the infinite dimensional dynamic
optimization problem into a finite dimension (MDNLP) problem, where all design
variables are treated as continuous ones;
2. Apply any standard nonlinear programming code to find an optimum in the design
space of continuous design variables;
3. Find the discrete design variables by using the deterministic discrete search methods,
e.g., penalty function, rounding-off or Lagrangian relaxation, at the final step.
1.2.3 Real-time optimal control system design
In this work, a real-time optimal control system is developed to command the fuel
optimal truck behavior online by using the optimizer as described in Section 1.2.2. Opti-
mal control policies are classified as either open-loop or closed-loop optimal controls. An
open-loop policy determines the optimal time program for the inputs to a dynamic system
corresponding to a particular initial condition. On the other hand, a closed-loop policy is
a stronger form in which the optimal feedback of a dynamic system?s states for any initial
condition is determined [9]. This work will focus on closed-loop policies because
? A closed-loop solution is more stable than the open-loop solution;
? Current NLP solvers are capable of getting fast convergence and generating reliable
numerical solutions for large-scale NLP problem.
The dominant open-loop design approach in the literature is some form of rule-based de-
sign, relying on engineering intuition and logic. The heuristically derived rule-based optimal
fuel controller was developed in [6] by Scania Inc, which is called Expert Cruise Controller
14
(ECC) and uses look ahead road information. The ECC implements different control strate-
gies for different road section types, i.e., crest or sag slope. But the ECC switches different
control strategies completely based on the road-map and therefore is highly sensitive to
road-map inaccuracy. On the other hand, optimal control strategies, e.g., DP, has been used
to generate the optimal sequence of control inputs to improve hybrid vehicle fuel economy,
which are then studied to derive implementable control rules in [34], [35].
A typical optimal closed-loopfeedback control is themodel predictive control (MPC) [36]
and the rolling horizon concept. Its main idea is to solve on-line a finite-horizon open-loop
optimal control problem considering the current state as the initial state for the problem as
indicated in Figure 1.5. The problem is formulated and solved at each discrete-time instance
with the following steps:
1. Obtain measurements of the states of the system;
2. Compute an optimal input signal by minimizing a given cost function over a certain
prediction horizon in the future using a model of the system;
3. Implement the first part of the optimal input signal until new measurements/estimates
of the state are available. Then, repeat with step 1.
x =f(x )K+1 K+1, K+1u
[10...0]
, Ku x K
Finitehorizon
MDNLP solver
[u ... ]0OPT TuN-1OPTu0OPT
Figure 1.5: Basic model predictive control loop [36]
15
Although nonlinear MPC has become a well-established control approach, its applica-
tion to time-critical systems requiring fast feedback is still a major computational challenge.
In [7], the MPC scheme was applied as a Model Predictive Cruise Control system (MPCC)
in heavy trucks to reduce the truck fuel consumption and travel time by using road topog-
raphy. In [37], authors investigated a new multi-level iteration scheme, and extended the
idea to real-time iterations. This novel approach took into account the natural hierarchy of
different time scales inherent in the dynamic model. The authors applied the investigated
multi-level iteration scheme to various vehicle optimal control applications and discussed the
computational performance of the scheme.
Normally, MPC is possible if the plant has sufficiently slow dynamics. If a plant has
fast dynamics, then the usual notions of explicit feedback theory are necessary for successful
implementation. In the system in this research, the slow and fast dynamics are separated
by the optimal speed trajectory generation and truck speed control, respectively. Trajectory
generation is the slow outer-loop while control is the fast inner-loop. The concepts of inner
and outer loops are formalized by a two degree-of-freedom (DOF) control system architecture
where the inner loop is used for stabilizing a nominal reference trajectory generated by the
outer loop [38]. Figure 1.6 demonstrates an inner-outer loop structure for achieving optimal
feedback control. Under this structure traditional linear or nonlinear control theory can be
used to design the inner loop while optimal control techniques are used for the outer loop
[39].
By applying this two DOF optimal control design concept, a two-level adaptive cruise
control (ACC) synthesis method was presented in [40]. In the outer loop, an indirect op-
timization method is used to solve a TPBVP problem and then find the desired vehicle
acceleration with the cost function consisting of a penalty for vehicle range and range rate
errors. In the inner loop, an adaptive control algorithm is designed to ensure the vehicle
follows the outer loop acceleration command accurately.
16
Plant
outer-loopfeedback
Finitehorizon
MDNLP solver
Controller
output
-errorsignal
outer-loopcontrol
+
commandsignal
Inner-loop
control
Figure 1.6: Real-time optimal feedback control through an inner-outer loop structure [39]
Additional two DOF optimal control approaches applied to various real-time vehicle
maneuvers, e.g., minimum time double lange change at high speed, were studied in [41].
In their work, the authors developed a two-level driver model. On the anticipation level,
optimal control problems for a reduced vehicle dynamics model are solved repeatedly on a
moving prediction horizon to yield near optimal setpoint trajectories for the full model. On
the stabilization level, a nonlinear position controller is developed to accurately track the
setpoint trajectories with a full motor vehicle dynamics model in real-time. In this work,
the optimal control problem is transformed to a NLP problem by a sparse direct collocation
method and then solved by a gradient based SQP solver.
In order to build a stable optimal feedback control system, a two DOF optimal control
approach is applied in the fuel-optimal control system in this research with the scheme as
depicted in Figure 1.6:
1. In the outer loop, the optimal control problem is solved using the MDNLP solver
repeatedly on a moving prediction horizon to yield near optimal setpoint trajectories;
2. In the inner loop, a feedback controller is developed to accurately track the optimal
trajectories over some period;
17
3. The procedure is repeated over the next prediction horizon.
1.3 Contributions
The contributions of this work are mainly in the following three aspects:
? A mixed discrete-continuous nonlinear programming (MDNLP) solver was designed
and experimentally validated to solve the fuel-optimal throttle, brake torque engine
retarder (generated from the engine retarder), velocity trajectory, and especially the
gear shifting. The optimal gear-shifting control has been widely studied to improve the
performance of the automatic transmission with respect to passengers comfort, gear
shift duration [42], and fuel efficiency [35]. However, the road map based fuel optimal
gear-shifting control has only been considered in [12], but has not been implemented
and validated in any previous road tests.
? A complete system scheme was built up to integrate the real-time optimal control and
map-matching system, and utilize commercial GIS road geometries that are accurate
nationwide.
? A sensitivity analysis was conducted by applying real road geometries to investigate
how the change of the terrain and the errors in the terrain data effect the gain in fuel
economy and the system performance.
1.4 Outline
In Chapter 2, roadgeometry, simulated roadgeometry, drive cycle, andfuel consumption
baseline are described. Chapter 3 details the heavy truck system modeling and the relation
between terrain variation and truck fuel consumption. The real-time optimal control system
design and implementation are described in Chapter 4. Chapter 5 shows simulation and
real road test results as well as their analyses. Work for sensitivity analysis is introduced
18
in Chapter 6. Finally, a summary of the work and the recommendation for future work are
listed in Chapter 7.
19
Chapter 2
Road Geometry and Baseline
Since road geometry is analyzed to obtain the best truck operations and maximal fuel
performance, the basic definitions for highway design are introduced in this chapter. Based
on these definitions, a simulated highway is generated to assist the analysis of truck fuel
consumption on different terrains before real road geometries are considered. The fuel con-
sumption baseline and drive cycle are defined to evaluate the designed real-time optimal
control (OC) system performance.
2.1 Road Geometry
In this section, the basic road definitions are provided and then a set of road profiles are
simulated. The simulated road profiles should be close to real road situations based on some
important road design parameters. Additionally, the calculation of real road grade and the
analysis of terrain type are given.
Based on [43] and suggestions from Intermap, the road profiles are classified into three
types: level, rolling, and mountainous using the following parameters:
? Degree of grade: the grade of the road slope;
? Number of transitions: number of road slopes;
? Frequency components: the frequency of the change of slopes.
2.1.1 Basic road definitions
To simplify the design, some road and vehicle conditions are fixed in this work, based
on [43]:
20
? Road type: rural freeways (arterial highways), which are designed for large volumes of
traffic at high speeds;
? Truck weight/power ratio: 120 kg/kW, which represents the size and type of vehicle
normally used for design control for main highways;
? Units: Metric, which can be changed to US customary upon request.
By further referencing [43], some important definitions for the road design are:
1. Design speed: a selected speed used to determine the various geometric design features
of the highway, which is set to 90, 110 or 120 km/h, in this project. The OC system
has a 90 km/h reference speed;
2. Degree of road grade: vertical elevation over longitudinal length of a road slope, G =
D/L, in percentage, as shown in Figure 2.1.
G
L
D
Figure 2.1: Road grade
3. Vertical alignments: a vertical curve is used to provide a smooth transition between
vertical tangents of different slope rates. Vertical (parabolic) curves consist of sym-
metric crest and sag, shown in Figure 2.2, and are constrained by:
? Minimum length of a vertical tangent (Lt): the minimum length of a short vertical
tangent between two consecutive vertical curves is Lt = 0.3v in meters, where v
is design speed in km/h.
21
Sagverticalcurve
Crestverticalcurve
Vertical
tangent
LLt
G1 G2
A
L/2
Ex
xVerticaltangent
Figure 2.2: Vertical curves and tangents
? Minimum length of a vertical curve (L): this is a major control parameter and
related to safety sight distance. It can be calculated by:
L = KA, A =|G1?G2|, K =
?
???
???
???
???
?
39, v = 90
74, v = 110
95, v = 120
L = 0.6v, if A < 1
Ex = (G2?G1)x
2
2L +G1x, Ex : elevation of curve
4. Terrain classifications:
? Level: highway sight distances are generally long and not blocked by vertical
restrictions;
? Rolling: highway slopes gently rise and fall, and there are occasional steep slopes;
? Mountainous: longitudinal changes in the elevation of the ground with respect to
the road are abrupt.
22
In general, rolling terrain generates steeper grades than level terrain, causing trucks to
reduce speeds; and mountainous terrain has even greater effects, causing some trucks
to operate at crawl speeds. For a rural highway, the maximum road grade is related to
the design speed and terrain type, as shown in Table 2.1. The minimum road grade is
around 0.5%, for the surface drainage design.
Table 2.1: Maximum road grade relative to design speed and terrain type
Terrain type Design speed (km/h)
90 110 120
Level (grade %) 4 3 3
Rolling 5 4 4
Mountainous 6 5 N/A
5. Frequency related parameters which are in a certain highway section include:
? Frequency component: the frequency of the change of the slope. The frequency
can be low, medium or high;
? Number of transitions: the approximate number of slope transitions can be cal-
culated, if the frequency component is given and the minimum length of each
vertical curve is known;
? Coupling between the slope transitions: how far two slopes are apart. This dis-
tance can be calculated, if both the frequency component and the number of
transitions are known.
6. Elevation of the entrance and exit: comparing with the entrance, the elevation of the
exit is higher or lower.
2.1.2 Parameter based highway simulation
The parameters defined in Section 2.1.1 are used to generate a simulated highway sec-
tion. First step, the user should choose some values or conditions of parameters, in order
23
to describe the special features of a highway profile, which is shown in Table 2.2. For the
purpose of simplicity, the highway length and design speed are only given three fixed values,
respectively.
Table 2.2: Fixed parameters for the parameter based highway simulation
Input Parameter Pre-defined condition
Highway length(km) 10 50 100
Design speed (km/h) 90 100 120
Terrain type Level Rolling Mountainous
Exit vs. Entrance Lower - Higher
Frequency component Low Medium High
In this research, six highway profiles with a 50 km length were generated. The associated
parameters are shown in Table 2.3. For example, Simulation 1 has a design speed of 110
km/h; terrain is rolling; and exit is lower than entrance and the frequency component is low.
Table 2.3: Parameter based highway simulation examples
Simulation Length Speed Terrain Elevation Frequency Figure
1 50 110 R L L Figure 2.3
2 50 110 R L M Figure 2.3
3 50 110 R L H Figure 2.3
4 50 90 L H M Figure 2.4
5 50 90 R H M Figure 2.4
6 50 90 M H M Figure 2.4
The diagrammatic comparison of simulations 1, 2 and 3 is shown in Figure 2.3. In
can be seen from Table 2.3, the only difference among them is the frequency component,
which is low, medium, and high for three cases, respectively. As the diagram shows, the
high frequency road (gray curve) has faster slope change than the medium frequency road
(dashed), which in turn has faster change than the low frequency road (black).
Simulation 4, 5, and 6 are compared together in Figure 2.4 to show the difference in
terrain type. It is clear that the level road(dark curve) has the smallest roadgrades compared
24
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
x 104
?100
?50
0
50
Length (m)
Elevation (m)
Generated highway, Length:50km   Speed:110km/h  Terrain:R  Frequency:L/M/H  Exit is:L
Low
Medium
High
Figure 2.3: Generated highway, comparison of simulations 1/2/3
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
x 104
?20
0
20
40
60
80
100
120
140
Length (m)
Elevation (m)
Generated highway, Length:50km   Speed:90km/h  Terrain:L/R/M  Frequency:M  Exit is:H
Level
Rolling
Mountainous
Figure 2.4: Generated highway, comparison of simulations 4/5/6
25
with the rolling road (dashed) and mountainous road (gray), which has the steepest grades.
In Table 2.2, the maximum grade for these three simulations is 4%, 5%, and 6%, respectively.
2.1.3 Calculation of real road grade
The simulated road geometries are generated to quantify the fuel consumption change
on different terrain types. While in the OC system implementation, the real road geometry
is required. The real road geometry applied is a 3D road vector, with accurate longitudinal
(x), lateral (y) positions, and elevation (z). The road slop can be obtained from the road
vector by calculating the point-to-point slope (both in x and y directions) at each point and
then passing a second order polynomial filter with a L meter window over the result. The
filter helps to remove the high frequency component from the instantaneous slope, leaving a
smooth profile. For a simple representation, all road profiles in this work are drawn only in
the x and z frame. The slope is multiplied by 100 to obtain a percentage slope value ? at
sampling point k as:
?(k + 1) = 100 z(k + 1)?z(k)radicalBig
(x(k + 1)?x(k))2 + (y(k + 1)?y(k))2
(2.1)
The original slope value is passed to a Savitzky-Golay smoothing filter [44]. The coeffi-
cients of the filter are obtained by applying a least squares adjustment. This adjustment is
used to identify a second order polynomial function which minimizes the sum of the square
of the residuals between the function and the original slope over a L meter window. The
value of the function at the point of interest is then selected as the filter output at that
point. The next point is then moved and the process is repeated.
2.1.4 Real road geometries and terrain type analysis
Intermap?s 3D road geometries acquired in California and West Virginia are applied in
this work. These consist of four test routes in California as shown in Figure 2.5, and one
26
Figure 2.5: Overview of Intermap?s road geometries in California
in West Virginia. In order to test the OC system on different terrain types, routes number
2 and 3 in CA, and the route in WV are used in this research. They are level, rolling, and
mountainous terrains, and named as routes R1, R3, and R5, respectively. It is also interested
in the reverse direction of routes R1, R3, and R5, which are named as R2, R4, and R6.
The details of these six road profiles are provided in Table 2.4, where the mean, max-
imum, and minimum road slopes are listed as a percentage. The ? in this table represents
the standard deviation of the road slope value.
Table 2.4: Intermap road profiles analysis
slope(%)
route length (m) mean max min ? terrain type
R1 37000 -0.21 2.65 -4.33 1.05 level
R2 37000 0.21 4.33 -2.65 1.05 level
R3 47000 0.27 4.88 -3.87 1.34 rolling
R4 47000 -0.27 3.87 -4.88 1.34 rolling
R5 54000 0.21 5.57 -5.43 3.05 mountainous
R6 54000 -0.21 5.43 -5.57 3.05 mountainous
The road maps for R1 and R2 are provided in Figure 2.6, where the road elevation and
grade maps are given for R1 and R2. It can be seen from the figure that road grades for R1
27
and R2 are mostly within the grade range of [-4% 4%], and the reference design speed is 90
km/h. Thus, by comparing to the terrain classification as described in Table 2.1, it is clear
that the R1 and R2 are both level terrains.
0 0.5 1 1.5 2 2.5 3 3.7
x 104
?90
?50
0
R1            altitude (m)
0 0.5 1 1.5 2 2.5 3 3.7
x 104
?4
0
3
R1         grade (%)
0 0.5 1 1.5 2 2.5 3 3.7
x 104
0
40
80
R2            altitude (m)
0 0.5 1 1.5 2 2.5 3 3.7
x 104
?3
0
4
distance (m)
R2         grade (%)
Figure 2.6: Road elevation and grade maps for R1 and R2
The road elevation and grade maps for R3 and R4 are depicted in Figure 2.7. It is seen
that road grades for R3 and R4 are mostly within the range of [-5% 5%]. Therefore, R3 and
R4 can be classified as the rolling terrain with reference to Table 2.1. Additionally, the maps
for R5 and R6 are shown in Figure 2.8. R5 and R6, which are within [-6% 6%] grade range,
have far larger road grades than R1 to R4. Thus, R5 and R6 are mountainous terrains. In
this section, the simulated roads R1 - R6 are not generated and then compared with the
corresponding real road geometries, since this is out of the scope of this research.
2.2 Driver Cycle and Baseline
In this section, the fuel consumption baseline for the specific road section and drive
cycle are defined to evaluate the performance of the designed OC system. A drive cycle
28
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
x 104
0
50
150
R3          altitude (m)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
x 104
?4
0
4
R3       grade (%)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
x 104
?140
?50
0
R4          altitude (m)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
x 104
?4
0
4
distance (m)
R4       grade (%)
Figure 2.7: Road elevation and grade maps for R3 and R4
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.4
x 104
0
300
R5          altitude (m)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.4
x 104
?6
0
6
R5       grade (%)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.4
x 104
?200
0
200
R6          altitude (m)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.4
x 104
?6
0
6
distance (m)
R6       grade (%)
Figure 2.8: Road elevation and grade maps for R5 and R6
constitutes a series of vehicle speeds as a function of time on a specific road section. For
fuel economy research, the definition and selection of the baseline, which is fuel consumption
29
for a normal drive cycle, is critically important. The main current practices in drive cycle
development are segment-splicing, Monte Carlo simulation, and ?engineering? approaches.
The first approach is based on real-driving data, and the second approach is simulated from
a realistic driving behavior model. The third approach, on the other hand, is defined by a
designer to implement some truck feasibility testing [45].
If the drive cycle developed by the first method is applied, the function of the OC system
could then be compared to the real truck driving condition, or even better, experienced
drivers? behavior, and therefore the gain in the fuel economy is more meaningful. However,
this driver cycle can hardly be developed in this work since it requires a large amount of
driving data collection on the test routes R1 to R6, which is out of the scope of the database
of this research.
Instead, the drive cycle is defined by the third method as a constant speed to imple-
ment some truck feasibility testing. The fuel consumption and travel time baseline is then
calculated from a standard cruise controller (CC) from the experimental truck to perform
this drive cycle. The CC is applied to maintain the desired vehicle velocity by changing
throttle position. Additionally, a function of brake pedal control is engaged only if the truck
reaches an upper speed limit. The gear selection is determined based on the engine speed
and current gear position.
This baseline is generic because the CC is highly engaged in the real-time truck driving.
Moreover, by integrating the automatic braking control in the CC, the baseline has the
feature close to the real drivers? behavior, that is keeping the cruise speed and braking only
if the speed limit is reached. Thus, with the application of this baseline controller, the
function of the OC system can be compared to some near-real truck driving conditions and
consequently, resulting in a realistic and meaningful gain in the fuel economy.
30
2.3 Conclusion
This chapter described real and simulated road geometries and the comparison baseline
that will be used to evaluate the optimal control system (OC) performance. First, some
important road design parameters, e.g., road grade, terrain type, and frequency component,
were defined, from [43]. The special values or conditions of these parameters were chosen to
describe main features of a road profile. Subsequently, simulations were conducted in Matlab
to generate various road profiles. Simulation results were finally provided and analyzed to
show that the applied road generation method is correct. More importantly, by using the
simulated road profiles, the relation between the fuel consumption and road geometry could
be analyzed. The features of real road geometries were also introduced in this chapter,
which include the calculation of road grade from 3D elevation data and the analysis of
terrain type. Additionally, the fuel consumption baseline and drive cycle were defined to
evaluate the designed OC performance.
31
Chapter 3
Heavy Truck Model and Terrain Based Fuel Consumption
A heavy truck model needed for the design of a model-based OC system is developed and
evaluated in this chapter. In addition, simulations are run by using the model to quantify
how a change in terrain type effects the truck fuel efficiency.
3.1 Heavy Truck Model
A Class 8 truck longitudinal model is described and the important truck parameters are
listed in Appendix A. The model includes the engine, driveline, wheel, and truck dynamics.
A tire model is not used, and therefore a no-slip condition is assumed, which is discussed in
Section 3.1.5. This model is a hybrid system, a system with both continuous and discrete
parts. The position and velocity are continuous states. Throttle position and brake are
continuous inputs, and gear shifting is a discrete control input. In this work, the hybrid
system is approximated by a continuous system.
3.1.1 Longitudinal dynamics
Longitudinal vehicle dynamics typically include many losses such as rolling resistance,
air drag, and road grade or slope. The developed model has one degree of freedom and is
derived using the equation of motion for the free body diagram shown in Figure 3.1. To
describe the longitudinal motion of a vehicle, the dynamics are derived from the loads on
the vehicle, and has one degree of freedom:
mdvdt = Fw?Fs?Frr?Fa (3.1)
32
where Fw is wheel drive force, Fs is longitudinal force due to road grade, Frr is rolling
resistance force, and Fa is air drag force:
Fs = mgsin?
Frr = Crrmg
Fa = 12?airCdAfrv2
where ?is roadgrade, Crr is rolling resistance coefficient, ?air is air density, Cd is aerodynamic
drag coefficient, Afr is truck frontal area, and v is truck velocity.
F
+
F
+
F
+
F
rollingresistance
airdrag
brake
slope
Fwheeldrive
phi
Figure 3.1: Longitudinal Free Body Diagram (FBD)
3.1.2 Engine map
The engine model is designed based on a rectangular engine map and shows a steady-
state relation between the current engine speed and the maximum engine torque. The engine
is normally operating in the range ?e?[1100, 1800] rpm, and the maximum engine torque
can be approximated as a function of the engine speed, ?e. The comparison of real and
approximated engine map is shown in Figure 3.2. With a normalized throttle position u, the
33
desired engine torque can be calculated from:
Tm = c1?3e +c2?2e +c3?e +c4
Te = Tmu (3.2)
where Tm and Te are maximum and desired torque, and c1 to c4 are coefficients calculated
from an engine map curve fitting.
600 800 1100 1400 1600 1800 2000 2200 24001000
1200
1400
1600
1800
2000
2200
2400
2600
2800
Engine speed (rpm)
Engine torque (Nm)
 
 
Engine map
Approximated engine map
Engine operating range
Figure 3.2: Comparison of real and approximated engine map
3.1.3 Engine efficiency and fuel consumption map
A Brake Specific Fuel Consumption (BSFC) map is a measure of fuel efficiency within an
internal combustion engine. The BSFC number, Bn, is the rate of fuel consumption divided
by the produced power and has the unit of g/kW-h. To calculate the engine efficiency,
the lower heating value LHV of the fuel is used, which is defined as the amount of heat
released by combusting a specified quantity of the fuel and returning the temperature of the
combustion products to 150 ?C. The LHV value for diesel fuel is 0.0119531 kW-h/g provided
34
by Eaton. Therefore, the relationship between BSFC number and the engine efficiency of
the applied diesel engine can be represented as follows:
?e = 10.0119531B
n
(3.3)
However, in order to make the calculation more straightforward, the truck fuel con-
sumption in this work is calculated depending on a modified BSFC map as shown in Figure
3.3, which directly gives the fuel consumption time rate dmfdt (g/sec). This map is derived
from the original BSFC map by using the relation as in Equation (3.4).
dmf
dt =
BnP
3600 (3.4)
where Bn is the original BSFC number and P is the engine power. Additionally, by substi-
tuting Bn from Equation (3.4) into Equation (3.3), the engine efficiency is rewritten as:
?e = dtdm
f
? P3600? 10.0119531 (3.5)
This equation gives a direct relation between the engine efficiency and the fuel consumption
time rate dmfdt (g/sec). Actually, the task of the truck fuel minimization is equal to a work
of the engine efficiency maximization. However, in the rest of this work the former instead
of the latter is targeted and presented.
By using a 3D polynomial least-square fitting [46], the fuel consumption time rate dmfdt
(g/sec) can be approximated as a continuous function of engine speed and power P, shown
in Equation (3.6).
dmf
dt = b1?
5
eP +b2?
4
eP +b3?
3
eP +b4?
2
eP + b5?eP +b6P (3.6)
35
where b1 to b6 are coefficients. Engine power P in kilowatt (kW) can be calculated from Te
and ?e by using the relation:
P = 2piTe?e60000
The real and approximated BSFC maps are compared in Figure 3.3, and the comparison
errors are shown in Figure 3.4, which are close to zero in the engine operating range. When
the engine is idling, an 800 rpm idle speed and 3 kW engine output are used. If the truck is
coasting at a different engine speed, a 3 kW load is used as well.
800 1000
1200 1400
1600 1800
2000
0
100
200
300
400
500
0
5
10
15
20
25
 
Engine speed (rpm)Engine power (Kw)
 
BSFC (g/sec)
Real BSFC map
Approximated BSFC map
Figure 3.3: Comparison of real and approximated BSFC time rate map
3.1.4 Driveline
A complete block diagram of the truck model is shown in Figure 3.5, which consists of
the engine, transmission, wheel, and external forces. The powertrain modeling assumes:
36
800 1000
1200 1400
1600 1800
2000
0
100
200
300
400
500
?4
?2
0
2
4
Engine speed (rpm)Engine power (Kw)
BSFC error (g/sec)
Figure 3.4: BSFC map approximation error: real minus approximated map
? Maximum engine torque is approximated from a rectangular engine map in Section
3.1.2;
? Driveline includes: stiff clutch, transmission, final drive, and wheel with no slip;
? Time delay on the gear shifting: one second without engine torque input.
u
Engine Transmission
Fa,Frr,Fs
dv/ds=
(1/v)F/m
Wheel v,t
Figure 3.5: Longitudinal FBD and powertrain model
The driveline is assumed stiff and considered to transmit the power generated from the
engine to clutch, transmission, propeller shaft, final drive, and finally to the wheel. The
37
propeller shaft is assumed massless. The relation between the engine and clutch is:
9.55Je ??e = Te?Tc (3.7)
where Te is the desired engine torque as calculated in Equation (3.2), Tc is the load from
clutch, Tw is the wheel torque, ?e and ?w are the engine and wheel rotation speed, and Je
and Jw are the engine and wheel inertia (kg-m2). The factor of 9.55 in the equation is used
to change the unit of ?e from rpm to rad/s.
The clutch in this work is presumed stiff, and therefore: Tc = Tt and ?e = ?c, where Tt
and ?c are the transmission torque and clutch rotation speed, respectively. Subsequently, the
gear shifting point g in the transmission is modeled using two parameters, the transmission
efficiency and ratio, ?t and nt, with the relation:
Tt?tnt = Tp (3.8)
?c = nt?t (3.9)
where Tp is the propeller shaft torque and ?t is the transmission rotation speed.
Similar to the clutch, the propeller shaft is assumed stiff as well. This gives Tp = Tf and
?t = ?p, where Tf and ?p are the load from the final drive and the propeller shaft rotation
speed, separately. The torque and rotation speed of the final drive are calculated from the
propeller shaft with the relation:
Tf?dnd = Tw (3.10)
?p = nd?w (3.11)
where ?t and nt are the efficiency and ratio of final drive, and Tw is the wheel torque.
38
Finally, the torque and rotation speed on the wheel can be written as:
Jw ??w = Tw?rFw?Tb (3.12)
where Jw is the wheel inertia (kg-m2), Fw is the wheel drive force, and Tb is the desired brake
torque generated from the engine retarder, which is determined by a normalized brake input
b ? [0, 1] multiplied by the maximum engine retarder brake torque Tbm (Tb = bTbm). In
addition, the relationship between the engine speed and truck velocity is defined as:
?e = 30pi ntndr v (3.13)
If the engine, transmission, final drive, and the wheel are considered together with the
longitudinal forces, a complete truck longitudinal model is:
dv
dt =
r
Jw +mr2 +?dn2d?tn2tJe ?(?dnd?tntTe?Fsr?Frrr?Far?Tb) (3.14)
As mentioned previously, gear shifting is a discrete control input. The discrete gear
ratio, nt, is approximated as continuous values, while in the OC operation the continuous
ratios will be rounded off to find the nearest discrete gear ratio, which is the so called
rounding-off method [47].
The road map is position dependent rather than time dependent, [33, 14]. Equations
(3.6) and (3.14) are differentiated with respect to position rather than time by substituting:
dt = 1vdp. This results in the fuel consumption position rate function and the complete truck
longitudinal model:
dmf
dp =
1
v?(b1?
5
eP +b2?
4
eP +b3?
3
eP +b4?
2
eP +b5?eP +b6P) (3.15)
dv
dp =
1
v?
r
Jw +mr2 +?dn2d?tn2tJe ?(?dnd?tntTe?Fsr?Frrr?Far?Tb) (3.16)
39
where p represents the truck position, and P is the engine power.
3.1.5 Tire slip and gradeability
Although at the beginning of this section, it was stated that a tire model is not used
and a no-slip condition (between the tire and the road) is assumed, it is still interested to
investigate how this assumption effects the vehicle model and control system performance.
Since only the truck longitudinal dynamics is modeled, the form of slip which can have
effect is the roll slip. Roll slip is defined as the relative motion between a tire and the surface
on which it is moving. In general, the roll slip has a large effect on truck?s gradeability, which
represents the maximum slope a truck can climb while maintaining a particular speed before
the roll slip occurs. This gradeability is affected by many factors including wheel radius,
gross weight, and surface condition.
In this research, the gradeability data for the experimental truck to maintain a set speed
of 25 m/s are provided by Eaton. Therefore, if the maximum slope doesn?t appear frequently
in the test route which is true for R1 - R6, the no-slip assumption will not heavily impact
the accuracy of the truck model and the performance of the control system.
3.2 Model Validation
In this section, the developed truck dynamics and powertrain model are validated by
comparing online test data from routes R5 and R6 and o?ine truck model simulation data.
Before the OC system tests are conducted, a series of truck baseline runs were performed by
using the CC to cruise on the reference speed of 25 m/s, and then test data were recorded.
A feedback CC block diagram is given in Figure 3.6, where a PID control is used to calculate
the desired engine torque to maintain the reference speed of 25 m/s.
The throttle input and gear shifting together with the calculated road slope collected
from the baseline runs are used as inputs to the truck simulation model. The simulation
outputs such as velocity, fuel rate, and total fuel consumption are then compared to the
40
Desired
engine
torque+_ PIDcruise
control
Truck
velocity
Desired
speed
setby
driver
Truck
velocity
Truckonreal-road
Realroad
Figure 3.6: Block diagram for the cruise controlled truck (CC)
truck velocity and fuel consumption measured from baseline runs on R5 and R6. The basic
validation system setup is shown in Figure 3.7, where the notations CC torque, CC gear,
CC speed, CC fuel rate, and CC fuel total are truck torque, gear shifting, speed, fuel rate,
and total fuel consumption measured from the baseline runs on R5 and R6.
CC_fuel_total
CC_fuel_rate
CC_speed
Road_grade
CC_gear
CC_torque
Truck dynamics model
CC_torque
CC_gear
Road grade
Speed
Fuel_rate
Fuel_toal
Scope 3
Scope 2
Scope 1
Figure 3.7: Block diagram for model validation
3.2.1 Using test data from R5
The measured data from the baseline test run (road grade, the CC torque, and truck
gear) are shown in Figure 3.8. The comparison of the CC speed (dark) and simulation model
output speed (dotted gray) is given in Figure 3.9. Additionally, the comparison of fuel rate
(liter/s) and total fuel consumption (liter), for the CC and the simulation model is shown in
Figure 3.10. It can be seen in Figure 3.9 that a speed error occurs at 100 - 150 s. It is because
there is a small difference between the brake torque values calculated in the simulation and
41
0 50 100 150 200 250 300 350 400 450?6
0
6
R5       grade (%)
0 50 100 150 200 250 300 350 400 450?1500
0
1000
2000
Nm
0 50 100 150 200 250 300 350 400 450
15
16
17
18
gear
time (s)
Figure 3.8: Measured data: road grade, CC torque, and gear, R5
0 50 100 150 200 250 300 350 400 450
20
22
25
28
30
time (s)
speed (m/s)
 
 
CC speed
model speed
Figure 3.9: Comparison of CC and simulation model speeds, R5
42
0 50 100 150 200 250 300 350 400 4500
0.01
0.02
fuel rate (liter/s)
 
 
CC fuel rate
model fuel rate
0 50 100 150 200 250 300 350 400 4500
2
4
6
time (s)
fuel total (liter)
 
 
CC fuel total
model fuel total
Figure 3.10: Comparison of CC and simulation model fuel use, R5
generated from the engine retarder in the experimental truck. Additionally, there are some
small speed errors at 250 - 450 s, which are due to the modeling error of the gear shifting.
As stated in Section 3.1.4, a one second time delay on the gear shifting is modeled, when
there is no engine torque input. However, this is just an approximated value, and the real
gear shifting time delay may vary based on different operation conditions. In this work,
these modeling errors are acceptable and will not largely impact the system performance,
since on the normal level and rolling highways braking and gear shifting are not frequently
demanded. Meanwhile, it can be seen in Figure 3.10 that the simulation and CC fuel rate
and total fuel consumption match each other quite well. Therefore, the developed truck
dynamics and powertrain model is accurate enough to predict the real truck performance
3.2.2 Using test data from R6
The measured CC test run data on R6 are shown in Figure 3.11, i.e., road grade, the
CC torque, and truck gear. The comparison of the CC speed and simulation model speed
43
0 50 100 150 200 250 300 350 400 450 500?6
0
6
R6       grade (%)
0 50 100 150 200 250 300 350 400 450 500
?500
0
1,000
2,000
Nm
0 50 100 150 200 250 300 350 400 450 500
15
16
17
gear
time (s)
Figure 3.11: Measured data: road grade, CC torque, and gear, R6
0 50 100 150 200 250 300 350 400 450 500
18
20
22
25
28
time (s)
speed (m/s)
 
 
CC speed
model speed
Figure 3.12: Comparison of CC and simulation model speed, R6
44
0 50 100 150 200 250 300 350 400 450 500
0
0.01
0.02
fuel rate (liter/s)
 
 
CC fuel rate
model fuel rate
0 50 100 150 200 250 300 350 400 450 5000
2
4
6
time (s)
fuel total (liter)
 
 
CC fuel total
model fuel total
Figure 3.13: Comparison of CC and simulation model fuel use, R6
is shown in Figure 3.12. It can be observed that the simulation model speed matches the
measured CC speed closely. There are some speed errors at 0 - 50 s and 350 - 500 s in
Figure 3.12, which are due to the modeling error of the gear shifting time delay as discussed
previously. Additionally, the errors occurred at 150 - 250 s are mainly resulted from the
modeling error in the brake torque. The comparison of fuel rate (liter/s) and total fuel use
(liter) for the CC and simulation model is presented in Figure 3.13. It can be seen in that
the simulation and CC fuel rate and total fuel consumption are close to each other.
Based on the comparison results in this section, it can be seen that the truck model
is accurate enough to predict a real truck?s dynamic movement and fuel consumption. By
using this model, the OC system can be designed and the high fidelity simulation tests can
be conducted to evaluate the system performance before the real road tests are conducted.
45
3.3 Terrain Based Fuel Consumption
Finally in this chapter, simulations using the developed truck model are performed to
generally quantify how the change in terrain type effects the truck fuel efficiency. The de-
signed truck model is simulated to run on different highway profiles, generated previously
in Section 2.1.2. A standard CC is used to track the constant speed. Through this simu-
lation, the relation between fuel consumption and terrain conditions is analyzed. The road
parameters fixed for the simulation are shown in Table 2.4.
Table 3.1: Simulated highways for fuel consumption analysis
Length Design speed (km/h) Terrain type Frequency Elevation
24 km 90/110 L/R/M Low/Medium/High High
In the following simulations, the fuel consumptions (liter) are calculated and compared
for different highway profiles, which have the same driving distance (24 km), and different
driving speeds (90 km/h and 110 km/h). The results are illustrated in Figures 3.14 and
3.15 as 3D plots, where the x, y, and z axes represent the change in terrain type, frequency
component, and the corresponding fuel consumption change, respectively. Several points can
be observed from these figures:
? At the same driving speed, the truck has a larger fuel consumption on the terrain with
mountainous type, high frequency component, or both compared to the other terrains,
as shown in Figure 3.14;
? Fuel consumption is heavily impacted by the change in terrain type, driving speed,
and road frequency component;
? Larger road grade, driving speed, and road frequency component result in larger fuel
consumption.
46
level
rolling
mountainous
low
medium
high8
8.05
8.1
8.15
8.2
8.25
8.3
8.35
8.4
 
Terrain typeFrequency component
 
Fuel consumption (L)
90km/h
Figure 3.14: Fuel consumption and terrain conditions, 90 km/h
level
rolling
mountainous
low
medium
high8
8.5
9
9.5
10
 
Terrain typeFrequency component
 
Fuel consumption (L)
110km/h
90km/h
Figure 3.15: Fuel consumption and terrain condition, comparing 90 and 110 km/h
47
3.4 Conclusion
In order to design the model-based OC algorithm and test the system performance in
a simulation environment, a heavy truck?s dynamics and powertrain model were developed
and validated in this chapter. Only longitudinal truck dynamics were considered and the
applied engine map, fuel consumption map, and truck parameters were provided by Eaton.
The model was validated by comparing the real road test data with the simulation data. In
addition, simulations were run by using the developed model to quantify how the change in
terrain type effects the truck fuel consumption. The simulation results showed that truck fuel
consumption is impacted by the change in terrain type, driving speed, and road frequency
component. A more in depth analysis of how the change in terrain type effects the truck
fuel economy will be provided in Chapter 5.
48
Chapter 4
Optimal Control System Design
In this chapter, a 3D GIS road geometry based optimal powertrain control system (OC)
is designed to reduce the heavy truck fuel consumption and travel time. The OC optimizer
attempts to find a constrained minimum of a nonlinear scalar function of several variables,
e.g., truck throttle u, gear g, brake b, and velocity v, based on the road geometry.
4.1 NLP solver operation
The direct collocation method is applied to transform the stated optimal control problem
into a general nonlinear programming (NLP) problem formulation described in Equation
(4.1). The resulting NLP problem is then solved by using the optimizer.
minimize f(x) (4.1)
subject to ci(x) = 0, i = 1,...,q
gj(x) ? 0, j = 1,...,m
xiL ? xi ?xiU, i = 1,...,n
where f, c, and g are the objective, equality constraint, and inequality constraint functions
respectively, xiL and xiU are lower and upper bounds for the variable xi, and q, m, and n are
the number of equality constraints, inequality constraints, and design variables, respectively.
The functions f and c are twice continuously differentiable in this work.
49
4.1.1 Direction collocation method
The main reason to use the direct collocation method is that it does not need to consider
explicitly deriving the necessary conditions such as maximum principle. This advantage
makes the method especially attractive for complicated optimization problems. In this work,
this method provides an approximated numerical solution to the optimization problem by
discretizing the states and control inputs in each prediction horizon (L = 3000 m) into a set
of step points (s = L/h = 120), with the step distance (h = 25 m). Thus, each prediction
horizon is broken into smaller position intervals as: p = {p1,p2,...,ps}. Subsequently,
the NLP problem is searching for the parameter vector including the number of 4s state
and control inputs at the grid points such as x ={u1,g1,b1,v1,u2,g2,b2,v2,...,us,gs,bs,vs}
that minimize the objective function subject to specified constraints. The key point of the
collocation method is to replace the original set of system dynamic constraints with a set
of defect constraints ?k = 0, which are imposed on each interval in the discretization. The
equality constraint is then represented as c(x) = [?1,?2,...,?s?1]T [14].
The collocation point is selected as the center of the segment between each set point.
The state and control trajectories between the step points could be interpolated either by
linear or cubic spline polynomial functions. If it is assumed that states vary linearly and
the control inputs are constant across the step interval, the defect constraints for a linear
collocation method can be written as in Equation (4.2).
?k = f(xkc,ukc)? ?xkc, k = 1,...,s?1 (4.2)
xkc = xk+1 +xk2 , ukc = uk
?xkc = xk+1?xkh
Additionally, for a cubic collocation method, states are assumed to vary cubically and
the control inputs vary linearly across the position step interval. The defect constraints are
50
described in Equation (4.3).
?k = f(xkc,ukc)? ?xkc, k = 1,...,s?1 (4.3)
xkc = xi +xk+12 + h8(?xk? ?xk+1)
ukc = uk +uk+12
?xkc = ? 32h(xk?xk+1)?(?xk + ?xk+1)4
In this work, the linear collocation method is applied, since the step length of 25 m is small.
For such a short interval, a high-order cubic trajectory interpolation method, which makes
the NLP problem really complex, would not significantly improve the system performance.
4.1.2 Evaluation of objective and constraint functions and their gradients
After the number of 4s (s is the number of step points) state and control inputs are
initialized, the objective function f(x), which is the sum of fuel consumption and travel
time, is evaluated using Euler?s numerical integration method with the step length h along
the state and control vectors of Equations (3.15) and (3.16):
f(x) = Jfuel +Jtime +Jgear (4.4)
Jfuel = Qh
s?1summationdisplay
k=1
1
vk
dmf
dp , (4.5)
Jtime = Rh
s?1summationdisplay
k=1
1
vk, (4.6)
Jgear = O
s?1summationdisplay
k=1
|gk?gk?1| (4.7)
where Jgear is used to eliminate the frequent gear shifting between neighboring grid points.
Q,R, and O are weighting factors which currently are determined by steady state model
analysis to weight fuel consumption more than travel time and gear shifting penalty.
51
In Equation (4.5), the fuel consumption position rate dmfdp has been given in Equation
(3.15) and is described again in the following.
dmf
dp =
1
v?(b1?
5
eP +b2?
4
eP +b3?
3
eP +b4?
2
eP +b5?eP +b6P)
where b1 to b6 are coefficients, P is the engine power, and ?e is the engine speed. The engine
power P in kilowatt (kW) can be calculated from Te and ?e by using the relation:
P = 2piTe?e60000
where Te is the desired engine torque and ?e is the engine speed. With a normalized throttle
position u, Te can be calculated from: Te = Tmu, where Tm is the maximum engine torque
approximated from the engine map. In addition, the relationship between the engine speed,
?e, and truck velocity, v, is defined as:
?e = 30pi ntndr v
The equations above describe how the objective function in Equation (4.5) can be related
to the variables need to be optimized, e.g., truck throttle u, gear g, brake b, and velocity v.
The analytical gradient and Hessian of the objective function, with respect to u,g,b,
and v, are?f(x) and?2f(x) shown below.
?Jtotal = [?Jtotal?u , ?Jtotal?g , ?Jtotal?b , ?Jtotal?v ] (4.8)
?2Jtotal =
?
??
??
??
??
??
?
?2Jtotal
?2u
?2Jtotal
?u?g
?2Jtotal
?u?b
?2Jtotal
?u?v
?2Jtotal
?g?u
?2Jtotal
?2g
?2Jtotal
?g?b
?2Jtotal
?g?v
?2Jtotal
?b?u
?2Jtotal
?b?g
?2Jtotal
?2b
?2Jtotal
?b?v
?2Jtotal
?v?u
?2Jtotal
?v?g
?2Jtotal
?v?b
?2Jtotal
?2v
?
??
??
??
??
??
?
(4.9)
52
The nonlinear equality constraint (4.10) is transformed to the defect constraints as
described in Equation (4.2):
ck(x) = ?k = vk+1?vk?hdvkcdp = 0 (4.10)
dvkc
dp =
1
vkc ?
r
Jw +mr2 +?dn2d?tn2tJe ?(?dnd?tntTe?Fsr?Frrr?Far?Tb) (4.11)
and the gradient and Hessian functions are?ck, and?2ck.
?ck = [?ck?u , ?ck?g , ?ck?b , ?ck?v ] (4.12)
?2ck =
?
??
??
??
??
??
?
?2ck
?2u
?2ck
?u?g
?2ck
?u?b
?2ck
?u?v
?2ck
?g?u
?2ck
?2g
?2ck
?g?b
?2ck
?g?v
?2ck
?b?u
?2ck
?b?g
?2ck
?2b
?2ck
?b?v
?2ck
?v?u
?2ck
?v?g
?2ck
?v?b
?2ck
?2v
?
??
??
??
??
??
?
(4.13)
Additionally, the linear inequality constraints g(x) is defined by: u ? [0, 1], g ? [1, 18],
b?[0, 1], and v?[vl, vu], where vl and vu are the lower and upper bounds of velocity.
4.1.3 Discrete gear ratio calculation
As stated in Section 1.2.2, the throttle and gear shifting are continuous and discrete
inputs respectively, which makes the NLP problem a mixed-discrete NLP (MDNLP) prob-
lem. In general, the MDNLP problem can be solved by two groups of optimization methods:
stochastic and deterministic methods. Some of the stochastic methods for global optimiza-
tion include the sequential random search and various evolutionary programming methods
such as simulated annealing and genetic algorithms. When the objective and constraint
functions are explicitly expressed, deterministic methods can be applied. These methods
include branch and bound, sequential linear programming, cutting plane techniques, outer
53
approximation, Lagrange relaxation approaches, dynamic rounding-off techniques, and so on
[29].
Additionally, as surveyed and determined previously in Section 1.2.2, in this research
an extension interior-point (IP) algorithm with a rounding-off method is applied to solve the
MDNLP problem. First, all discrete gear ratios, nt?[14.40, 0.73], are handled as continuous
variables and optimized by using the IP method. Secondly, the optimal discrete gear ratios
are obtained by rounding up each continuous gear ratio to the nearest discrete value above it,
corresponding to a downshift. This method works well especially for those problems whose
available discrete sizes are small [47]. In the problem each continuous gear ratio only has two
nearest discrete gear ratios to round to, one above and one below, and the truck normally
runs in a high gear on highways, which reduces the discrete sizes even further.
The two disadvantages of using a rounding-off method could be: the best discrete design
point is not always selected; and the obtained discrete optimum may not be able to satisfy
all feasibilities [48]. In Section 5.3.1, experimental results will be given to show how these
disadvantages are overcame.
4.1.4 MDNLP solution module
For the MDNLP problem at hand, a solution suggested is to couple a direct collocation
method with a deterministic discrete variable search strategy with the following steps:
1. Apply the direction collocation method to transform the infinite optimal control prob-
lem into a finite dimension (MDNLP) problem, where all design variables are treated
as continuous;
2. The IP method, a standard NLP solver, is employed to find the optimum in the design
space of continuous design variables;
3. The deterministic discrete search method (i.e., dynamic rounding-off) is introduced at
the final step to find the discrete design variables.
54
The applied IP solver is from the MATLAB function ?fmincon?. The algorithm is es-
sentially a barrier method in which the subproblems are solved by a sequential quadratic
programming (SQP) iteration with trust regions [9, 10]. The complete IP optimizer function
is presented in Figure 4.1.
Truck
DynamicsModel
InitialguessofControlandState:
throttle( ),gear( );brake( )
velocity( );w/length4S
u g b
v
Objectivefunction:
f( ),griadent
$Hessian
u,g,b,v
Equalitycontraint:
c( ),gradient
&Hessian
u,g,b,v
Fuelconsumption(fmass)
traveltime(t) Truck u,g,b&v
NLP
solution
module
yes
Optimalcontrol&state:
u,g,b&v
no
Outputsfromcurrentiteration,
,u,g,b&v areusedasinitial
valuesfornextSQP iteration
Roadgrade
fromEH&
dataprocessing
FormulateLagrangianfunction
&SQP barrier subproblem
InputstotheNLP module
SolveSQP problemforsearch
direction byCGmethodd
Evaluate ameritfunction
thendefinenewestimate
din
xk+1
Reachtheterminalconditionof
optimalityeval.function E(x,e,u)
Figure 4.1: Complete NLP solver algorithm flow chart
By using the IP solver, each barrier subproblem is of the form:
min(x,b) f(x)???4si=1lnei (4.14)
subject to c(x) = 0, g(x) +e = 0 (4.15)
55
where ? > 0 is a barrier parameter and the slack variable e is assumed to be positive. The
trust region strategies are used to globalize the SQP iteration because they facilitate the
use of the second derivative information when the problem is non-convex. The algorithm
consists of five main stages:
? Formulate the Lagrangian function, L, of the barrier problem based on Equations
(4.14) and (4.15), which is defined as:
L(x,e,?c,?g) = f(x)???4si=1lnei +
?Tc c(x) +?Tg (g(x) +e) (4.16)
where ?g and ?c are Lagrange multipliers with equality and inequality constraints.
? Define the search direction dx = x?xi and de = e?ei and formulate the quadratic
barrier subproblem based on Equations (4.14) - (4.16):
min(x,e) ?f(xk)Tdx + 12dTx?2xxLkdx?
?S?1k de + 12dTe?2eeLkde (4.17)
subject to ?c(xk)Tdx + c(xk) = rc
?g(xk)Tdx +de +g(xk) +ek = rg
(dx,de)?Tk
This is a so called SQP trust region approach, where?2xxL and?2eeL are the Hessian
of the Lagrangian with respect to x and e, respectively, the vector r = (rc, rg) is a
residual vector, and S=diag(e1,...,e4s). The closed and bounded set Tk defines the
region around x, where the approximated model and constraints in Equations (4.17)
can be sufficiently trusted. The variables ?g and ?c are computed by a least squares
approach.
56
? Solve the SQP problem and find an approximated solution of the optimum search
direction d = (dx, de), by using the conjugate gradient (CG) method.
? If the direction d provides sufficient decrease in the merit function ?(x,e;?), then
xk+1 = xk + dx, ek+1 = ek + de, and compute new ?g and ?c; else set xk+1 = xk,
ek+1 = ek, and shrink the trust region.
? Stop criterion is: E(x,e;?)???, where E(x,e;?) is a function defined to measure the
optimality conditions of the barrier problem, and ?? is a small positive value.
Finally, the optimal discrete gear ratio is obtained by rounding up each continuous gear
ratio to the nearest discrete value above it, corresponding to a downshift.
4.1.5 Global and local optimization analysis
In real world optimization problems, functions of many variables have a large number of
local minima. Local optimization methods are those methods used to straightforwardly find
an arbitrary local minima. On the other hand, global optimization methods are developed
to find the global minimum of a function, which is much more challenging and has been
difficult to solve for many problems so far.
Stochastic methods such as simulated annealing and genetic algorithms are global op-
timization methods. Stochastic methods usually start from one point or multiple points
drawn randomly from the search region. Trial points are generated according to some distri-
bution (usually a uniform distribution) over the search region, and a better point is usually
accepted or ranked higher than other points. Most deterministic methods, e.g., SQP, IP,
usually use gradient information and are local optimization methods. Sometime the stan-
dard SQP and IP algorithms can avoid a local minimum and find a global minimum for some
special problems, e.g., a convex optimization problem.
57
A set S ? Rn is said to be convex if whenever x, y ? S and 0 ? t ? 1, there is
(1?t)x + ty ? S, which implies that a set is convex if the line segment joining any two
points in the set lies within the set as given in Figure 4.2.
y
(t=1)
(1-t)x+ty
x
(t=0)
Figure 4.2: Convex set
A function f is said to be convex if Df is a convex set and if whenever x, y?Df, and
0?t?1, there is:
f((1?t)x +ty) ? (1?t)f(x) +tf(y) (4.18)
This definition means that a function is convex if the line segment joining any two points
of the function curve lies entirely above the function curve as depicted in Figure 4.3. If the
objective function is convex, inequality constraints are convex, and the equality constraint
functions are affine, the problem is called a convex optimization NLP problem [49].
For a convex problem, any starting point can be picked up to start a local search, and
it is guaranteed to obtain the global minimum. Unfortunately, most optimization problems
are nonconvex, and there are many local optima. Thus, different starting points may re-
sult in quite different final solutions for local optimization methods. Most researchers have
recognized the problem of finding a good starting point, and some have even recommended
58
x
(t=0)
y
(t=1)(1-t)x+ty
f((1-t)x+ty)
f(x)
f(y)
(1-t)f(x)+tf(y)
Figure 4.3: Convex function
making several attempts (trying several times, for example) at finding good starting points
[50].
In a traditional truck diesel engine, without any electric control inputs, the Brake Spe-
cific Fuel Consumption (BSFC) map typically has a convex shape [3]. However, determined
by various control inputs such as throttle and gearshift, the BSFC time rate map applied
in this work does not have a convex shape even in the operating range ? [1100 1800]rpm,
which is depicted in Figure (4.4). Therefore, the objective function as shown in Equation
(4.4), as well as the NLP problem in this work, are not convex. This makes it non-trivial to
find the global minimum by using the IP method.
However, it can be seen from Figure 4.4, the BSFC map is relatively flat under the
nominal highway truck operation condition, i.e., relatively smooth and slow changes of the
engine power and speed, which corresponds to a small fuel consumption variation range on
the BSFC map. Thus, the nonconvex problem could have a small number of local minima,
when the upper and lower bounds are tightly specified as in Section 4.1.2. For the problem
at hand, by defining the initial guess as shown later in Section 4.4.1, the IP can exhibit a
rapid second-order convergence toward a local minimum, which could be identical or close to
the global minimum. A simple test further shows that by using any initial guess satisfying
the inequality constraints in Section 4.1.2 on any road conditions the optimal solutions
59
1100 1500
180050100150200250300350400450
0
5
10
15
20
 
Engine speed (rpm)Engine power (Kw)
 
BSFC (g/sec)
Figure 4.4: Zoomed-in BSFC time rate map
converge to the lower or higher speed bounds if only the minimal fuel or time is demanded
in the objective function, respectively. These results are in accordance with the global
minimum which can be expected in the common driving behavior that is: driving with low
speed consumes the minimal fuel; and driving with minimal travel time demands large fuel
consumption.
Similarly, if the complete objective function as described in Equation (4.4) is taken into
account, simulation results display that for any feasible initial guess, which is the arbitrary
choice of throttle within [0, 1], zero brake, the top gear of 18, and the constant set speed,
the solver is able to quickly converge to the unique optimal solution. This solution could be
identical or close to the global minimum as well, since the applied objective function is just
a weighted sum of the minimal fuel, time, and the gear shifting.
Additionally, when the objective function isnot convex, the fuel optimal speed trajectory
may very heavily depend on the road grade. Furthermore, if a problem covers a range of
speeds and accelerations that calls for gear shifts, the gear shifting is highly nonlinear and
60
generates oscillation between gears, which could be eliminated by using the penalty function
as in Equation (4.7).
4.1.6 Series NLP solver operation
The NLP solver designed previously is modified in this section to sovle the optimal brake
torque in a better way. An example of running the optimizer on a positive 4% single crest is
shown in Figure 4.5, where the elevation map, optimal speed, engine torque, and truck gear
are given from the top to the bottom plots. Such an optimal solution can be obtained with
any feasible initial guess stated above.
0 500 1000 1,300 2000 2,300 3,000 3,500
0
20
40
altitude (m)
0 500 1000 1300 2000 2300 3000 350022
25
28
speed (m/s)  
 
0 500 1000 1300 2000 2300 3000 35000
1000
2000
torque (Nm)  
 
0 500 1000 1300 2000 2300 3000 3500
10
gear point
position (m)
 
 
OC engine torque
OC brake torque
Figure 4.5: Optimal velocity, engine/brake torque, and gear shifting, on a 4% crest
However, on a large downhill terrain, if the constant set speed is taken as the initial
guess, it could be possible that large brake toque Tb is calculated from the optimizer to
maintain the constant speed. The brake torque Tb is determined by a brake input b?[0, 1]
multiplied by a maximum torque (Tb = bTbm). However, this optimal solution wastes the
potential energy which could be otherwise gained on the downhill. Therefore, the single
61
NLP optimizer in Figure 4.1 is modified to demand the least possible braking, which is both
beneficial for fuel efficiency and vehicle operation.
The basic flow chart of using NLP optimizers in a series operation is illustrated in Figure
4.6, which includes the following steps:
1. NLP first run (NLPr1): brake input Tb is omitted from Equation (4.11), as well as from
the state and control inputs that need to be optimized. The only system control inputs
are truck throttle and gear, and the optimal solution includes optimal throttle, truck
gear, and velocity trajectory;
2. Speed limit check: detect if the optimal speed from NLPr1 has reached vu, the upper
speed bound. If it is true, a NLP second run is triggered. Otherwise, the solution from
NLPr1 is deemed as the final optimal solution and Tb is set as a zero vector;
3. NLP second run (NLPr2): Tb is taken into account in Equation (4.11) and the state
and control inputs that need to be optimized. The control inputs are throttle, brake,
and truck gear, and the initial guess is the optimal solution from NLPr1 plus brake as a
zero vector. Afterwards, the solution from NLPr2 is used as the final optimal solution.
Another benefit of using this method is that it improves the computation efficiency.
Since on the normal level and rolling highways without a heavy traffic the truck brake is
not frequently commanded, it is reasonable to run the NLPr1 first on most roads. This way
the optimizer minimizes a reduced size parameter vector which consists of only the truck
throttle, gear, and velocity. Therefore, it is faster and more efficient than calculating the full
size parameter vector all the time which includes also the brake torque.
By using this method, the maximum fuel saving, maximum truck speed, and minimum
brake command are gained on a large single downhill. The optimal solution by using the
NLP optimizer series operation on a -4% single sag slope is demonstrated in Figure 4.7. It
is seen that the truck reduces speed and engine torque before the sag and then gains speed
from coasting down the sag slope. It can be observed from the bottom plot that only if the
62
NLP optimizer(r1):
optimizeparameter
vector, x={u,g,v}
Ifmax(v )=vO u ?
InitialguessofControland
State:throttle(u),gear(g);
velocity(v);w/length3S
NLP optimizer(r2):
optimizeparameter
vector, x={u,g,v,b}
Optimalsolution(r1):
x1 ={u1 ,g1 ,v1 }O O O O Initialguess,length4s:
x1 ={u1 ,g1 ,v1 , }O O O O b
false
Finaloptimalsolution:
x1 ={u1 ,g1 ,v1 }O
b
O O O
1 =0O
true
Finaloptimalsolution:
x2 ={u2 ,g2 ,v2 }O O O O, b2O
Figure 4.6: Series NLP optimizer operation for brake calculation
0 500 1100 1500 2100 2500 3000 3500
?40
?20
0
altitude (m)
0 500 1100 1500 2100 2500 3000 350022
25
28
speed (m/s)
 
 
0 500 1100 1500 2100 2500 3000 3500?3000
?2000
?1000
0
1000
torque (Nm)
position (m)
 
 
OC engine torque
OC brake torque
Figure 4.7: Optimal velocity, engine/brake torque, and gear shifting, on a -4% sag
63
truck reaches the velocity upper bound vu, brake is commanded. This is of a great benefit
to real road driving.
4.2 Real-time optimal control system
The optimal velocity calculated by using the NLP solver needs to be performed in real
time. This is accomplished by a feedback controller. In the system in this research, the slow
and fast dynamics are separated by the NLP solver and truck speed control, respectively.
Trajectory generated in the NLP solver is the slow outer-loop while the control is the fast
inner-loop. The concepts of inner and outer loops are formalized by a two degree-of-freedom
(DOF) control system architecture where the inner loop is used for stabilizing a nominal
reference velocity trajectory generated by the outer loop [38]. Figure 4.8 demonstrates an
inner-outer loop structure for achieving optimal feedback control. Under this structure,
traditional PID control is used to design the feedback regulation on the inner loop while the
outer loop uses the NLP solver.
Truck
Outer-loopfeedback:{ }u,g,b,v
NLP
optimizer
Feedback
regulation
output
_velocityerror
Outer-loopoptimalcontrol:
feedforward u orbO O
+
Optimalvelocity, vO
ubc cor feedback
compensation
truckvelocity, v
Outer-loopoptimalcontrol:
feedforwardgearshifting gO
Engineor
brake
torque
command
uorb+
+
Figure 4.8: Real-time fuel optimal feedback control through two DOF structure
64
The function of the two DOF optimal feedback control system was detailed in Section
1.2.3, which consists of the following steps for the fuel-optimal control system:
1. In the outer loop, the optimal control problem is solved using the NLP solver repeatedly
on a moving prediction horizon to yield near optimal velocity trajectories. Meanwhile,
the optimal controls such as uo, go, bo are fed forward to the inner loop. In the outer
loop feedback, u and g are the measured engine and engine brake torque;
2. In the inner loop, a feedback (PID) regulation controller is developed to calculate the
control compensation uc or bc, based on the velocity error between the optimal and
real truck velocities;
3. Finally, the control signals, u = uo + uc, b = bo + bc, and go, are used to accurately
track the optimal velocity trajectory over some period;
4. The procedure is repeated over the next prediction horizon.
4.3 Complete real time system structure
The real time test system consists of various modules, including the map-matching
system and an optimal powertrain control system (OC) with the NLP solver, as presented
in Figure 4.9.
4.3.1 CAN interface and Electronic Horizon
The controller area network (CAN) interface gets sensor inputs from CAN receivers and
sends them to the main software module. It also receives control commands from software
modules and then sends to a CAN transmitter. Electronic horizon (EH) is a map-matching
system to utilize the truck?s current position and the road information ahead, based on
measurements from GPS, inertial navigation system (INS) sensors, and the road geometry.
EH outputs bothroadgeometry informationandpositioning information. The roadgeometry
65
CAN
Receiver
J1939inputs
Map-matched
roadvector
GPS
measurements
Truckon
real-road
Truckdynamic
states
Engine
Control
Unit
& Trans.
INS
Sensors
ADC Laptop2EHorizon
Laptop3
Laptop1
CANdata Interface
CAN
Transmit
Commanded
torque
braking
gearshifting
Softwaremodule1(S1)
Softwaremodule2(S2)
NLP
Optimizer
CAN&EH
data
processing
Supervisor
system
Lookup
table
Optimal
(OPTp)
u,g,b,v
Feedback
regulation
(torque)Optimalvelocity
Optimaltorque
-
+
S1/S2
inter
-face
truckvelocity
OPTp
CAN&EH
Roadgrade(a)&
EHpredictiondata(EHp)
CAN&EH
Triggerflags
( )NLP &OC
EHp,a,flags
Optimalbraking
EH
+
+
Optimalgear
Feed-
forward
servo
Figure 4.9: Real time experimental system setup
ahead of the vehicle?s current location - called the ?horizon? - is sent as an ordered series of
Shape Point (SP) messages. The vehicle position is sent as a map-matched Position Message
(PM) with coordinates relative to the horizon information that have previously been sent.
This allows the application to know where the vehicle is with respect to the road geometry
that it already received from the SP messages.
The data structure in the SP and PM are listed in the following:
66
? shpIndex: Index for each shape point;
? dE: Distance between every two shape points in the east direction;
? dN: Distance between every two shape points in the north direction;
? dZ: Elevation difference between every two shape points;
? branchBit: Flag for the branch road.
Normally, the distance between every two shape points is around 3.5 m, and therefore there
are around 900 shape points in a prediction horizon which is 3 km long, as determined in
Section 4.1.1. The EH update is depicted in Figure 4.10.
Predictionhorizon,900points:
ShapePointMessageforall
pointsweresent
3000m
Truckcurrentposition:
PositionMessageis
sentforthisposition
Ehorizondataupdate
Figure 4.10: Electronic Horizon system information update
4.3.2 Software Modules 1 and 2
Software module 1 (S1) mainly consists of:
? CAN and EH data processing: calculate distance and road grade for a prediction
horizon, and save them to an EH buffer;
? Supervisor system: read EH and CAN inputs and handle different OC operation con-
ditions, e.g., start, stop, traffic in/out, fork road, by sending different ?flags?;
67
? Lookup table: output map-matched optimal states and control inputs, which are within
the truck operation limitations, from an OC solutions buffer;
? Optimal velocity tracking: apply the two DOF feedback control structure as described
in Section 4.2, where a torque control mode is used as a feedback regulation and the
optimal torque command is applied as a feedforward servo control. This local tracking
controller can regulate the system to closely track the desired trajectory and guarantee
the closed-loop system is stable.
Software module 2 (S2) runs the NLP optimizer algorithm.
S1 and S2 are implemented in MATLAB and SIMULINK in Laptop 3 which communi-
cate to a CAN data interface in Laptop 1 as shown in in Figure 4.9. In Laptop 3 the NLP
optimizer and other subsystems such as data processing and supervisor system are run on
two different Matlab platforms S1 and S2, which communicate to each other by exchanging
the corresponding data from a unique workspace. Such a parallel system structure is crucial
for the correct functioning of the multi-rate system in the real time application where the
update rate of the subsystems in S1 is 0.01s and the required NLP optimization time in S2
is approximately 1s. If all subsystem functions were run in a series structure in S1, the fast
rate data subsystems would be stalled by the slow rate NLP optimizer and consequently
the map data from EH would be delayed significantly. A clear description of the complete
system flow chart is given in Figure B.6 in Appendix B.
4.4 Real time system operation
The OC is a look-ahead controller which solves the optimization problem for a certain
prediction horizon ahead, and performs the optimal velocity trajectory by applying the
desired torque and optimal gear.
68
4.4.1 OC prediction update and initialization
In this work, the prediction horizon L and step distance h are chosen as 3000 m and 25
m, respectively, and there are 120 step points, s = L/h = 120. Thus, the NLP problem is
searching for the optimal parameter vector x ={u,g,b,v}, which consists of the number of
4s state and control inputs.
The selection of L and h is based on the road profile, truck length, and computation
time. The slope length of a single highway crest or sag is normally shorter than 3000 m [43].
Therefore, the 3000 m horizon is sufficiently long for the NLP solver to ?see? the upcoming
hills. The step distance h is selected close to the length of the experimental truck. It has a
length of 22.86 m which is made up of a conventional tractor and a single 16.15 m trailer.
Additionally, it is evident that the shorter the horizon, the less costly the solution of the
on-line optimization problem. However, when a really short prediction horizon is used, the
actual truck velocity trajectory will differ from the predicted optimal trajectory, even if no
model plant mismatch and no disturbances are present. It is mainly because the solution
for the repeated minimization over a finite horizon and the solution for the infinite horizon
problem differ significantly if a short horizon is chosen [51]. Thus, a much longer prediction
horizon, 3000 m, is used.
AO B C D E F G
5000 1000 1500 2000 2500 3000 3500
iter.1:predictionhorizon
iter.2
iter. 3
4000m
H
Figure 4.11: Recursive implementation of the optimal control system
Inthe real time application, the OCworks repeatedly withthe prediction horizonmoving
forward, as in Figure 4.11. While the truck runs on the starting section OA, the solver
calculates the optimal u, b, g, and v, for the prediction horizon OF, and then saves them to
69
a buffer, which is the first iteration (iter.1). It is assumed that the OC starts while the truck
is on a level road with constant speed close to the reference speed of 25 m/s. Therefore, the
initial guess of u, b, g, and v can be simply chosen as level road steady-state values, i.e.,
u = 0.4, v=25 m/s, g = 18, for NLPr1 in the series NLP solver operation.
When the truck runs on AB, it ?reads? out the map-matched optimal solutions obtained
on iter.1 and performs the optimal velocity trajectory by applying the calculated torque and
optimal gear shifting. Meanwhile, the NLP solver calculates the optimal solutions for the
next horizon AG, which is the second iteration (iter.2). The initial guess here is the optimal
solution for AF from iter.1 plus the level road steady-state values for the small section FG.
It is evident the optimal solution for AB from iter.1 is used as the initial guess for iter.2
and is performed by the truck in real-time. Thus, on AB the deviation between the truck?s
actual velocity trajectory and the optimal trajectory calculated on iter.2 is relatively small,
which assures the continuation of the optimal trajectory in the buffer as well as the actual
truck speed.
4.4.2 Optimization time
It can be seen from Section 4.4.1 that the optimization time tOP is a key issue for the
OC real-time operation. As shown in Figure 4.11, the NLP solver needs to solve the optimal
solution for the next prediction horizon L = 3000 m when the truck runs on the window
moving section Lw=500 m, e.g., on OA to calculate the optimal solution for OF. If the
truck reference velocity is 25 m/s, then tOP must be less than 20 s. This NLP solver is run
on a Windows XP Laptop (Intel Core2 6300 1.86 Hz, 2 Gb of RAM).
Here, tOP can be reduced by providing the NLP solver with gradients of objective and
constraint functions, as in Equations (4.8), (4.9), (4.12), and (4.13). This way the number
of function evaluations at each ?fmincon? iteration is largely reduced. Consequently, the
computation time for each prediction horizon is reduced to around 1 s, when the truck
moves 25 m at a 25 m/s reference speed. The computation time is quick enough for the
70
real-time implementation on the PC hardware mentioned above. By applying this method,
the MDNLP solver can quickly solve more complex problems, e.g., smaller h and longer L.
Additionally, by comparison, it is found that with a longer L and shorter h, the gain in fuel
economy could be improved, which could be further quantified in future work.
4.5 Conclusion
A 3D GIS road geometry based optimal powertrain control system was designed to re-
duce the heavy truck fuel consumption and travel time. A direct collocation method was
applied to transform the optimal control problem into a mixed-discrete nonlinear program-
ming (MDNLP) problem to find the constrained minimum of a nonlinear scalar function
of several state and control inputs, e.g., truck throttle u, gear g, brake b, and velocity v,
based on the road geometry. An OC optimizer which uses an interior-point algorithm plus
a rounding-off method was designed to solve this MDNLP problem.
The real time test system consists of various modules, including the map-matching
system and the OC with the MDNLP solver. The OC is a look-ahead controller, which
solves the optimization problem for a 3000 m prediction horizon ahead of the truck and
performs the optimal velocity trajectory by applying the desired torque and optimal gear.
For each prediction horizon, the OC computation time is around 1 s, which is quick enough
for the real-time implementation loaded on the selected PC hardware.
71
Chapter 5
Road Tests and Result Analysis
The developed OC system is implemented in MATLAB and SIMULINK using a model-
based design method. Both simulation and real road tests are conducted to evaluate the
performance of the OC. In this chapter, the basic OC function is tested and analyzed using
the simple simulated terrain. Subsequently, real road geometries R1 to R4 are used in a high
fidelity simulation environment to further validate the OC system performance. Finally, the
real road tests on routes R5 and R6 are conducted and the tests results are analyzed.
In this work, the reference speeds are set ranging from 25 m/s to 31.1 m/s and the
maximum speed variation is 2 m/s. As stated in [43], trucks generally increase speed by up
to about 7 percent on downgrades and decrease speed by 8 percent or more on upgrades
as compared to their operation on level ground. Therefore, the 2 m/s variation would be
acceptable for real world driving, and comfortable for truck drivers.
5.1 Experimental system setup
In this section, both the simulation system and real-time experimental system setups
are described.
5.1.1 Simulation system setup
In order to precisely simulate the real experimental environment and evaluate the de-
signed OC system before the real road test, a high fidelity simulation setup is developed.
The control system is then evaluated off-line by using the simulation model to examine and
tune the algorithms and parameters. The complete simulation system as shown in Figure
5.1 is built in MATLAB and SIMULINK by the efforts both from Auburn and Eaton. The
72
simulation setup includes a simulated map-matching system, a real OC system, and a simu-
lated heavy truck model. The first two modules are designed by Auburn, and the last one is
provided from Eaton. The system update rate is 0.01 s, which is the same as the real road
test system.
Truckmodelontheroad
Outer-loopfeedback:{ }u,g,b,v
NLP
optimizer
Feedback
regulation
_velocityerror
Outer-loopoptimalcontrol:
feedforward u orbO O
+
Optimalvelocity, vO
u bc cor
feed-
-back
truckvelocity, v
Outer-loopoptimalcontrol:
feedforwardgearshifting gO
Engine
/brake
torque
uorb
++ Engine Trans-
-mission wheel
vehicle
system
EH
simulator
Map-matched
roadvector
Figure 5.1: Simulation system setup
In the simulation test, a heavy truck model is replaced the real truck and interfaced
with the other systems. The truck model includes three main modules: environment and
driver cycle, operator, and plan and controls. The detailed functions of each module are
listed as follows:
? Environment and drive cycle: the drive cycle is defined as a constant speed of 25 m/s,
and environment parameters such as the road conditions are generated from Intermap?s
3D road geometry.
? Operator: it consists of a modified PID cruise controller to generate both acceleration
and brake pedal commands and then send to the driver outputs.
73
? Plant and controls: the plant side includes the engine, torque converter, transmission,
final drive, wheel, and vehicle longitudinal dynamics. The controls contain an engine
control and shift control.
By using this model, the baseline CC control run can be conducted and the fuel consumption
and travel time baseline is deemed reliable.
In the simulation test, the optimal velocity profile calculated from the OC is used to
replaced the constant speed of 25m/s as the drive cycle in the environment and drive cycle
module. To perform this drive cycle, the cruise controller in the operator module is used to
generate the torque compensation, which together with the calculated optimal engine and
brake torque are sent as the engine and engine brake commands to the engine system blocks
in the plant and controls module. Additionally, the optimal gear shifting from the OC is
sent as the transmission command directly to the transmission system block.
5.1.2 Real-time experimental system setup
The real time experimental test system which consists of various modules, including the
map-matching system and the OC with the NLP solver, has been discussed in Section 4.2
and is shown in Figure 5.2 again.
In the real-time experiment, the heavy truck is a Class 8 Caterpillar truck. It is equipped
with an internal combustion diesel engine: CAT C13, 12.5 liter diesel engine, 6 cylinders,
max horsepower: 410 kW at 1900 rpm, max torque: 2509 Nm at 1200 rpm. An Eaton
Fuller AutoShift 18 speeds transmission is installed in the truck, which is a shift-by wire
automated manual transmission (AMT) system. This allows gear shifting operation without
driver involvement, similar to an automatic transmission, while possessing the high efficiency
of a manual transmission.
The communication between the ECU and the actuators and sensors are based on a
J1939 protocol on top of a CAN 2.0B at a baud rate of 1 Mb per second. A laptop-
CAN interface card is used to interface the CAN receive/transmit via a RS232 port on the
74
CAN
Receiver
J1939inputs
Map-matched
roadvector
GPS
measurements
Truckon
real-road
Truckdynamic
states
Engine
Control
Unit
& Trans.
INS
Sensors
ADC Laptop2EHorizon
Laptop3
Laptop1
CANdata Interface
CAN
Transmit
Commanded
torque
braking
gearshifting
Softwaremodule1(S1)
Softwaremodule2(S2)
NLP
Optimizer
CAN&EH
data
processing
Supervisor
system
Lookup
table
Optimal
(OPTp)
u,g,b,v
Feedback
regulation
(torque)Optimalvelocity
Optimaltorque
-
+
S1/S2
inter
-face
truckvelocity
OPTp
CAN&EH
Roadgrade(a)&
EHpredictiondata(EHp)
CAN&EH
Triggerflags
( )NLP &OC
EHp,a,flags
Optimalbraking
EH
+
+
Optimalgear
Feed-
forward
servo
Figure 5.2: Real time experimental system setup
Laptop 1 as shown in Figure 5.2. From the Vector CANape software installed on the laptop,
important sensors measurements such as engine torque, engine speed, fuel rate, engine brake
torque, transmission speed, gear position, wheel speed, gyroscope data, etc., can be obtained.
Additionally, an EH control unit integrated on the Laptop 2 calculates the truck position
using a low cost GPS, wheel speed, and gyroscope data. The map data are then continuously
transmitted in a standardized format to the Laptop 1 through the CAN bus. The complete
OC system is run on the Laptop 3 (Windows XP Laptop, Intel Core2 6300 1.86 Hz, 2 Gb
of RAM), where the update rate of the subsystems in S1 is 0.01s and the required NLP
75
optimization time in S2 is approximately 1s. The communication between Laptop 1 and 3
is via a USB connection.
This rapid prototyping system enables the engineers to easily test the vehicle on the
road in a real driving phase. From the real-time measurement, the engineers could quickly
analyze the performance of the OC, modify the NLP solver, and build the modified code to
prototype vehicle computer in a fast and cost-effective manner [34].
5.2 Simulation tests with simulated roads
This section describes how the change of terrain effects system performance. Numerical
solutions are obtained to show and support the analyses. First, the comparison of the OC
and CC fuel consumption and travel time on a single crest and sag is discussed. Second,
the change of fuel savings and travel time on different road grades and slope lengths are
simulated and analyzed.
5.2.1 Single sag and crest
The comparison of the OC and CC performances, with a 25 m/s set speed, on simulated
single hills is show in this section. As stated in Section 2.2, the CC is applied to maintain
the desired vehicle velocity and a function of brake pedal control is engaged if the truck
reaches an upper speed limit of 27 m/s. On the other hand, the OC has a speed variation
of?2 m/s. Simulations are conducted on a typical single sag and crest in highway design,
which has a slope length of 1000 m, elevation of?40 m, and a resulting road grade of?4%,
respectively. The elevation maps are given in the top plot of Figures 5.3 and 5.5.
On the -4% sag, the OC is able to reduce 6.86% fuel consumption with 0.1% travel
time increase, compared with the CC. The comparison of system performance and fuel
consumption is shown in Figures 5.3 and 5.4. It is seen that the OC reduces truck speed,
engine torque, and fuel rate before the sag and then gains speed from coasting down the
sag slope. In this way, the OC is able to reduce the truck fuel consumption as well as to
76
0 500 1100 1500 2100 2500 3000 3500
?40
?20
0
altitude (m)
Max road slope ?4%, ? fuel =6.86%, ? time= ?0.1%
0 500 1100 1500 2100 2500 3000 350023
25
27
speed (m/s)
 
 
0 500 1100 1500 2100 2500 3000 3500?3000
?2000
?1000
0
1000
torque (Nm)
position (m)
 
 
CC
OC
CC engine torque
CC brake torque
OC engine torque
OC brake torque
Figure 5.3: Comparison of velocity, engine/brake torque, and gear: CC & OC, on a -4% sag
maintain nearly the same travel time. Additionally, it can be seen from the bottom plot of
Figure 5.3 that the OC commands less braking than the CC does, by reducing speed before
the sag slope. This is of a great benefit to real road driving as it reduces brake wear.
The comparison of system performance on a 4% single crest is shown in Figures 5.5 and
5.6, where the OC is able to reduce the fuel consumption by 0.68%, while increasing the
travel time by 0.59%. It is seen that the OC accelerates the truck by requiring large engine
torque and fuel rate through 1000 - 1300 m prior to climbing the crest. While on the crest,
the OC reduces torque but the CC demands large torque. An additional benefit is gained
from the gear shifting command. It is clear from the bottom plot of Figure 5.5 that by
increasing truck speed before the crest slope, there is less speed loss and subsequently less
downshifting as required by the OC?s operation.
77
0 500 1000 1500 2000 2500 3000 3500
?40
?20
0
altitude (m)
0 500 1000 1500 2000 2500 3000 35000
0.1
0.2
gallon
 
 
CC
OC
0 500 1000 1500 2000 2500 3000 35000
1
2
x 10?3
gallon/s
position (m)
 
 
Figure 5.4: Comparison of fuel consumption and rate: CC & OC, on a -4% sag
0 500 1000 1,300 2000 2,300 3,000 3,500
0
20
40
altitude (m)
Max road slope 4%, ? fuel= 0.86%, ? time= 0.59 %
0 500 1000 1300 2000 2300 3000 350023
25
27
speed (m/s)  
 CC
OC
0 500 1000 1300 2000 2300 3000 35000
1000
2000
torque (Nm)  
 
0 500 1000 1300 2000 2300 3000 3500
17
18
gear point
position (m)
 
 
Figure 5.5: Comparison of velocity, engine/brake torque, and gear: CC & OC, on a 4% crest
78
0 500 1000 1500 2000 2500 3000 3500
0
20
40
altitude (m)
0 500 1000 1500 2000 2500 3000 35000
0.2
0.4
gallon
 
 
CC
OC
0 500 1000 1500 2000 2500 3000 3500
2
4
6
x 10?3
gallon/s
position (m)
 
 CC
OC
Figure 5.6: Comparison of fuel consumption and rate: CC & OC, on a 4% crest
5.2.2 Different road grade and slope length
The comparison of the OC and CC performances, with a 25 m/s set speed, on single
hills with different road grades and slope lengths is discussed in this section. The road grades
and slope lengths vary from -5% to 5% and 0 to 1500 m, respectively. For each combination
of road grade and slope length, a simulation is conducted to calculate the fuel saving and
travel time change of the OC compared to the CC. The changes in fuel saving and increase
travel time are shown in Figures 5.7 and 5.8, where the positive percentage value represents
savings.
It can be seen that the maximum fuel saving, 12.2%, is obtained on the -5% road grade
and 1500 m slope length. On the contrary, the OC consumes 1.83% more fuel than the CC
on the maximum road grade and slope length 5% and 1500 m, respectively. Additionally,
for most road grades smaller than 4%, the fuel saving is positive which means the OC is
able to gain fuel saving over the CC. Figure 5.8 shows that the OC incurs very small travel
time increases, less than -1%, compared to the CC. The OC can gain the largest travel time
79
?5
0
5 0
500
1000
1500?5
0
5
10
15
grade length (m)
road grade (%)
fuel saving (%)
Figure 5.7: Fuel savings on different road grades and slope lengths, OC vs. CC
?5
0
5 0
500
1000
1500
?1
0
1
grade length (m)
road grade (%)
travel time change (%)
Figure 5.8: Travel time increases on different road grades and lengths, OC vs. CC
80
reduction, 2.1%, on the 5% road grade and 1500 m slope length corresponding to the road
condition where the maximum fuel increase is obtained.
In general, the gain in fuel economy and the change of travel time are directly related
to the change of road grade and slope length. Therefore, on large single sag sections large
fuel savings could be gained, while on large crest sections the OC may consume more fuel
but reduce travel time, etc.
5.3 Simulation tests with real road geometries
Subsequently, simulation tests are conducted to evaluate the OC system performance
on different real road geometries, R1 to R4. The details of all six road profiles were provided
previously in Table 2.4 and repeated in Table 5.1 in this chapter, where the mean, maximum,
and minimum road slopes are listed as percentages. The comparison of the OC and CC
system fuel consumption and travel time are shown and analyzed. Finally, how the change
of set speed effects the fuel saving is investigated.
Table 5.1: Intermap road profiles analysis
slope(%)
route length (m) mean max min ? terrain type
R1 37000 -0.21 2.65 -4.33 1.05 level
R2 37000 0.21 4.33 -2.65 1.05 level
R3 47000 0.27 4.88 -3.87 1.34 rolling
R4 47000 -0.27 3.87 -4.88 1.34 rolling
R5 54000 0.21 5.57 -5.43 3.05 mountainous
R6 54000 -0.21 5.43 -5.57 3.05 mountainous
5.3.1 Real road geometries tests and results analyses
The OC and CC performances are compared on real road geometries R1 to R4. The set
speed is 25 m/s, the speed variation for the OC is?2 m/s, and the upper speed limit for the
CC is 27 m/s. The comparison of fuel efficiency (FE) in miles/gallon, fuel consumption in
81
gallons (F), and travel time (T) from the OC and CC is shown in Table 5.2, where positive
percentage values represent savings. It is clear that the OC gains an average fuel saving
2.86% and 2.66% with 1.0% travel time increases on R1/2 and R3/4, respectively, when
compared to the CC.
Table 5.2: Comparison of fuel consumption and travel time, R1 to R4
Route FECC FCC FOC Diff(%) TCC(s) TOC Diff(%)
R1 12.41 2.64 2.57 2.78 1462.6 1478.2 -1.1
R2 8.87 3.15 3.07 2.40 1484.5 1497.4 -0.8
Mean 7.99 2.90 2.82 2.66 1473.6 1492.4 -1.0
R3 6.53 4.50 4.38 2.60 1869.1 1883.8 -0.8
R4 9.17 3.20 3.10 3.10 1861.4 1883.7 -1.1
Mean 7.62 3.85 3.74 2.86 1865.2 1883.8 -1.0
Furthermore, Table 5.2 shows that the average fuel saving from R3/4 (2.86%) is larger
than that from R1/2 (2.66%). The reason is that the gain in fuel saving on rolling terrains
R3/4 is larger than that on level terrains R1/2. Additionally, when looking at the same road
section but different directions such as R1 versus R2 or R3 versus R4, the gains of fuel saving
on R1 (2.78%) is larger than that on R2 (2.40%). Similarly, fuel savings on R4 is larger than
on R3. This difference is in that R1 and R4 are downhill terrains which have negative mean
road grade and R2 and R3 are uphill roads with positive mean road grade as can be seen
in Table 5.1. In general, the observation here on real road geometries is in accordance with
what was found in Section 5.2.2. Therefore, the gain in fuel saving could be more significant
on the rolling terrain with negative mean road grade.
Additionally, it is also necessary to investigate how the travel time increase effects the
fuel saving. Therefore, another group of baseline runs in simulation are conducted on R1 to
R4 and the CC reference speed is slowed down (to the different values on R1 to R4) to make
the CC and OC has almost the same travel time. Then, the fuel consumption from the OC
is compared with the new CC runs and the result are listed in Table 5.3. It is seen the OC
82
is still able to gain an average fuel saving 2.40% and 2.01% without travel time increases on
R1/2 and R3/4, respectively. These fuel savings are still acceptable for this research.
Table 5.3: Comparison of fuel consumption with same travel time, R1 to R4
Route FCC FOC Diff(%) TCC(s) TOC Diff(%)
R1 2.61 2.57 2.00 1478.0 1478.2 -0.02
R2 3.13 3.07 2.02 1497.0 1497.4 -0.03
Mean 2.87 2.82 2.01 1487.5 1487.8 -0.02
R3 4.47 4.38 2.20 1883.4 1883.8 -0.03
R4 3.18 3.10 2.58 1883.2 1883.7 -0.03
Mean 3.83 3.74 2.40 1883.3 1883.8 -0.03
Finally, the maximum CC fuel efficiency obtained on R1 is 12.41miles/gallon, because
it is a level downhill terrain and therefore has better fuel efficiency than its reverse direction
R2, which is an uphill road. R3 generally has the worst fuel efficiency among all roads for
the reason that it is an uphill rolling terrain. The condition is similar to what was observed
in Section 3.3.
In order to analyze the OC and CC system performance, the simulation results on R3
are shown since R3 is a typical rolling terrain. The comparison of engine and brake torque,
truck gear, speed, fuel rate, and total fuel consumption from the CC and OC is shown in
Figures 5.9 and 5.10. It can be seen that both systems perform the drive cycle, and have a
maximum speed of 27 m/s.
Additionally, it can be observed from the bottom plots of Figures 5.9 that the OC and
CC have similar gear shifting points. Thus, the OC gear shifting calculated by a rounding-off
method as described in Section 4.1.3 is feasible for truck driving conditions which have been
defined as various constraints in Section 4.1.2. Moreover, the OC requires less downshifting
than the CC, which is an optimal gear selection to reduce fuel consumption. Thus, by using
a rounding-off method for the problem at hand, the disadvantages as discussed in Section
4.1.3 could be overcome. Additionally, by considering the term Jgear in the cost function
(4.4), the rapidly repeated gear shifts are prevented.
83
0 0.5 1 1.5 2 2.5 3 3.5 4.3
x 104
0
50
100
150
altitude (m)
0 0.5 1 1.5 2 2.5 3 3.5 4.3
x 104
23
25
27
speed (m/s)  
 
CC
OC
0 0.5 1 1.5 2 2.5 3 3.5 4.3
x 104
?2000
0
2000
torque (Nm)  
 
CC engine torque
CC brake torque
OC engine torque
OC brake torque
0 0.5 1 1.5 2 2.5 3 3.5 4.3
x 104
17
18
gear point
position (m)
 
 
Figure 5.9: Comparison of velocity, torque, and gear on R3 with 25 m/s set speed, OC vs.
CC
0 0.5 1 1.5 2 2.5 3 3.5 4.3
x 104
0
50
100
150
altitude (m)
0 0.5 1 1.5 2 2.5 3 3.5 4.3
x 104
0
2
4
gallon
 
 
CC
OC
0 0.5 1 1.5 2 2.5 3 3.5 4.3
x 104
0
5
x 10?3
gallon/s
position (m)
 
 
Figure 5.10: Comparison of fuel consumption and rate on R3 with 25 m/s set speed, OC vs.
CC
84
4,500
0
20
40
altitude (m)
4,500 6300 7400 9400
23
24
26
27
speed (m/s)  
 
CC
OC
4,500 7400 9400?2000
0
2000
torque (Nm)  
 
CC engine torque
CC brake torque
OC engine torque
OC brake torque
4,500 6300
17
18
gear point
position (m)
 
 
decelerate before a sag curve, reduce the need for braking
and gain velocity by the potential energy on the sag curve
accelerate before a crest curve to reduce the 
speed loss, the needs for large engine 
torque and the down?shifting on the crest
Figure 5.11: Zoomed-in comparison of velocity, torque, and gear on R3 with 25 m/s set
speed, OC vs.CC
Figure 5.11 shows a section of the R3 tests, which illustrates the following basic functions
of the OC:
? Accelerate the truck before a crest hill to reduce the speed loss and the need for large
engine torque and frequent down-shifting on it, which is shown at 4.5-6.3 km. The
engine torque is kept large before but not throughout the crest, where the CC keeps
large torque.
? Require less downshifting than the CC to reduce fuel consumption and speed loss
compared to the CC on the large crest hill, as shown at 4.5-6.3 km.
? Decelerate the truck before a sag hill in order to gain the velocity from potential energy
and reduce the need for braking on the sag slope, which can be seen between 7.4 to
9.4 km (where the engine torque is reduced in front of a sag slope).
85
25 26.7 28.9 31.1
?2
0
2
4
Fuel saving and travel time change with different set speeds on R3, OC vs. CC
difference (%)
25 26.7 28.9 31.1
?2
0
2
4
Fuel saving and time change with different set speeds on R4, OC vs. CC
set speed (m/s)
difference (%)
 
 
fuel saving
travel time change
Figure 5.12: Fuel saving and travel time change with different set speeds, OC vs CC
5.3.2 Analyses of different set speeds for fuel savings
The reference speed thus far has been 25 m/s. However, it is also interested about how
the change of the set speed effects the gain in fuel saving and the change of travel time from
using the OC. Hence, more simulation tests are conducted on real roads R3 and R4, with
different reference speeds, 25 m/s, 26.7 m/s, 28.9 m/s, and 31.1 m/s which correspond to
56, 60, 65 and 70 mph and are typical US highway speed limits.
The simulation results are depicted in Figure 5.12, where the gain in fuel saving and
the change of travel time in percentages are plotted as dark and gray bars, respectively. The
same situations can be found both on R3 and R4: the faster the set speed, the larger the
gain in fuel saving (at the cost of increasing travel time). Hence, it could be beneficial to
use the OC system with high driving speed if the travel time increase is acceptable.
In addition, the OC and CC system performance on R4 with the maximum set speed
of 31.1 m/s is analyzed. The comparison of engine and brake torque, truck gear, speed, fuel
rate, and total fuel consumption from the CC and OC is shown in Figures 5.13 and 5.14.
86
0 0.5 1 1.5 2 2.5 3 3.5 4 4.3
x 104
?100
?50
0
altitude (m)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.3
x 104
29.1
31.1
33.1
speed (m/s)  
 CCOC
0 0.5 1 1.5 2 2.5 3 3.5 4 4.3
x 104
?1000
0
1000
2000
torque (Nm)  
 
CC engine torque
CC brake torque
OC engine torque
OC brake torque
0 0.5 1 1.5 2 2.5 3 3.5 4 4.3
x 104
18
gear point
position (m)
 
 
Figure 5.13: Comparison of velocity, torque, and gear on R4 with 31.1 m/s set speed, OC
vs. CC
R4 is the reverse direction of R3, and a downhill terrain with negative mean road grade as
indicated in Table 5.1. Therefore, although both systems perform the drive cycle and have a
maximum speed of 33.1 m/s, the OC has larger speed loss than the CC in that it functions to
reduce speed if there are sag slopes coming in, which appear more often in R4. Furthermore,
it can be seen from the third plot in Figure 5.13, that on such a downhill terrain, the OC
demands far less braking than the CC does and neither controller demands downshifting
commands. Finally, as presented in the second plot of Figure 5.14, there is significant fuel
savings by using the OC.
5.4 Real road test
Different from [5] and [8], the road test in this work is conducted to evaluate the OC
performance on mountainous terrains R5 and R6. The road maps were shown previously in
Figure 2.8. By testing the designed OC on R5, similar performance is obtained, as shown
in Figure 5.15. It is seen that the OC requires large engine torque to climb a crest at 850
87
0 0.5 1 1.5 2 2.5 3 3.5 4 4.3
x 104
?100
?50
0
altitude (m)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.3
x 104
0
2
4
gallon
 
 
0 0.5 1 1.5 2 2.5 3 3.5 4 4.3
x 104
0
5
x 10?3
gallon/s
position (m)
 
 
CC
OC
Figure 5.14: Comparison of fuel consumption and rate on R4 with 31.1 m/s set speed, OC
vs. CC
m, which is earlier than the CC. Then the OC reduces the torque quicker than the CC
while a sag slope is predicted at 3900 m. Additionally, the OC maintains a higher gear for
this section than the CC, where the gray and black curves are for the CC and OC results,
respectively.
The comparison of fuel consumption (F) and travel time (T) is shown in Table 5.4,
which includes R5, and its two sections, S1 [0, 38000] m and S2 [38001, 54243] m. It is seen
that for R5, the OC consumes a little more fuel (0.46%) than the CC does, while the OC is
able to save 1% fuel on section S1.
Table 5.4: Comparison of fuel consumption and travel time for R5, and its sections
Route mean grade FCC FOC Diff(%) TCC(s) TOC Diff(%)
R5 0.88 % 26.20 26.32 -0.46 2263.7 2257.2 0.27
R5(S1) 0.58 % 17.35 17.18 1.00 1364.0 1366.6 -0.19
R5(S2) 1.49 % 8.85 9.14 -3.28 899.7 890.6 0.92
88
0 500 850 1500 2000 2500 3000 3500 3900 4500 5000
?100
1020
30
elevation (m)
0 500 850 1500 2000 2500 3000 3500 3900 4500 500022
24
26
28
velocity (m/s)  
 
0 500 850 1500 2000 2500 3000 3500 3900 4500 5000
0
50
100
engine torque (%)
 
 
0 500 850 1500 2000 2500 3000 3500 3900 450016
17
18
gear
distance (m)
CC
OC
OC braking
Figure 5.15: Comparison of velocity, engine torque, and gear position on a section of R5
0 0.6 0.95 1.2 1.5 2 2.5 3 3.8 4 4.5 5 5.5
x 104
0
100
200
300
400
elevation (m)
0 0.6 1.2 1.5 2 2.5 3 3.8 4 4.5 5 5.5
x 104
0
10
20
30
fuel consumption (liter)
distance (m)
 
 
CC
OC
3.24 3.26
x 104
17
17.2
17.4
 
 
5.41 5.42 5.43
x 104
26.1
26.2
26.3
 
 
6000 9500 12000
0
50
100
B
C
A
Figure 5.16: Comparison of fuel consumption w.r.t.road geometry on R5, CC vs.OC
89
Additionally the comparison of fuel consumption related to road geometry is shown in
Figure 5.16. Fuel savings are not significant on S1 mainly because this section is highly
mountainous, with a steep road grade and long slope length. An example is shown in the
zoomed-in plot C in Figure 5.16, where the slope has maximum road grade of 5% and slope
length longer than 3 km. To climb such a large crest at a ?crawl? speed, the OC has to
require full engine torque at a low gear, the same as the CC. Similarly, on a long sag slope,
both the OC and CC control the truck to coast down, using an engine idling output of 3
kW and a corresponding engine idling fuel consumption. On section S2, the OC consumes
more fuel than the CC, as shown in plot B in Figure 5.16. This is because S2 is nearly a
constant uphill route, with a mean road grade of 1.49%, as shown in Table 5.4. For a long
crest slope, the OC functions to accelerate the truck beforehand to reduce the speed loss,
which consumes more fuel than the CC.
Similar to its functions on R5, the OC consumes a little more fuel (0.36%) than the CC
on R6 where the OC is only able to save fuel consumption on some sections but consumes
more on the others, which is shown in Table 5.5. However, it can be observed from the
elevation map in Figure 5.17, there is an altitude difference of 300 m over R6 and the mean
road grade is positive, so there is less room for reducing fuel consumption by decelerating
before downhills.
Table 5.5: Comparison of fuel consumption and travel time for R6
Route FCC FOC Diff(%) TCC(s) TOC Diff(%)
R6 22.57 22.65 -0.36 2230.5 2220.7 0.45
By testing the designed OC system on rolling and mountainous terrains, the effect of
the terrain change on the gain in fuel economy is investigated. It is seen that the OC is not
really effective to save fuel consumption on a highly mountainous terrain, especially when
the crest road is steep and slope length is long.
90
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
x 104
?50
0
50
100
150
200
250
300
elevation (m)
distance (m)
Figure 5.17: Elevation map of R6
5.5 Conclusion
In this chapter, simulation and real road tests were conducted to evaluate the perfor-
mance of the designed OC system, compared to the CC. First, the simulated single hills were
used to show that the basic functions of the OC fuel saving are from: accelerating the truck
before a crest slope to reduce the speed loss, large engine torque, and downshifting on the
crest; or decelerating before a sag slope and then gaining velocity from potential energy on
the slope. Subsequently, real road geometries R1 to R4 were used in a high fidelity simu-
lation environment to further validate the OC system performance and show the designed
system is able to reduce fuel consumption up to 3.0% on level or rolling terrains with small
increases in travel time, when compared to the CC. Finally, real road tests on routes R5 and
R6 were conducted and the tests results were analyzed. It was seen that the OC could only
save small amounts of fuel on highly mountainous terrain, which have a steep crest slope
and long slope length. Thus, it was found that the gain in fuel economy is directly effected
by the change in terrain type.
91
Chapter 6
Sensitivity Analysis of Road Map Errors
Thus far, the road maps applied in the OC system are considered without any errors,
which means in Figure 4.9 the road map in the OC system perfectly matches the real road.
However, this is not true for a real road test since road map errors could be generated from
many resources such as elevation data acquisition, the map-matching system, road grade
calculation, etc.
The road maps applied in this work are provided by Intermap which are commercial
GIS road geometries and are part of a commercial data set that will be accurate nationwide.
Additionally, the map matching system from Intermap is a commercial product and is of high
accuracy. But it is still necessary to investigate error sensitivity to determine how the errors
in the terrain data effect the gain in fuel economy and the system behavior. The results can
be used to quantify the accuracy requirement for the road map to gain fuel economy.
6.1 Terrain Error Sensitivity
The terrain error sensitivity is investigated to find how errors in the terrain data affect
the control system performance. In general, the GIS road map error is represented as a root
mean square error (RMSE), which is the square root of the mean square error (MSE). MSE
is obtained by calculating the square of the deviations of road map points in xm, ym, and
zm from their true position as in x, y, z, summing up the measurements and then dividing
by the total number of points. For example in x direction:
RMSE =
radicalBiggsummationtext
N
i=1(xmi?xi)2
n (6.1)
92
The road map applied in this work is generated from the digital surface model (DSM)
dataset by using Intermap?s airborne Interferometric Synthetic Aperture Radar (IFSAR)
technology. The map is a surface view of the earth containing both location and elevation
information. The DSM dataset as well as the road map have the pixel size, horizontal
accuracy RMSE, and vertical accuracy RMSE as 5 m, 2 m, and 1 m, respectively.
Intermap Technologies produces digital elevation models, digital surface model (DSM)
products from our airborne Interferometric Synthetic Aperture Radar (IFSAR) technology.
The DSM dataset as well as the road map have the step spacing, horizontal accuracy RMSE,
and vertical accuracy RMSE as 5 m, 2 m, and 1 m, respectively.
In order to test the OC system performance with low accuracy maps, some error is
injected into the road maps R1 - R6 which have been used in the previous chapter. Among
those maps, R3 is taken as an example for the analysis and the results are deemed general
for the reason that R3 is a typical rolling terrain. Some road profiles are produced by adding
certain amounts of error to the original R3 map based on different error injection schemes.
The errors considered in this work and their definitions are as follows:
? Absolute error (AE): a horizontal shift in the position of the slope
? Relative error (RE): a vertical difference of the slope value
Both AE and RE are general errors in real-road maps, where AE could be results of the
accuracy limitations of the map-matching system and GPS receiver, and RE is due to the
GIS elevation data acquisition or road grade calculation errors.
6.1.1 Different road maps
Several road profiles are produced by adding certain amounts of error to the original
road geometry R3. In the simulation in this chapter, Intermap high accuracy road geometry
is deemed and applied as the real road. The description of road and various road maps are
given as follows:
93
? Real road R3r: real road of route 3
? Road map R3: Intermap road geometry of route 3, which is of high accuracy
? Road map R3.1: R3 with an AE and RE of 80 and 30 cm
? Road map R3.2: R3 with an AE and RE of 100 and 20 cm
? Road map R3.3: R3 with an AE and RE of 150 and 30 cm
? Road map R3.4: R3 with an AE and RE of 300 and 30 cm
? Road map R3.5: R3 with an AE and RE of 300 and 100 cm
In order to show the RMSE errors in a more straightforward way, R3.1 to R3.5 are
subtracted by R3 to obtain an approximation of the vertical error in meters as descried in
Table 6.1, where the mean, maximum, and minimum errors are listed in meters. The ?
in this table represents the standard deviation of the slope error value. The comparison of
vertical error distribution density is presented in Figure 6.1.
Table 6.1: Analysis of vertical errors in maps R3.1 to R3.5
map mean(m) max min ?
R3.1 -0.024 8.898 -5.716 0.776
R3.2 0.016 3.234 -9.793 1.053
R3.3 1.016 4.234 -8.793 1.203
R3.4 0.033 6.467 -19.586 2.106
R3.5 0.049 9.701 -29.380 3.159
The comparison of R3 (dark), R3.2 (gray), and R3.5 (dashed gray) is shown in Figure
6.2, where the top plot is the elevation, the middle plot is the road grade, and the bottom
plot is the zoomed-in road grade comparison. From the figure, it can be seen that the AE
results in the hills in R3 shifting in position either to the left or right. On the other hand,
by adding RE the elevation data changes and thereby road grades from R3.2 and R3.5 are
different from R3, among which R3.5 has the most significant errors.
94
?10 ?5 0 5 10
0
2
4
6
8
10
12
14
16
Error density (%)
Elevation errors (m)
 
 R3.1
R3.2
R3.3
R3.4
R3.5
Figure 6.1: Comparison of vertical error distribution density, R3.1 to R3.5
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
x 104
0
50
100
150
elevation(m)
 
 
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
x 104
?5
0
5
grade (%)
2.5 3 3.5 4
x 104
?5
0
5
grade (%)
distance (m)
R3.2
R3.5
R3
Figure 6.2: Comparison of road maps with different accuracies, R3 vs. R3.2 and R3.5
In addition, road maps R3.4 and R3.5 have similar AE of 3 m, which is close to the
horizontal position accuracy RMSE (4 m) of the commercial GPS receivers applied in the
real road test. Hence, it is reasonable to see the OC simulation test using R3.4 as a real
95
road test, since in this simulation only the road map errors are taken into account which has
the RMSE accuracy similar to that of the GPS receiver. The errors in different tests can be
compared in the following:
? Horizontal error of simulation test using R3.4: AE (3 m) on the top of R3;
? Horizontal error of real road test using R3: horizonal GPS RMSE (4 m) on top of R3.
6.1.2 Simulation setup
For the purpose of numerically quantifying the impact from the road map errors on the
fuel savings from using road maps R3 and R3.1 to R3.5, the following steps are conducted
for the simulation:
1. Run the CC on real road R3r, where the total fuel usage is set as the fuel consumption
baseline (BL);
2. Run the OC based on R3: fuel usage is compared to the BL and then the gain in
fuel saving using the high accuracy map is obtained, which is the fuel saving baseline
(FSBL);
3. Run the OC based on R3.1 to R3.5: each fuel usage is compared to the BL and the
fuel savings by using low accuracy maps are saved;
4. Each fuel saving from step 3 is compared to the fuel saving baseline in step 2, and the
differences in fuel saving by using maps R3 and R3.1 to R3.5 are found.
This simulation procedure can be seen in Fig.6.3.
6.1.3 Simulation results
In this section, the simulation tests for the terrain error sensitivity are conducted and
results are analyzed. The truck speed is set at 25 m/s, and all the OC simulations obtain
nearly the same travel time. Different fuel usages from the OC using different road maps,
96
CC
Fuel
consumption
Baseline
OCR3
Road
geometry
RealRoad,R3r
Fuelsaving
Baseline
Fuelsaving
R3.1-R3.5
Differencein
Fuelsaving
basedon
mapsR3and
R3.1-R3.5
Compare
to
make
Compare
to
make
RealRoad,R3r
RealRoad
R3r
OCR3.1-R3.5
Low-
accuracy
roadmaps
Compare
tomake
Fuel
consumption:
usingR3
Fuel
consumption:
usingR3.1-R3.5
Figure 6.3: Block diagram of simulation setup for terrain error sensitivity analysis
R3 and R3.1 - R3.5, are compared with the BL. The gains of fuel savings with respect to
different road maps are then obtained, and illustrated in Figure 6.4, where the dark bars
represent the fuel saving. The gray bars represent the relative difference in fuel saving, which
are calculated by subtracting the FSBL by fuel saving using R3.1 to R3.5. The first dark
bar in the figure corresponds to the FSBL. In general, the gain in fuel savings is directly
related to the road map accuracy (i.e., the more accurate the road map, the larger the gain
in fuel savings).
Additionally, as indicated in Figure 6.4, the fuel savings from R3.1 to R3.4 are all larger
than 2.0%, while for R3.5 the gain in fuel saving is less than 1% although it has the same
AE as R3.4. This can be explained by the fact that R3.5 has the largest RE (1 m) among all
road profiles which can be seen looking back to Section 6.1.1. Therefore, it can be concluded
that RE has a larger impact than AE on the OC fuel saving.
The reason the fuel saving is not largely impacted by AE is that a couple of meters
shifting in the slope position is insignificant when compared to the general kilometer slope
length as well as the 25 meters sampling distance. However, if there is a large positive
RE presented in the map which increases the road grade, the OC could command larger
97
R3 R3.1 R3.2 R3.3 R3.4 R3.5?2
?1.5
?1
?0.5
0
0.5
1
1.5
2
2.5
3
difference (%)
different road maps
 
 Fuel saving 
Relative diff. [(R3.1 to R3.5) ?R3]
Figure 6.4: Fuel saving using different road maps: R3 and R3.1-R3.5
engine torque and unnecessary downshifting to climb the presumed steeper crest. On the
other hand, if a large negative RE appears in the map which functions to decrease the road
grade, the OC will command larger speed reduction or braking. It would require large torque
compensation from the feedback velocity tracking subsystem in real driving to maintain the
optimal speed trajectory. Both would result in large fuel usage and consequently reduce the
gain in fuel savings.
Furthermore, as discussed in Section 6.1.1, the OC simulation test using R3.4 has similar
horizontal accuracy to the real road test where the applied GPS receiver has RMSE of
approximately 4 m. As demonstrated in Figure 6.4, the OC using R3.4 is able to gain 2.0%
fuel saving, which additionally verifies the OC is still able to gain fuel saving on the real
road test even if there are horizontal errors in the GPS receiver and road map.
Other than effecting the gain in fuel economy, road map errors also impact the OC sys-
tem performance and make it function incorrectly. The comparison of the OC performances
by using different road maps, in terms of v, u, and g in a section from 35 to 45 km, is given
98
in Figure 6.5. By using R3.2 and R3.5, the OC system could not function fully correctly if
the following errors occurred:
? Negative RE (road grade decreased): Results in the deceleration of the truck and
reduction in engine torque before a false sag hill in the map. Since on a real road
trucks can not gain the speed from potential energy on the sag, large engine torque
and downshifting are commanded to accelerate the truck back to the set speed, which
is displayed between 36 to 38 km;
? Positive RE (road grade increased): Results in the acceleration of the truck before a
fake crest hill by demanding large engine torque, which increases the truck speed in
real road, as can be seen between 43 to 44 km.
Those system functions produce unpredicted large fuel consumption in the OC system and
therefore reduce the fuel saving.
3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5
?4?2
02
grade (%)  
 
3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5
x 104
23
25
speed (m/s)
3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5
x 104
0
2560
torque (Nm)
3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5
x 104
9
9.5
10
gear
position (m)
R3
R3.2
R3.5
Figure 6.5: Zoomed-in comparison of the OC performances by using maps, R3, R3.2, and
R3.5
99
From the simulation results above, it is clear that road map errors largely effect both
the gain in fuel saving and the system performance. Because correct implementation of the
OC highly relies on the prediction road maps in real time, the road maps are required to
have high accuracy.
6.2 Conclusion
This chapter described results of the terrain map error sensitivity analyses. The changes
of fuel economy and system performance with respect to road maps with different errors were
discussed. It was found that the road map error effects both the fuel economy and the system
performance. The impact from the absolute error (a shift in the slope position) on the fuel
saving is not as evident as that from the relative error (a different slope value). Even if the
impact from absolute error on the gain in fuel saving is not evident, this impact on system
performance is significant. Therefore, in real-time implementation, road maps are required
to have small absolute and relative errors.
Additionally, this chapter has shown that by using road maps with the absolute error
close to the GPS receiver error accuracy, the OC simulation emulates a real road test in
terms of horizontal error accuracy. The test results show that the OC is still able to gain
acceptable fuel saving, which verifies the OC could function in a reasonable manner even if
horizontal errors in the GPS receiver and road map are fixed to present accuracies in real
road scenarios.
100
Chapter 7
Conclusion
7.1 Concluding Remarks
This work described the research to investigate the benefit of using a 3D road geometry
based optimal powertrain control (OC) system in reducing the heavy truck fuel consumption.
The OC was designed using a nonlinear programming solver to predict truck engine or
brake torque, gear shifting, and velocity trajectory based on road geometry to minimize
fuel consumption and travel time. Computer simulations and real road tests of a Class 8
truck were conducted with Intermap?s real 3D road geometry to evaluate the OC system
performance.
Chapter 1 presented the motivation and objectives of conducting this work. Addition-
ally, the background and literature were studied to cover not only the closely related topics
such as fuel optimal vehicle trajectory optimization and real-time fuel optimal control sys-
tem design, but some more general theoretical aspects as well, i.e., optimal control problems,
mixed-discrete nonlinear programming (NLP) solution, real-time optimal control system de-
sign. After analyzing and comparing the prior work, the contributions of this work were
given at the end of Chapter 1.
Real and simulated road geometries and the comparison baseline to evaluate the OC
performance were given in Chapter 2. First, some important road design parameters, e.g.,
road grade, terrain type, frequency component, were defined to describe the main features
of a road profile and to generate the simulated road section. Second, by using the simulated
road profiles, the relation between the fuel consumption and road geometry was be ana-
lyzed. Furthermore, the features of real road geometries R1 to R6 were introduced, which
include the calculation of road grade from 3D elevation data, the illumination of real road
101
elevation/grade maps, and the analysis of terrain type. As a final step, a cruise controller
(CC) with the automatic braking function was applied to perform the defined drive cycle,
generate the fuel consumption baseline, and evaluate the designed OC system performance.
Chapter 3 described the work to develop and validate heavy truck dynamics and pow-
ertrain models, for the purpose of designing the model-based OC system and testing the
system performance in a simulation environment. Only longitudinal truck dynamics were
considered and the applied engine map, Brake Specific Fuel Consumption (BSFC) map, and
truck parameters were provided by Eaton Corp. The model was validated by comparing the
real road test data with the simulation data. In addition, simulations were run by using
the developed model to quantify how the change in terrain type effects the truck fuel con-
sumption and show that fuel consumption is impacted by the change in terrain type, driving
speed, and road frequency component.
In Chapter 4, a 3D GIS road geometry based OC system was designed to reduce the
heavy truck fuel consumption and travel time. A direct collocation method was applied
to transform the optimal control problem into a mixed-discrete nonlinear programming
(MDNLP) problem to find the constrained minimum of a nonlinear scalar function of several
variables such as the normalized truck throttle command u, brake command b, gear point
g, and velocity v. An optimizer of the OC which uses an interior-point algorithm plus a
rounding-off method was designed to solve this MDNLP problem. The real time operation
system consists of various modules, including the map-matching system and the OC with
the MDNLP solver. The OC is a look-ahead controller, which solves the optimization prob-
lem for a 3000 m prediction horizon ahead, and performs the optimal velocity trajectory by
applying the calculated torque and optimal gear.
Simulation and real road tests were presented in Chapter 5 to evaluate the performance
of the designed OC system, compared to the CC. First, the simulated single hills were used
to show that the basic functions of the OC fuel saving are to accelerate the truck before
a crest slope or decelerate it before a sag slope. Subsequently, real road geometries R1 to
102
R4 were used in a high fidelity simulation environment to further validate the OC system
performance and show the designed system is able to reduce fuel consumption up to 3.0% on
level terrains (R1 and R2) or rolling terrains (R3 and R4) with small travel time increases.
Finally, the real road tests on routes R5 and R6 were conducted and test results denoted
that the OC could only save a small amount of fuel on highly mountainous terrain, which
has the steep crest slope and long slope length. Thus, it was found that the gain in fuel
economy is directly effected by the change in terrain type.
Finally, in Chapter 6 the terrain error sensitivity analysis, i.e., how the errors in the
road map impact the OC fuel saving and system performance, was investigated. It was
found that the road error effects both the fuel economy and the system performance. Some
conclusion could be: the impact from the absolute error (a shift in the slope position) on
the fuel saving is not as evident as that from the relative error (a different slope value); even
if the impact from absolute error on the gain in fuel saving is not evident, this impact on
system performance is significant such as commanding incorrect engine torque, gear shifting,
velocity trajectory, etc. Therefore, in real-time implementation, road maps are required to
have small absolute and relative errors.
7.2 Future Work
7.2.1 Modification of the optimal control system
Future work would consider modifying the OC for a better real-time implementation,
and testing the system on a wide range of terrain types such as conducting road tests on
typical level and rolling terrains. Additionally, it is proposed to set up a Monte Carlo
simulation where the road elevation varies to predict a mean saving on three terrain types,
as well as to simulate and predict the fuel saving on any specific routes. For instance, by
setting up a corresponding Monte Carlo simulation for a route which has 45% level, 35%
rolling, and 20% mountainous terrains, it would be possible to forecast the fuel saving on
this route by using the designed road geometry based optimal control system.
103
7.2.2 Design of an optimal power management system for a hybrid electric
truck
More crucially, the design of a road map based hybrid electric truck fuel optimization
system would be considered as an meaningful extension of this work, since knowledge of the
road information ahead could be helpful to improve the hybrid electric truck?s fuel efficiency.
In general, the hybrid electric truck produced by Eaton employs a parallel-type diesel-
electric architecture which integrates an advanced diesel engine, an electric traction motor,
Lithium-Ion batteries, an automatic clutch, and an automated manual transmission system.
The motor is directly linked between the output of the clutch and the input to the trans-
mission. This architecture provides the regenerative braking during deceleration and allows
efficient motor assist and recharge operations by the engine [34].
Hence, in future work the optimal power management system (OPM) of the hybrid
electric truck?s powertrain could be developed to command the engine torque, motor torque,
and gear selection to minimize the hybrid electric truck?s fuel consumption using 3D road
geometries. The gain in fuel economy using the OPM could be quantified when compared
to the baseline control which could be a classic load leveling type rule-based algorithm
implemented on the same hybrid electric truck. The idea of this approach is based on
the concept of ?load-leveling?, which attempts to operate the irreversible energy conversion
device such as an internal combustion engine in an efficient region and uses the reversible
energy storage device as a load leveling device, to compensate the rest of the power demand.
Finally, the proposed OPM would have the following basic functions:
? Determine the suitable operation modes: motor only, engine only, and power assist.
? Command the proper torque level and its split between the motor and engine, and
maintain adequate energy in the battery.
? Decelerate the truck before a downhill by reducing engine/motor torque in order to
gain the velocity from potential energy. The OPM recharges the battery when the
104
truck is coasting down from the downhill. If necessary, the regenerative braking is
commanded by applying a negative torque to the electric motor.
? Accelerate the truck and require downshifting before a uphill in order to reduce the
speed loss and the need for large engine torque on the hill. The engine torque is kept
large before but not throughout the hill.
105
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109
Appendix A
Abbreviations and frequently used symbols
A.1 List of Abbreviations
Abbreviation Description
ACC Adaptive cruise control
AE Absolute error: a horizontal shift in the curve position
BL Baseline
BSFC Brake specific fuel consumption
CAN Controller area network
CC Cruise control system
DP Dynamic programming
DSM Digital surface model
ECU Electronic control uint
EH Electric horizon, name of a map matching system
GIS Geographic information system
GPS Global positioning system
INS Initial navigation system
IP Interior point method
PCC Predictive cruise control
MDNLP Mixed-discrete nonlinear programming
MINLP Mixed-integer nonlinear programming
MPC Model predictive control
NLP Nonlinear programming
OC Optimal control system
RE Relative error: a vertical different slope value for the curve
rpm Revolutions per minute
SQP Sequential quadratic programming
TPBVP Two-point boundary value problem
110
A.2 List of frequently used symbols
The experimental truck is a Caterpillar Class 8 tractor and trailer. Frequently used
symbols as well as those truck parameters applied in this work are listed in the following
table.
Symbol Description Value Unit
Afr Truck frontal area 7.43 m2
b Braking pedal position in percentage %
Cd Aerodynamic drag coefficient 0.65 -
Crr Rolling resistance coefficient 0.0072 -
Fw Wheel drive force N
Fs Longitudinal force due to road grade N
Frr Rolling resistance force N
Fa Air drag force N
g Truck gear 18 -
h Step length 25 m
L Prediction horizon 3000 m
m Truck mass 31.7 tons
mf Fuel consumption liter
nt Transmission ratio -
nd Final drive ratio 3.25 -
p Position meter
P Engine power kW
Je Engine rotation inertia 3.0 kg-m2
Jw Wheel rotation inertia 3.21 kg-m2
r Wheel radius 0.51 m
s Number of set points 120 -
Tm Maximum engine torque 2509 Nm
Te Desired engine torque Nm
Tw Wheel torque Nm
Tbm Maximum engine retarder brake torque 4500 Nm
Tb Desired braking torque Nm
u Throttle percentage position
v Truck velocity m/s
? Road grade %
?air Air density 1.23 kg/m3
?e Engine rotation speed rpm
?w Wheel rotation speed rad/s
?t Transmission efficiency 0.985 -
?d Final drive efficiency 0.97 -
t Time s
111
Appendix B
Implementation of optimal control system for real road test
The real time test system which consists of various modules, including the map-matching
system and the OC with the NLP solver, has been discussed in Section 4.2 and is shown
in Figure B.1 again. In this chapter, the detailed system implementation for each module
either in Software module 1 (S1) or 2 (S2) is given.
CAN
Receiver
J1939inputs
Map-matched
roadvector
GPS
measurements
Truckon
real-road
Truckdynamic
states
Engine
Control
Unit
& Trans.
INS
Sensors
ADC Laptop2EHorizon
Laptop3
Laptop1
CANdata Interface
CAN
Transmit
Commanded
torque
braking
gearshifting
Softwaremodule1(S1)
Softwaremodule2(S2)
NLP
Optimizer
CAN&EH
data
processing
Supervisor
system
Lookup
table
Optimal
(OPTp)
u,g,b,v
Feedback
regulation
(torque)Optimalvelocity
Optimaltorque
-
+
S1/S2
inter
-face
truckvelocity
OPTp
CAN&EH
Roadgrade(a)&
EHpredictiondata(EHp)
CAN&EH
Triggerflags
( )NLP &OC
EHp,a,flags
Optimalbraking
EH
+
+
Optimalgear
Feed-
forward
servo
Figure B.1: Real time experimental system setup
112
The complete system scheme of S1 in Laptop 3, which communicates with Laptop 1 by
CAN data interface, is presented in Figure B.2. It is seen that S1 acquires EH road geometry
and J1939 vehicle states data from a CAN receive block, and sends general commands and
engine control commands to a CAN transmitter. Meanwhile, S1 exchanges data with S2,
where the NLP optimizer runs to calculate the optimal solution. In the following, the scheme
and functions of S1 and S2 are given in detail.
(Communicate with EHorizon) (Communicate with J1939)
Software module1
Electronic_Horizon
J1939_Inputs
Gen_III_Cmds
Engine_Cmds
CAN Transmit
Gen_III_Cmds
Engine_Cmds
CAN Receive
Electronic_Horizon
J1939_Inputs
 Vector CAN Configuration2
Vector CAN 
Configuration 
(config2)  Vector CAN Configuration1
Vector CAN 
Configuration 
(config1)
Figure B.2: Complete system scheme of S1, and CAN receive/transmit blocks
B.1 Software module 1
When looking into the S1 block, the system structure is displayed in Figure B.3, which
is made up of the vehicle speed control enabler, real-time optimal control (OC) system,
feedback regulation, and engine torque management blocks. Vehicle speed control enabler
block reads truck speed from J1939 data and generates the output ?Mas Allowed?, which has
a value of 1 to indicate the OC is turned on if truck speed is larger than 20 m/s. The OC block
acquires both vehicle and EH data, and generates and outputs both the optimal solution
and override commands, where the former includes ?Setspeed? (optimal speed trajectory),
optimal torque, and truck gear and the latter are generated to override the ECU with the
optimal solution.
113
Engine_Cmds
2
1
Vehicle Speed Control Enabler
J1939_Inputs MAS_Allowed
Optimal control system
Electronic_Horizon
J1939_Inputs
Mas_allowed
GearCmd
torque_override
gear_override
Setspeed
opt torque
opt_throttle
AND
opt_u
[speed_e]
[Mas_Allowed]
[gear_override]
torque_override
GearOvrdCmd
[Electronic_Horizon]
[torque]
[J1939_Inputs]
[gear_override]
torque
torque_override
GearOvrdCmd
[Electronic_Horizon]
[J1939_Inputs]
Mas_Allowed
[J1939_Inputs]
speed_e
[Mas_Allowed]
MAS_Enable
[J1939_Inputs]
Feedback regulation
MAS_Allowed
Set Speed
J1939_Inputs
opt torque
Torque Command Nm
speed _error
Engine_torque_cmd_management
MAS_Allowed
torque
t_override
speed _error
+torque_override
?torque_override
+torque
?torque
Count To 250 and Repeat
count_out
J1939_Inputs
2
Electronic_Horizon
1
GEN_III_Cmds
GENIII_Gear_Override_Cmd
GENIII_Eng_Brake_Override_Cmd
GENIII_Torque_Override_Mode
GENIII_Torque_Override_Cmd
GENIII_Eng_Brake_Override_Mode
GENIII_Gear_Override_Mode
Figure B.3: System scheme of S1
Feedback regulation block is designed to track the optimal speed by applying a torque
control mode as a feedback regulation and the optimal torque command as a feedforward
servo control. The generated engine torque command is not real time applicable until it has
been checked in engine torque command management block for truck operation limitations.
The outputs from this block are engine and braking override and torque commands, respec-
tively, which together with the gear override and shifting commands from the OC block are
sent as ?Gen III Cmds? to the CAN transmit block.
114
B.1.1 Optimal control system scheme
The OC system block is the essential part of the complete system, which includes three
mainsystem blocks: ?CAN andEH dataprocessing?, ?Supervisor system?, and?Map-matching
lookup table?, as demonstrated in Figure B.4. The J1939 data applied are acceleration pedal
on/off, braking on/off, vehicle speed, selected gear, and current engine speed.
opt_throttle
6
opt torque
5
gear_override
4
torque_override
3
opt gear
2
opt velocity
1
Supervisor system
throttle 0/1
brake 0/1
pindex
branchBit
speed
pireach
reset
Mas_allowed
flag_ini
flag_g
Set speed
vini
Map?matching
Lookup table
pIndx
speed
reset
vini
cgear
crpm
yv
yg
ytorque
yu
[crpm]
[cgear]
[speed]
[pindex]
[branchBit]
[cgear]
[speed]
[speed]
reset
reset
pireach
[pindex]
[crpm]
[cgear]
[speed]
[pindex]
[branchBit]
Element 100 
100
Element  100
100
Direct Lookup
Table (n?D)2
 1?D T[k]
T
 1?D T[k]
T
CAN and EH data processing 
p100
ShIndx
dE
dN
dZ
branch
branchBit
pIndx
speed
vini
cgear
Mas_allowed
3
J1939_Inputs
2
Electronic_Horizon
1
<ehorizon_point_shIndex_array>
<ehorizon_point_dE_array>
<ehorizon_point_dN_array>
<ehorizon_point_dZ_array>
<accel_pedal_position>
<vehicle_speed>
<brake_switch>
<selected_gear>
<engine_speed>
<ehorizon_point_Branch_array>
<relative_mapmatching_shpIndex>
Figure B.4: Optimal control system scheme
From EH, the road geometry ahead of the vehicle?s current location - called the ?horizon?
- is sent as an array of Shape Point (SP) messages. The key EH data acquired by ?CAN and
EH data processing? block are listed in the following:
? shpIndex array: Index array for all shape points in the prediction horizon;
115
? p100: The 100th point in shpIndenx array. The actual prediction horizon is starting
from this point to the end point.
? dE, dN and dZ array: Distance array between every two shape points in east and
north direction and elevation difference array between every two shape points;
? relative map-matching shpIndex (pindex): Index for the current vehicle position which
can be matching to the shpIndex array;
? branchBit: Flag for the branch road.
Normally, the distance between every two shape points is around 3.5 m, and therefore there
are around 900 shape points in a prediction horizon. The EH update is depicted in Figure
B.5.
Predictionhorizon,900points:
ShapePointMessageforall
pointsweresent
3000m
Truckcurrentposition:
PositionMessageis
sentforthisposition
Ehorizondataupdate
Figure B.5: Electronic Horizon system information update
A simplified OC system flow chart and how S1 and S2 interface to each other in parallel
are depicted in Figure B.6. The supervisor system is implemented in Stateflow and consists
of two main state variables, ?flag ini? and ?flag b? which represent the operation conditions of
the OC system and the NLP optimizer, respectively. For example, if ?MAS allowed? is larger
than zero, then the OC is set on and ?CAN and EH processing? block is enabled. This data
processing block is written by embedded Matlab files with different M functions. Function
?checkEH.m? checks if there are sufficient nonzero points in the ?EH shpIndex array?. If true,
116
Supervisor system
(Stateflow)
flag_ini=0:
OCoff
flag_ini=3
flag_ini=1
flag_ini=2
MAS_allowed
=0=1
reset=0 pireach=1
flag_b=1
flag_ini>0
CAN&EH
processing
Lookup
table
checkEH.m
tempEH.m
find_pi.m:read
map-matching
optimalsolution
fromOPTbuffer
reset=0
pireach=1
OPTbuffer
ReadEH.m:calculate
roadgrade,initialize
optimalstates,and
savetoOPTbuffer
Opt_main_EH.m:
read initialdata,
calculateoptimal
solution &save
back to OPTbuffer
NLP
optimizer
optimal
velocity
gear&
torque
Software
module1 (S1)
Software
module2 (S2)
overridesignals:
commandECUto
acceptoptimal
solutions
EHdata
J1939 data
Figure B.6: Optimal control system flow chart
it sends a flag, ?reset=0?. If ?reset=0?, function ?tempEH.m? is operated to detect if the point
p100 has reached a prediction position point. If true, ?pireach=1? is set. Subsequently, in
function ?readEH.m?, road grade/distance array is calculated based on EH data and optimal
solution is initialized for the prediction horizon which together with the ?EH shpIndex array?
are all put into a buffer, called ?OPTbuffer?.
At the same time, ?reset=0? and ?pireach=1? are sent back to the supervisor system and
subsequently it sets ?flag ini=2? and ?flag b=1?, which trigger the NLP solver in S2 to function
117
in parallel with S1 by: acquire the road grade and initial data array from ?OPTbuffer?;
calculate the optimal velocity, torque, and gear shifting; and save the optimal solution array
back to the ?OPTbuffer? with the position in accordance with ?EH shpIndex array?.
Finally, if ?flag ini? is larger than zero, a function ?find pi.m? in ?Lookup table? block is
trigged to read the map-matched optimal states and control from ?OPTbuffer? and output
to an upper level block. Additionally, the entry ?flag ini? from the supervisor system is
outputted as the engine torque override command. In the following sections, each block in
S1 and S2 is given in detail.
B.1.2 Supervisor system
Supervisor system is implemented in Sateflow to handle different the OC operation
conditions, e.g., start, stop, traffic in/out, fork road, by sending different ?flags?, as shown in
Figures B.7 and B.8.
Four states, i.e., OC, NLP, Gear, t fork, can be identified in Figure B.8, which represent
the operation conditions of the OC system, the NLP solver, gear shifting and fork road
detection as follows:
? OC state:
1. OC off, flag ini=0: the OC system is set off;
2. OC ini, flag ini=1: the OC system is initialized; While shpIndex array has zero
elements in next 900 points, or previous 150 pindex are all equal, the OC functions
as a cruise control system, which outputs a constant set speed;
3. OC read, flag ini=2: a predicted shpIndex point is reached, and the NLP solver
is triggered/run in S2;
4. OC on, flag ini=3: the OC system is on normal running, and waits for another
NLP trigger, flag ini=2, for the next prediction horizon;
118
Indicate where OPT
 gear engaged
flag_g
2
flag_ini
1
Memory1
Memory
Integer Delay
 ?150
Z   
Indicate fork road before
buffer reset
tf
flag_ini
flag_b
ps
startg
flag_ini
dist
Flow Chart for supervisor system
flag_ini1
flag_inip
pindex
pindexp
ps
distance
folk_d
pireach
reset
mas_allowed
startg
flag_b
flag_ini
flag_g
tfMas_allowed5
reset
4
pireach
3
branchBit
2
pindex
1
Figure B.7: Supervisor system scheme
5. State flow of OC: OC off ?? (if MAS allowed==1) ?? OC ini ?? OC read
??OC on??(if MAS allowed==0)??OPT off.
? NLP state:
1. NLP off, flag b=0: the NLP solver is set off;
2. NLP on, flag b=1: the NLP solver is triggered (by flag ini==2) for a fuel mini-
mization calculation. It is applied at most situations;
3. NLP on2, flag b=2: the NLP solver is triggered (by flag ini==2) for a constant
speed tracking calculation. It is applied after the OPT system is first initialized,
flag ini=1 ?? flag ini=2; or the road grade in the prediction horizon is highly
nonlinear, e.g., large grade/grade change;
4. State flow of NLP: NLP off??NLP on or NLP on2??NLP off.
119
OC 1
OC_read
entry:flag _ini =2;
OC_ini
entry:flag _ini =1;
OC_off
entry:flag _ini =0;
OC_on
entry :flag _ini =3;
NLP 2NLP_on
entry: flag _b=1;
NLP_off
entry:flag _b=0;
NLP_on2
entry: flag _b=2;
Gear 3Gear _opt
entry :flag _g=1;
Gear_auto
entry:flag _g=0;
t_fork 4t_fork_1
entry:tf=1;
t_fork_0
entry: tf=0;
[distance ==0]
1
[mas_allowed ==0]
2
[distance >=500  & pireach ==1& reset==0 ]
1
[pindex ==pindexp ]
3
[distance >=3000   & (pindex ~=pindexp )]
2
[mas_allowed ==0]
1
[reset==1|| (pindex ==pindexp )]
3
[ mas_allowed ==1 ]
[mas_allowed ==0]
2
[flag _ini ==3 || flag _ini ==1|| flag _ini ==0]
[ flag _ini ==3 & flag _inip ==2 & pindex >ps]1
[ flag _ini ==3 & flag _inip ==2 & pindex <ps]
2
[flag _ini ==3 || flag _ini ==1 || flag _ini ==0]
[flag _ini ==0 || reset==1|| (pindex ==pindexp )]
[pindex >=(startg?5) & flag _ini >1 ] [flag _ini ==3]
[flag _ini ==0 & fork_d==1 ]
Figure B.8: Supervisor system Stateflow chart
? Gear state:
1. Gear auto, flag g=0: command the system to run automatic gear shifting. It is
applied when the OC system is turned on and truck is passing the first 500 m
after the OC is initialized; or when shpIndex array has zero elements in next 900
points, or previous 150 pindex are all equal;
2. Gear opt, flag g=1: command the system to run optimal gear shifting. It is
applied when the OC system is on and truck has passed 500 m after the OC is
initialized
3. State flow of gear state: Gear auto??Gear opt.
? t fork state:
120
1. t fork 0, tf=0: command the OC to function as normal since there is no fork road
indicated in the prediction horizon;
2. t fork 1, tf=1: command the OC to restart and re-initialize since there is a fork
road in the prediction horizon. For example in Figure B.9, if there is a folk road
starting from point F, the NLP optimizer calculates the optimal solution for FG,
while truck heads on FH. EH can detect this folk road and send a flag ?fork d=1?,
which changes the state to t fork 1;
3. State flow of t fork state: t fork 0??t fork 1.
O A BC DE F
G
H
Lw
L
Figure B.9: Fork road condition
B.1.3 CAN and EH data processing
This block is designed to calculate distance and road grade for a prediction horizon,
initialize the optimal solution, and save them to ?OPTbuffer?. It is mainly written by an
embedded Matlab file block which includes M functions as follows:
? checkEH.m: check if there are 900 nonzero points in the EH shpindex array. If true,
send a flag, ?reset=0?;
? out flago.m: detect if the previous NLP calculation finishes in a 500 m interval. If
true, send a flag, ?flag o=0?, otherwise, ?flag o>0? ;
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? tempEH.m: if ?reset=0?, detect if the 100th point in index array has reached a predic-
tion point. If true, save current 900 points EH data into a temporary buffer ?EHbuffer?,
and send a flag, ?pireach=1?;
? processEH.m: if ?pireach==1?, read EHbuffer, from which select 3 km data, and save
to a new buffer, ?EHbuffer900?; Find indices corresponding to position 0.5 k/1 k/1.5
k/2 km, and save to a vector, ?startpic?, to trigger next iteration;
? readEH.m: read buffer ?EHbuffer900?, calculate road grade, and distance and initialize
optimal solution for each iteration. Save all data into a new buffer, ?OPTbuffer?;
? process flagb.m: detect which kind of optimal calculation is required such as for fuel
minimization, or speed tracking.
B.1.4 Map-matching lookup table
This block is designed to read map-matched optimal states and control inputs corre-
sponding to the current shpIndex, ?pindex? from ?OPTbuffer?, and send them to the block
in the upper system level. It is mainly written by an embedded Matlab file block which
includes M functions as follows:
? find pi.m: find and output optimal velocity, engine, brake torque, and gear shifting
from ?OPTbuffer?, corresponding to the current shpIndex;
? find g.m: detect if the commanded gear shifting can run the engine over or under
speed. If true, change the commanded gear to the nearest available one.
B.2 Software module 2
At the final step, the system scheme of the NLP solver in S2 is illuminated in Figure
B.10, where the M file embedded block, ?r flagb? reads the variables ?flag ini? and ?flag b?
saved from the ?Supervisor system? block in S1, and sends them to the NLP solver block.
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NLP Optimizer
flag_ini
flag_b
Memory1
Memory
Interface S2 vs. S1
flag_bp
flag_inip
flag_ini
flag_b
r_flagb
Figure B.10: Nonlinear programming solver system scheme in S2
The NLP solver is generated by a M file s-function ?opt main EHr.m?, which runs when-
ever ?flag b? is larger than zero, to acquire the road grade and initial data array from ?OPT-
buffer?; calculate the optimal velocity, torque, and gear shifting; and save the map-matched
optimal solution array back to ?OPTbuffer?. While working, it calls M files as follows:
? opt con gear uvgs.m: call optimization function and return the optimal solution;
? fmincon.m: nonlinear constrained optimizer calling from optimization toolbox;
? obj truck gear uvgs.m: the objective function;
? con truck gear ugvs.m: constraint functions;
? hessinterior.m: calculate and provide Hessian to the NLP solver.
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