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Vehicle Propulsion Systems Introduction to Modeling and Optimization Second Edition Lino Guzzella and Antonio Sciarretta

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Vehicle Propulsion Systems Introduction to Modeling and Optimization Second Edition Lino Guzzella and Antonio Sciarretta

Preface

Who should read this text?
This text is intended for persons interested in the analysis and optimization of
vehicle propulsion systems. Its focus lies on the control-oriented mathematical
description of the physical processes and on the model-based optimization of
the system structure and of the supervisory control algorithms.
This text has evolved from a lecture series held during the last years in the
mechanical engineering department at the Swiss Federal Institute of Technology
(ETH), Zurich. The presumed audience is graduate mechanical or electrical
engineering students. The prerequisites are general engineering topics
and a first course in optimal control theory. Readers with little preparation
in that area are referred to [30]. The most important results of parameter
optimization and optimal control theory are summarized in Appendix II.
Why has this text been written?
Individual mobility relies to a large extent on passenger cars. These vehicles
are responsible for a large part of the world’s consumption of primary energy
carriers, mostly fossil liquid hydrocarbons. The specific application profiles of
these vehicles, combined with the inexorably increasing demand for mobility,
have led to a situation where the reduction of fuel consumption has become
a top priority for the society and the economy.
Many approaches that permit to reduce the fuel consumption of passenger
cars have been presented so far and new ideas emerge on a regular basis. In
most – if not all – cases these new systems are more complex than the traditional
approaches. Additional electric motors, storage devices, torque converters,
etc. are added with the intention to improve the system behavior. For
such complex systems the traditional heuristic design approaches fail.
The only way to deal with such a high complexity is to employ mathematical
models of the relevant processes and to use these models in a systematic
(“model-based”) way. This text focuses on such approaches and provides an
introduction to the modeling and optimization problems typically encountered
by designers of new propulsion systems for passenger cars.
What can be learned from this text?
This book analyzes the longitudinal behavior of road vehicles only. Its main
emphasis is on the analysis and minimization of the energy consumption.
Other aspects that are discussed are drivability and performance.
The starting point for all subsequent steps is the derivation of simple yet
realistic mathematical models that describe the behavior of vehicles, prime
movers, energy converters, and energy storage systems. Typically, these models
are used in a subsequent optimization step to synthesize optimal vehicle
configurations and energy management strategies.
Examples of modeling and optimization problems are included in Appendix
I. These case studies are intended to familiarize the reader with the
methods and tools used in powertrain optimization projects.
What cannot be learned from this text?
This text does not consider the pollutant emissions of the various powertrain
systems because the relevant mechanisms of the pollutant formation are
described on much shorter time scales than those of the fuel consumption.
Moreover, the pollutant emissions of some prime movers are virtually zero or
can be brought to that level with the help of appropriate exhaust gas purification
systems. Readers interested in these aspects can find more information
in [100].
Comfort issues (noise, harshness, and vibrations) are neglected as well.
Only those aspects of the lateral and horizontal vehicle dynamics that influence
the energy consumption are briefly mentioned. All other aspects of
the horizontal and lateral vehicle dynamics, such as vehicle stability, roll-over
dynamics, etc. are not discussed.

Acknowledgments

Many people have implicitly helped us to prepare this manuscript. Specifically
our teachers, colleagues, and students have contributed to bring us to the
point where we felt ready to write this text. Several people have helped us
more explicitly in preparing this manuscript: Hansueli H¨orler, who taught us
the basic laws of engine thermodynamics, Alois Amstutz and Chris Onder who
contributed to the development of the lecture series behind this text, those
of our doctoral students whose dissertations have been used as the nucleus
of several sections (we reference their work at the appropriate places), and
Brigitte Rohrbach, who translated our manuscripts from “Italish” to English.
June 2005 Lino Guzzella and Antonio Sciarretta

Why a second edition?

The discussions about fuel economy of passenger cars have become even more
intense since the first edition of this book appeared. Concerns about the limited
resources of fossil fuels and the detrimental effects of greenhouse gases
have spurred the interest of many people in industry and academia to work
towards reduced fuel consumption of automobiles. Not surprisingly, the first
edition of this monograph sold out rather rapidly. When the publisher asked
us about a second edition, we decided to use this opportunity to revise the
text, to correct several errors, and to add new material.
The following list includes the most important changes and additions we
made:
• The section describing battery models has been expanded.
• A new section on power split devices has been added.
• A new section on pneumatic hybrid systems has been added.
• The chapter introducing supervisory control algorithm has been rewritten
and expanded.
• Two new case studies have been added.
• A new appendix that introduces the main ideas of dynamic programming
has been added.
Acknowledgements
We want to express our gratitude to the many colleagues and students who
reported to us errors and omissions in the first edition of this text. Several
people have helped us improving this monograph, in particular Christopher
Onder who actively participated in the revisions.
June 2007 Lino Guzzella and Antonio Sciarretta

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Upstream Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Energy Density of On-Board Energy Carriers . . . . . . . . . . . . . . . 10
1.5 Pathways to Better Fuel Economy . . . . . . . . . . . . . . . . . . . . . . . . . 12
2 Vehicle Energy and Fuel Consumption – Basic Concepts . . . 13
2.1 Vehicle Energy Losses and Performance Analysis . . . . . . . . . . . . 13
2.1.1 Energy Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.2 Performance and Drivability . . . . . . . . . . . . . . . . . . . . . . . . 18
2.1.3 Vehicle Operating Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2 Mechanical Energy Demand in Driving Cycles . . . . . . . . . . . . . . . 21
2.2.1 Test Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.2 Mechanical Energy Demand . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.3 Some Remarks on the Energy Consumption . . . . . . . . . . 27
2.3 Methods and Tools for the Prediction of Fuel Consumption . . . 32
2.3.1 Average Operating Point Approach . . . . . . . . . . . . . . . . . . 32
2.3.2 Quasistatic Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.3.3 Dynamic Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.3.4 Optimization Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.3.5 Software Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3 IC-Engine-Based Propulsion Systems . . . . . . . . . . . . . . . . . . . . . . 43
3.1 IC Engine Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.1.2 Normalized Engine Variables . . . . . . . . . . . . . . . . . . . . . . . . 44
3.1.3 Engine Efficiency Representation . . . . . . . . . . . . . . . . . . . . 45
3.2 Gear-Box Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2.2 Selection of Gear Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
X Contents
3.2.3 Gear-Box Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.2.4 Losses in Friction Clutches and Torque Converters . . . . . 51
3.3 Fuel Consumption of IC Engine Powertrains . . . . . . . . . . . . . . . . 54
3.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.3.2 Average Operating Point Method. . . . . . . . . . . . . . . . . . . . 54
3.3.3 Quasistatic Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4 Electric and Hybrid-Electric Propulsion Systems . . . . . . . . . . 59
4.1 Electric Propulsion Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.2 Hybrid-Electric Propulsion Systems . . . . . . . . . . . . . . . . . . . . . . . . 60
4.2.1 System Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.2.2 Power Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.2.3 Concepts Realized . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.2.4 Modeling of Hybrid Vehicles . . . . . . . . . . . . . . . . . . . . . . . . 69
4.3 Electric Motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.3.1 Quasistatic Modeling of Electric Motors . . . . . . . . . . . . . . 74
4.3.2 Dynamic Modeling of Electric Motors . . . . . . . . . . . . . . . . 89
4.3.3 Causality Representation of Generators . . . . . . . . . . . . . . 90
4.4 Batteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.4.1 Quasistatic Modeling of Batteries . . . . . . . . . . . . . . . . . . . 95
4.4.2 Dynamic Modeling of Batteries . . . . . . . . . . . . . . . . . . . . . 103
4.5 Supercapacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.5.1 Quasistatic Modeling of Supercapacitors . . . . . . . . . . . . . . 111
4.5.2 Dynamic Modeling of Supercapacitors . . . . . . . . . . . . . . . . 115
4.6 Electric Power Links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
4.6.1 Quasistatic Modeling of Electric Power Links . . . . . . . . . 117
4.6.2 Dynamic Modeling of Electric Power Links . . . . . . . . . . . 117
4.7 Torque Couplers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.7.1 Quasistatic Modeling of Torque Couplers . . . . . . . . . . . . . 119
4.7.2 Dynamic Modeling of Torque Couplers . . . . . . . . . . . . . . . 120
4.8 Power Split Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.8.1 Quasistatic Modeling of Power Split Devices . . . . . . . . . . 121
4.8.2 Dynamic Modeling of Power Split Devices . . . . . . . . . . . . 126
5 Non-electric Hybrid Propulsion Systems . . . . . . . . . . . . . . . . . . . 131
5.1 Short-Term Storage Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
5.2 Flywheels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
5.2.1 Quasistatic Modeling of Flywheel Accumulators . . . . . . . 137
5.2.2 Dynamic Modeling of Flywheel Accumulators . . . . . . . . . 138
5.3 Continuously Variable Transmissions . . . . . . . . . . . . . . . . . . . . . . . 140
5.3.1 Quasistatic Modeling of CVTs . . . . . . . . . . . . . . . . . . . . . . 141
5.3.2 Dynamic Modeling of CVTs . . . . . . . . . . . . . . . . . . . . . . . . 144
5.4 Hydraulic Accumulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
5.4.1 Quasistatic Modeling of Hydraulic Accumulators . . . . . . 146
5.4.2 Dynamic Modeling of Hydraulic Accumulators . . . . . . . . 152
Contents XI
5.5 Hydraulic Pumps/Motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
5.5.1 Quasistatic Modeling of Hydraulic Pumps/Motors . . . . . 154
5.5.2 Dynamic Modeling of Hydraulic Pumps/Motors . . . . . . . 156
5.6 Pneumatic Hybrid Engine Systems . . . . . . . . . . . . . . . . . . . . . . . . 157
5.6.1 Modeling of Operation Modes . . . . . . . . . . . . . . . . . . . . . . . 158
6 Fuel-Cell Propulsion Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
6.1 Fuel-Cell Electric Vehicles and Fuel-Cell Hybrid Vehicles . . . . . 165
6.1.1 Concepts Realized . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
6.2 Fuel Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
6.2.1 Quasistatic Modeling of Fuel Cells . . . . . . . . . . . . . . . . . . . 179
6.2.2 Dynamic Modeling of Fuel Cells . . . . . . . . . . . . . . . . . . . . . 193
6.3 Reformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
6.3.1 Quasistatic Modeling of Fuel Reformers . . . . . . . . . . . . . . 200
6.3.2 Dynamic Modeling of Fuel Reformers . . . . . . . . . . . . . . . . 204
7 Supervisory Control Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
7.2 Heuristic Control Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
7.3 Optimal Control Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
7.3.1 Optimal Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
7.3.2 Optimization Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
7.3.3 Real-time Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . 219
8 Appendix I – Case Studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
8.1 Case Study 1: Gear Ratio Optimization . . . . . . . . . . . . . . . . . . . . 227
8.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
8.1.2 Software Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
8.1.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
8.2 Case Study 2: Dual-Clutch System – Gear Shifting . . . . . . . . . . . 231
8.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
8.2.2 Model Description and Problem Formulation . . . . . . . . . . 231
8.2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
8.3 Case Study 3: IC Engine and Flywheel Powertrain . . . . . . . . . . . 234
8.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
8.3.2 Modeling and Experimental Validation . . . . . . . . . . . . . . . 236
8.3.3 Numerical Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
8.3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
8.4 Case Study 4: Supervisory Control for a Parallel HEV. . . . . . . . 241
8.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
8.4.2 Modeling and Experimental Validation . . . . . . . . . . . . . . . 241
8.4.3 Control Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
8.4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
8.5 Case Study 5: Optimal Rendez-Vous Maneuvers . . . . . . . . . . . . . 251
8.5.1 Modeling and Problem Formulation . . . . . . . . . . . . . . . . . . 251
XII Contents
8.5.2 Optimal Control for a Specified Final Distance . . . . . . . . 253
8.5.3 Optimal Control for an Unspecified Final Distance . . . . 257
8.6 Case Study 6: Fuel Optimal Trajectories of a Racing FCEV . . . 261
8.6.1 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
8.6.2 Optimal Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
8.6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
8.7 Case Study 7: Optimal Control of a Series Hybrid Bus . . . . . . . 270
8.7.1 Modeling and Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . 270
8.7.2 Optimal Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
8.7.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
8.8 Case Study 8: Hybrid Pneumatic Engine . . . . . . . . . . . . . . . . . . . 280
8.8.1 HPE Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
8.8.2 Driveline Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282
8.8.3 Air Tank Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
8.8.4 Optimal Control Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . 284
8.8.5 Optimal Control Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
9 Appendix II – Optimal Control Theory . . . . . . . . . . . . . . . . . . . . 289
9.1 Parameter Optimization Problems . . . . . . . . . . . . . . . . . . . . . . . . . 289
9.1.1 Problems Without Constraints . . . . . . . . . . . . . . . . . . . . . . 289
9.1.2 Numerical Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
9.1.3 Minimization with Equality Constraints . . . . . . . . . . . . . . 293
9.1.4 Minimization with Inequality Constraints . . . . . . . . . . . . . 296
9.2 Optimal Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298
9.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298
9.2.2 Optimal Control for the Basic Problem. . . . . . . . . . . . . . . 298
9.2.3 First Integral of the Hamiltonian . . . . . . . . . . . . . . . . . . . . 302
9.2.4 Optimal Control with Specified Final State . . . . . . . . . . . 304
9.2.5 Optimal Control with Unspecified Final Time . . . . . . . . . 305
9.2.6 Optimal Control with Bounded Inputs . . . . . . . . . . . . . . . 306
10 Appendix III – Dynamic Programming . . . . . . . . . . . . . . . . . . . . 311
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
10.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312
10.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312
10.2.2 Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315
10.3 Implementation Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315
10.3.1 Grid Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316
10.3.2 Nearest Neighbor or Interpolation . . . . . . . . . . . . . . . . . . . 316
10.3.3 Scalar or Set Implementation . . . . . . . . . . . . . . . . . . . . . . . 318
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323