Abstract

Widely published research shows that significant fuel economy improvements through optimal control of a vehicle powertrain are possible if the future vehicle velocity is known and real-time optimization calculations can be performed. In this research, however, we seek to advance the field of optimal powertrain control by limiting future vehicle operation knowledge and using no real-time optimization calculations. We have realized optimal control of acceleration events (AEs) in real-time by studying optimal control trends across 384 real world drive cycles and deriving an optimal control strategy for specific acceleration event categories using dynamic programming (DP). This optimal control strategy is then applied to all other acceleration events in its category, as well as separate standard and custom drive cycles using a look-up table. Fuel economy improvements of 2% average for acceleration events and 3.9% for an independent drive cycle were observed when compared to our rigorously validated 2010 Toyota Prius model. Our conclusion is that optimal control can be implemented in real-time using standard vehicle controllers assuming extremely limited information about future vehicle operation is known such as an approximate starting and ending velocity for an acceleration event.

References

1.
International Energy Agency
,
2017
, “
Key World Energy Statistics
,” International Energy Agency, Vienna, Austria, Report.
2.
van Moerkerk
,
M.
, and
Crijns-Graus
,
W.
,
2016
, “
A Comparison of Oil Supply Risks in EU, US, japan, china and India Under Different Climate Scenarios
,”
Energy Policy
,
88
, pp.
148
158
.10.1016/j.enpol.2015.10.015
3.
International Energy Agency
,
2016
, “
World Energy Outlook Special Report: Energy and Air Pollution
,” International Energy Agency, Vienna, Austria, Report.
4.
World Health Organization
,
2016
, “
World Health Statistics 2016: Monitoring Health for the Sustainable Development Goals (SDGs)
,” World Health Organization, Geneva, Switzerland, Report.
5.
National Research Council, Division on Earth and Life Studies, Board on Atmospheric Sciences and Climate, and America's Climate Choices: Panel on Advancing the Science of Climate Change
,
2011
,
Advancing the Science of Climate Change
,
National Academies Press
,
Washington, DC
.
6.
International Energy Agency
,
2016
, “
CO2 Emissions from Fuel Combustion
,” International Energy Agency, Vienna, Austria, Report.
7.
International Energy Agency
,
2017
, “
CO2 Emissions from Fuel Combustion 2017
,” International Energy Agency, Vienna, Austria, Report.
8.
Atabani
,
A. E.
,
Badruddin
,
I. A.
,
Mekhilef
,
S.
, and
Silitonga
,
A. S.
,
2011
, “
A Review on Global Fuel Economy Standards, Labels and Technologies in the Transportation Sector
,”
Renewable Sustainable Energy Rev.
,
15
(
9
), pp.
4586
4610
.10.1016/j.rser.2011.07.092
9.
Global Fuel Economy Initiative,
2009
, “
50 by 50 Global Fuel Economy Initiative
,” Global Fuel Economy Initiative, London,
Report
.https://www.globalfueleconomy.org/data-and-research/publications/50by50-global-fuel-economy-initiative
10.
Global Fuel Economy Initiative
,
2017
, “
Global Fuel Economy: An Update For COP22
,” Global Fuel Economy Initiative, London,
Report
.https://www.globalfueleconomy.org/media/412594/gfei-cop22-update-lr-spreads.pdf
11.
Ewing
,
J.
,
2017
, “
France Plans to End Sales of Gas and Diesel Cars by 2040
,” The New York Times, New York, accessed Mar. 9, 2020, https://www.nytimes.com/2017/07/06/business/energy-environment/france-cars-ban-gas-diesel.html
12.
Sengupta
,
S.
,
2017
, “
Both Climate Leader and Oil Giant? A Norwegian Paradox
,” The New York Times, New York, accessed Mar. 9, 2020, https://www.nytimes.com/2017/06/17/world/europe/norway-climate-oil.html
13.
Castle
,
S.
,
2017
, “
Britain to Ban New Diesel and Gas Cars by 2040
,” The New York Times, New York, accessed Mar. 9, 2020, https://www.nytimes.com/2017/07/26/world/europe/uk-diesel-petrol-emissions.html
14.
Bradsher
,
K.
,
2017
, “
China Hastens the World Toward an Electric-Car Future
,” The New York Times, New York, accessed Mar. 9, 2020, https://www.nytimes.com/2017/10/09/business/china-hastens-the-world-toward-an-electric-car-future.html
15.
Anand
,
G.
,
2017
, “
India, Once a Coal Goliath, is Fast Turning Green
,” The New York Times, New York, accessed Mar. 9, 2020, https://www.nytimes.com/2017/06/02/world/asia/india-coal-green-energy-climate.html
16.
Jacobs Juncture
,
M.
,
2016
, “
High Pressure for Low Emissions: How Civil Society Created the Paris Climate Agreement
,” Wiley Online Library, Hoboken, NJ.
17.
Christoff
,
P.
,
2016
, “
The Promissory Note: COP 21 and the Paris Climate Agreement
,”
Environ. Polit.
,
25
(
5
), pp.
765
787
.10.1080/09644016.2016.1191818
18.
International Energy Agency
,
2015
, “
Energy and Climate Change—World Energy Outlook Special Report
,” International Energy Agency, Vienna, Austria, Report.
19.
United Nations Framework Convention on Climate Change
,
2015
, “
Paris Declaration on Electro-Mobility and Climate Change and Call to Action
,” United Nations Framework Convention on Climate Change, Bonn, Germany,
epub
.https://unfccc.int/news/the-paris-declaration-on-electro-mobility-and-climate-change-and-call-to-action
20.
Global Fuel Economy Initiative
,
2016
, “
Global Fuel Economy: An Update for COP22
,” Global Fuel Economy Initiative, London, Report.
21.
Global Fuel Economy Initiative
,
2017
, “
GFEI Action for More Fuel Efficient Vehicles: COP23 Update (Global Fuel Economy—An Update For Cop23)
,” Global Fuel Economy Initiative, London, Report.
22.
Global Fuel Economy Initiative,
2011
, “
50 by 50 Prospects and Progress
,” Global Fuel Economy Initiative, London, Report.
23.
Office of Transportation, Air Quality U.S. Environmental Protection Agency National Highway Traffic Safety Administration U.S. Department of Transportation, and the California Air Resources Board
,
2016
, Draft Technical Assessment Report: Midterm Evaluation of Light-Duty Vehicle Greenhouse Gas Emission Standards and Corporate Average Fuel Economy Standards for Model Years 2022–2025,” Report No. EPA-420-D-16-900.
24.
Lin
,
C.-C.
,
Peng
,
H.
,
Grizzle
,
J. W.
,
Liu
,
J.
, and
Busdiecker
,
M.
,
2003
, “
Control System Development for an Advanced-Technology Medium-Duty Hybrid Electric Truck
,”
SAE
Paper No. 2003-01-3369.10.4271/2003-01-3369
25.
Lin
,
C.-C.
,
Kang
,
J.-M.
,
Grizzle
,
J. W.
, and
Peng
,
H.
,
2001
, “
Energy Management Strategy for a Parallel Hybrid Electric Truck
,”
Proceedings of the American Control Conference (Cat. No.01CH37148)
, Vol.
4
, Arlington, VA, June 25–27, pp.
2878
2883.
26.
Lin
,
C.-C.
,
Kim
,
M.-J.
,
Peng
,
H.
, and
Grizzle
,
J. W.
,
2006
, “
System-Level Model and Stochastic Optimal Control for a PEM Fuel Cell Hybrid Vehicle
,”
ASME J. Dyn. Syst. Meas. Control
,
128
(
4
), pp.
878
890
.10.1115/1.2362785
27.
Kolmanovsky
,
I. V.
,
Lezhnev
,
L.
, and
Maizenberg
,
T. L.
,
2008
, “
Discrete-Time Drift Counteraction Stochastic Optimal Control: Theory and Application-Motivated Examples
,”
Automatica.
,
44
(
1
), pp.
177
184
.10.1016/j.automatica.2007.06.002
28.
Opila
,
D. F.
,
Wang
,
X.
,
McGee
,
R.
, and
Grizzle
,
J. W.
,
2013
, “
Real-Time Implementation and Hardware Testing of a Hybrid Vehicle Energy Management Controller Based on Stochastic Dynamic Programming
,”
ASME J. Dyn. Syst. Meas. Control
,
135
(
2
), p.
021002
.10.1115/1.4007238
29.
Vagg
,
C.
,
Akehurst
,
S.
,
Brace
,
C. J.
, and
Ash
,
L.
,
2016
, “
Stochastic Dynamic Programming in the Real-World Control of Hybrid Electric Vehicles
,”
IEEE Trans. Control Syst. Technol.
,
24
(
3
), pp.
853
866
.10.1109/TCST.2015.2498141
30.
Musardo
,
C.
,
Rizzoni
,
G.
,
Guezennec
,
Y.
, and
Staccia
,
B.
,
2005
, “
A-ECMS: An Adaptive Algorithm for Hybrid Electric Vehicle Energy Management
,”
Eur. J. Control
,
11
(
4–5
), pp.
509
524
.10.3166/ejc.11.509-524
31.
Yang
,
C.
,
Du
,
S.
,
Li
,
L.
,
You
,
S.
,
Yang
,
Y.
, and
Zhao
,
Y.
,
2017
, “
Adaptive Real-Time Optimal Energy Management Strategy Based on Equivalent Factors Optimization for Plug-in Hybrid Electric Vehicle
,”
Appl. Energy
,
203
(
Suppl. C
), pp.
883
896
.10.1016/j.apenergy.2017.06.106
32.
Borhan
,
H.
, and
Vahidi
,
A.
,
2012
, “
Model Predictive Control of a Hybrid Electric Powertrain With Combined Battery and Ultracapacitor Energy Storage System
,”
Int. J. Powertrains
,
1
(
4
), p.
351
.10.1504/IJPT.2012.049645
33.
HomChaudhuri
,
B.
,
Vahidi
,
A.
, and
Pisu
,
P.
,
2017
, “
Fast Model Predictive Control-Based Fuel Efficient Control Strategy for a Group of Connected Vehicles in Urban Road Conditions
,”
IEEE Trans. Control Syst. Technol.
,
25
(
2
), pp.
760
767
.10.1109/TCST.2016.2572603
34.
Bianchi
,
D.
,
Rolando
,
L.
,
Serrao
,
L.
,
Onori
,
S.
,
Rizzoni
,
G.
,
Al-Khayat
,
N.
,
Hsieh
,
T.-M.
, and
Kang
,
P.
,
2010
, “
A Rule-Based Strategy for a Series/Parallel Hybrid Electric Vehicle: An Approach Based on Dynamic Programming
,”
ASME
Paper No. DSCC2010-4233.10.1115/DSCC2010-4233
35.
Onori
,
S.
,
Serrao
,
L.
, and
Rizzoni
,
G.
,
2016
, “
Equivalent Consumption Minimization Strategy
,”
Hybrid Electric Vehicles
(Springer Briefs in Electrical and Computer Engineering),
Springer
,
London
, pp.
65
77
.
36.
Paganelli
,
G.
,
Guezennec
,
Y.
, and
Rizzoni
,
G.
,
2002
, “
Optimizing Control Strategy for Hybrid Fuel Cell Vehicle
,”
SAE
Paper No. 2002-01-0102.10.4271/2002-01-0102
37.
Asher
,
Z. D.
,
Patil
,
A. A.
,
Wifvat
,
V. T.
,
Frank
,
A. A.
,
Samuelsen
,
S.
, and
Bradley
,
T. H.
,
2019
, “
Identification and Review of the Research Gaps Preventing a Realization of Optimal Energy Management Strategies in Vehicles
,”
SAE Int. J. Alt. Power.
,
8
(
2
), pp. 133–149.10.4271/08-08-02-0009
38.
Asher
,
Z. D.
,
Cummings
,
T.
, and
Bradley
,
T. H.
,
2016
, “
The Effect of Hill Planning and Route Type Identification Prediction Signal Quality on Hybrid Vehicle Fuel Economy
,”
SAE
Paper No. 2016-01-1240.10.4271/2016-01-1240
39.
Cummings
,
T.
,
Bradley
,
T. H.
, and
Asher
,
Z. D.
,
2015
, “
The Effect of Trip Preview Prediction Signal Quality on Hybrid Vehicle Fuel Economy
,”
IFAC-PapersOnLine
,
48
(
15
), pp.
271
276
.10.1016/j.ifacol.2015.10.039
40.
Asher
,
Z. D.
,
Baker
,
D. A.
, and
Bradley
,
T. H.
,
2017
, “
Prediction Error Applied to Hybrid Electric Vehicle Optimal Fuel Economy
,”
IEEE Trans. Control Syst. Technol.
,
26
(
6
), pp.
2121
2134
.10.1109/TCST.2017.2747502
41.
Asher
,
Z. D.
,
Tunnell
,
J. A.
,
Baker
,
D. A.
,
Fitzgerald
,
R. J.
,
Banaei-Kashani
,
F.
,
Pasricha
,
S.
, and
Bradley
,
T. H.
,
2018
, “
Enabling Prediction for Optimal Fuel Economy Vehicle Control
,”
SAE
Paper No. 2018-01-1015.10.4271/2018-01-1015
42.
Baker
,
D.
,
Asher
,
Z. D.
, and
Bradley
,
T.
,
2018
, “
V2V Communication Based Real-World Velocity Predictions for Improved HEV Fuel Economy
,”
SAE
Paper No. 2018-01-1000.10.4271/2018-01-1000
43.
Gaikwad
,
T. D.
,
Asher
,
Z. D.
,
Liu
,
K.
,
Huang
,
M.
, and
Kolmanovsky
,
I.
,
2019
, “
Vehicle Velocity Prediction and Energy Management Strategy: Part 2—Integration of Machine Learning Vehicle Velocity Prediction With Optimal Energy Management to Improve Fuel Economy
,”
SAE
Paper No. 2019-01-1212.10.4271/2019-01-1212
44.
Asher
,
Z.
,
Baker
,
D.
, and
Bradley
,
T. H.
,
2019
, “
Systems and Methods for Prediction Windows for Optimal Powertrain Control
,” U.S. Patent No.
USPTO 20190375421:A1
.https://patentimages.storage.googleapis.com/8d/dd/6a/054642b942ab70/US20190375421A1.pdf
45.
Akcelik
,
R.
, and
Biggs
,
D. C.
,
1987
, “
Acceleration Profile Models for Vehicles in Road Traffic
,”
Transp. Sci.
,
21
(
1
), pp.
36
54
.10.1287/trsc.21.1.36
46.
Akçelik
,
R.
, and
Besley
,
M.
,
2001
, “
Acceleration and Deceleration Models
,”
23rd Conference of Australian Institutes of Transport Research
(
CAITR 2001
), Monash University, Melbourne, Australia, Vol.
10
, Dec. 10–12, p.
12
.https://www.researchgate.net/publication/238778191_Acceleration_and_deceleration_models
47.
Wang
,
J.
,
Dixon
,
K.
,
Li
,
H.
, and
Ogle
,
J.
,
2004
, “
Normal Acceleration Behavior of Passenger Vehicles Starting From Rest at All-Way Stop-Controlled Intersections
,”
Transp. Res. Rec.: J. Transp. Res. Board
,
1883
(
1
), pp.
158
166
.10.3141/1883-18
48.
LeBlanc
,
D. J.
,
Sivak
,
M.
, and
Bogard
,
S.
,
2010
, “
Using Naturalistic Driving Data to Assess Variations in Fuel Efficiency Among Individual Drivers
,”
University of Michigan
, Ann Arbor, MI.https://deepblue.lib.umich.edu/handle/2027.42/78449
49.
Long
,
G.
,
2000
, “
Acceleration Characteristics of Starting Vehicles
,”
Transp. Res. Rec.: J. Transp. Res. Board
,
1737
(
1
), pp.
58
70
.10.3141/1737-08
50.
The U.S. Department of Energy Office of Energy Efficiency and Renewable Energy, 2018, “
2018 Best and Worst Fuel Economy Vehicles
,”
The U.S. Department of Energy Office of Energy Efficiency and Renewable Energy, Washington, DC, accessed Mar. 5, 2020, https://www.fueleconomy.gov/feg/best-worst.shtml
51.
Kim
,
N.
,
Rousseau
,
A.
, and
Rask
,
E.
,
2012
, “
Autonomie Model Validation With Test Data for 2010 Toyota Prius
,”
SAE
Paper No. 2012-01-1040.10.4271/2012-01-1040
52.
Argonne National Lab
,
2015
, “Downloadable Dynamometer Database, Apr. Title of the Publication Associated with this Dataset: Test Summary Sheet,” Argonne National Lab, Lemont, IL.
53.
Rajamani
,
R.
,
2011
,
Vehicle Dynamics and Control
,
Springer Science & Business Media
,
Berlin
.
54.
Arata
,
J. P.
, III
,
2011
, “
Simulation and Control Strategy Development of Power-Split Hybrid-Electric Vehicles
,”
Ph.D. thesis
, Georgia Institute of Technology, Atlanta, GA.https://smartech.gatech.edu/handle/1853/42790
55.
Kawamoto
,
N.
,
Naiki
,
K.
,
Kawai
,
T.
,
Shikida
,
T.
, and
Tomatsuri
,
M.
,
2009
, “
Development of New 1.8-Liter Engine for Hybrid Vehicles
,”
SAE
Paper No. 2009-01-1061.10.4271/2009-01-1061
56.
Burress, T. A., Campbell, S. L., Coomer, C., Ayers, C. W., Wereszczak, A. A., Cunningham, J. P., Marlino, L. D., Seiber, L. E., and Lin, H.-T.,
2011
, “
Evaluation of the 2010 Toyota Prius Hybrid Synergy Drive System
,” Oak Ridge National Lab, Oak Ridge, TN,
Report
.https://info.ornl.gov/sites/publications/files/Pub26762.pdf
57.
Gunst
,
R. F.
,
1996
, “
Response Surface Methodology: Process and Product Optimization Using Designed Experiments
,”
Technometrics
,
38
(
3
), pp.
284
286
.10.1080/00401706.1996.10484509
58.
Frank
,
A. A.
,
2000
, “
Control Method and Apparatus for Internal Combustion Engine Electric Hybrid Vehicles
,” U.S. Patent No.
USPTO 6054844
.https://patentimages.storage.googleapis.com/da/aa/bb/50e3f2baf53493/US6054844.pdf
59.
Yang
,
S.
,
Wang
,
W.
,
Zhang
,
F.
,
Hu
,
Y.
, and
Xi
,
J.
,
2018
, “
Driving-Style-Oriented Adaptive Equivalent Consumption Minimization Strategies for HEVs
,”
IEEE Trans. Veh. Technol.
,
67
(
10
), pp.
9249
9261
.10.1109/TVT.2018.2855146
60.
Bertsekas
,
D. P.
,
Bertsekas
,
D. P.
,
Bertsekas
,
D. P.
, and
Bertsekas
,
D. P.
,
1995
,
Dynamic Programming and Optimal Control
, Vol.
1
,
Athena Scientific
,
Belmont, MA
.
61.
Bellman
,
R.
,
1956
, “
Dynamic Programming and Lagrange Multipliers
,”
Proc. Natl. Acad. Sci. U. S. A
,
42
(
10
), pp.
767
769
.10.1073/pnas.42.10.767
62.
SAE International
,
2002
, “
Recommended Practice for Measuring the Exhaust Emissions and Fuel Economy of Hybrid-Electric Vehicles
,”
SAE
Paper No. J1711.10.4271/J1711
63.
Montazeri-Gh
,
M.
, and
Naghizadeh
,
M.
,
2003
, “
Development of Car Drive Cycle for Simulation of Emissions and Fuel Economy
,”
Proceedings of 15th European Simulation Symposium
, Delft, The Netherlands, Oct. 26–29.https://pdfs.semanticscholar.org/e712/344e6d28683bc24f90a5a7f87560a70252f5.pdf
64.
Gautam
,
M.
,
Clark
,
N.
,
Riddle
,
W.
,
Nine
,
R.
, and
Wayne
,
W. S.
, and others,
2002
, “
Development and Initial Use of a Heavy-Duty Diesel Truck Test Schedule for Emissions Characterization
,”
65.
Sandoval Leon
,
J. A.
,
2011
, “
Study of Transit Bus Duty Cycle and Its Influence on Fuel Economy and Emissions of Diesel-Electric Hybrids
,”
Ph.D. thesis
, West Virginia University, Ann Arbor, United States.https://researchrepository.wvu.edu/cgi/viewcontent.cgi?article=4055∓context=etd
66.
Fairley
,
R. E.
, and
Thayer
,
R. H.
,
1997
, “
The Concept of Operations: The Bridge From Operational Requirements to Technical Specifications
,”
Ann. Software Eng.
,
3
(
1
), pp.
417
432
.10.1023/A:1018985904689
67.
U.S. Environmental Protection Agency
,
2006
, “
Final Technical Support Document: Fuel Economy Labeling of Motor Vehicle Revisions to Improve Calculation of Fuel Economy Estimates
,” Office of Transportation and Air Quality, Report No. EPA420-R-06-017.
68.
Chen
,
L.
,
Zhu
,
F.
,
Zhang
,
M.
,
Huo
,
Y.
,
Yin
,
C.
, and
Peng
,
H.
,
2011
, “
Design and Analysis of an Electrical Variable Transmission for a Series–Parallel Hybrid Electric Vehicle
,”
IEEE Trans. Veh. Technol.
,
60
(
5
), pp.
2354
2363
.10.1109/TVT.2011.2134876
69.
Ganji
,
B.
,
Kouzani
,
A. Z.
, and
Trinh
,
H. M.
,
2010
, “
Drive Cycle Analysis of the Performance of Hybrid Electric Vehicles
,”
Life System Modeling and Intelligent Computing
,
Springer
,
Berlin, Heidelberg
, pp.
434
444
.
70.
Barnitt
,
R. A.
,
Brooker
,
A. D.
, and
Ramroth
,
L.
,
2010
, “
Model-Based Analysis of Electric Drive Options for Medium-Duty Parcel Delivery Vehicles
,” National Renewable Energy Lab (NREL), Golden, CO, Report No.
NREL/CP-5400-49253
. https://www.nrel.gov/docs/fy11osti/49253.pdf
71.
Amrhein
,
M.
, and
Krein
,
P. T.
,
2005
, “
Dynamic Simulation for Analysis of Hybrid Electric Vehicle System and Subsystem Interactions, Including Power Electronics
,”
IEEE Trans. Veh. Technol.
,
54
(
3
), pp.
825
836
.10.1109/TVT.2005.847231
72.
Aceves
,
S. M.
, and
Smith
,
J. R.
,
1996
, “
Hybrid and Conventional Hydrogen Engine Vehicles That Meet EZEV Emissions
,” Lawrence Livermore National Lab, Livermore, CA, Report No.
UCRL-JC-125891, CONF-970210-6.
https://www.osti.gov/servlets/purl/496115
73.
Geller
,
B. M.
, and
Bradley
,
T. H.
,
2015
, “
Analyzing Drive Cycles for Hybrid Electric Vehicle Simulation and Optimization
,”
ASME J. Mech. Des.
,
137
(
4
), p.
041401
.10.1115/1.4029583
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