Research Papers

Torque Distribution Strategies for Energy-Efficient Electric Vehicles With Multiple Drivetrains

[+] Author and Article Information
B. Lenzo

Centre for Automotive Engineering,
Department of Mechanical Engineering Sciences,
Faculty of Engineering and
Physical Sciences (FEPS),
University of Surrey,
Guildford GU2 7XH, UK;
Department of Engineering and Mathematics,
Sheffield Hallam University,
Sheffield S1 1WB, UK

G. De Filippis, P. Gruber, S. Fallah

Centre for Automotive Engineering,
Department of Mechanical Engineering Sciences,
Faculty of Engineering and
Physical Sciences (FEPS),
University of Surrey,
Guildford GU2 7XH, UK

A. M. Dizqah

Centre for Mobility and Transport,
Coventry University,
Coventry CV1 5FB, UK;
Centre for Automotive Engineering,
Department of Mechanical Engineering Sciences,
Faculty of Engineering and
Physical Sciences (FEPS),
University of Surrey,
Guildford GU2 7XH, UK

A. Sorniotti

Centre for Automotive Engineering,
Department of Mechanical Engineering Sciences,
Faculty of Engineering and
Physical Sciences (FEPS),
University of Surrey,
Guildford GU2 7XH, UK
e-mail: a.sorniotti@surrey.ac.uk

W. De Nijs

Flanders MAKE,
Lommel 3920, Belgium

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received August 16, 2016; final manuscript received April 21, 2017; published online August 9, 2017. Assoc. Editor: Beshah Ayalew.

J. Dyn. Sys., Meas., Control 139(12), 121004 (Aug 09, 2017) (13 pages) Paper No: DS-16-1402; doi: 10.1115/1.4037003 History: Received August 16, 2016; Revised April 21, 2017

The paper discusses novel computationally efficient torque distribution strategies for electric vehicles with individually controlled drivetrains, aimed at minimizing the overall power losses while providing the required level of wheel torque and yaw moment. Analytical solutions of the torque control allocation problem are derived and effects of load transfers due to driving/braking and cornering are studied and discussed in detail. Influences of different drivetrain characteristics on the front and rear axles are described. The results of an analytically derived algorithm are contrasted with those from two other control allocation strategies, based on the offline numerical solution of more detailed formulations of the control allocation problem (i.e., a multiparametric nonlinear programming (mp-NLP) problem). The control allocation algorithms are experimentally validated with an electric vehicle with four identical drivetrains along multiple driving cycles and in steady-state cornering. The experiments show that the computationally efficient algorithms represent a very good compromise between low energy consumption and controller complexity.

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De Novellis, L. , Sorniotti, A. , Gruber, P. , Orus, J. , Rodriguez Fortun, J. M. , Theunissen, J. , and De Smet, J. , 2015, “ Direct Yaw Moment Control Actuated Through Electric Drivetrains and Friction Brakes: Theoretical Design and Experimental Assessment,” Mechatronics, 26, pp. 1–15. [CrossRef]
De Novellis, L. , Sorniotti, A. , and Gruber, P. , 2014, “ Wheel Torque Distribution Criteria for Electric Vehicles With Torque-Vectoring Differentials,” IEEE Trans. Veh. Technol., 63(4), pp. 1593–1602. [CrossRef]
Lu, Q. , Gentile, P. , Tota, A. , Sorniotti, A. , Gruber, P. , Costamagna, F. , and De Smet, J. , 2016, “ Enhancing Vehicle Cornering Limit Through Sideslip and Yaw Rate Control,” Mech. Syst. Signal Process., 75, pp. 455–472. [CrossRef]
Goggia, T. , Sorniotti, A. , De Novellis, L. , Ferrara, A. , Gruber, P. , Theunissen, J. , Steenbeke, D. , Knauder, B. , and Zehetner, J. , 2015, “ Integral Sliding Mode for the Torque-Vectoring Control of Fully Electric Vehicles: Theoretical Design and Experimental Assessment,” IEEE Trans. Veh. Technol., 64(5), pp. 1701–1715. [CrossRef]
De Novellis, L. , Sorniotti, A. , and Gruber, P. , 2013, “ Optimal Wheel Torque Distribution for a Four-Wheel-Drive Fully Electric Vehicle,” SAE Int. J. Passenger Cars-Mech. Syst., 6(1), pp. 128–136. [CrossRef]
Chen, Y. , and Wang, J. , 2014, “ Adaptive Energy-Efficient Control Allocation for Planar Motion Control of Over-Actuated Electric Ground Vehicles,” IEEE Trans. Control Syst. Technol., 22(4), pp. 1362–1373. [CrossRef]
Suzuki, Y. , Kano, Y. , and Abe, M. , 2014, “ A Study on Tyre Force Distribution Controls for Full Drive-by-Wire Electric Vehicle,” Veh. Syst. Dy., 52(Suppl. 1), pp. 235–250. [CrossRef]
Li, B. , Goodarzi, A. , Khajepour, A. , Chen, S. K. , and Litkouhi, B. , 2015, “ An Optimal Torque Distribution Control Strategy for Four-Independent Wheel Drive Electric Vehicles,” Veh. Syst. Dyn., 53(8), pp. 1172–1189. [CrossRef]
de Castro, R. , Tanelli, M. , Esteves Araújo, R. , and Savaresi, S. M. , 2014, “ Design of Safety-Oriented Control Allocation Strategies for Overactuated Electric Vehicles,” Veh. Syst. Dyn., 52(8), pp. 1017–1046. [CrossRef]
Wong, A. , Kasinathan, D. , Khajepour, A. , Chen, S. K. , and Litkouhi, B. , 2016, “ Integrated Torque Vectoring and Power Management Framework for Electric Vehicles,” Control Eng. Pract., 48, pp. 22–36. [CrossRef]
Johansen, T. A. , and Fossen, T. I. , 2013, “ Control Allocation: A Survey,” Automatica, 49(5), pp. 1087–1103. [CrossRef]
Härkegård, O. , and Glad, S. T. , 2005, “ Resolving Actuator Redundancy—Optimal Control vs. Control Allocation,” Automatica, 41(1), pp. 137–144.
Bodson, M. , 2002, “ Evaluation of Optimization Methods for Control Allocation,” J. Guid., Control, Dyn., 25(4), pp. 703–711. [CrossRef]
Kang, J. , and Heo, H. , 2012, “ Control Allocation Based Optimal Torque Vectoring for 4WD Electric Vehicle,” SAE Technical Paper No. 2012-01-0246.
Xiong, L. , and Yu, Z. , 2009, “ Control Allocation of Vehicle Dynamics Control for a 4 In-Wheel-Motored EV,” IEEE Power Electronics and Intelligent Transportation System Conference (PEITS), Shenzhen, China, Dec. 19–20, Vol. 2, pp. 307–311.
Pennycott, A. , De Novellis, L. , Sabbatini, A. , Gruber, P. , and Sorniotti, A. , 2014, “ Reducing the Motor Power Losses of a Four-Wheel Drive, Fully Electric Vehicle Via Wheel Torque Allocation,” Proc. Inst. Mech. Eng., Part D, 228(7), pp. 830–839. [CrossRef]
Yuan, X. , and Wang, J. , 2012, “ Torque Distribution Strategy for a Front- and Rear-Wheel-Driven Electric Vehicle,” IEEE Trans. Veh. Technol., 61(8), pp. 3365–3374. [CrossRef]
Chen, Y. , and Wang, J. , 2012, “ Fast and Global Optimal Energy-Efficient Control Allocation With Applications to Over-Actuated Electric Ground Vehicles,” IEEE Trans. Control Syst. Technol., 20(5), pp. 1202–1211. [CrossRef]
Chen, Y. , and Wang, J. , 2014, “ Design and Experimental Evaluations on Energy Efficient Control Allocation Methods for Overactuated Electric Vehicles: Longitudinal Motion Case,” IEEE/ASME Trans. Mechatronics, 19(2), pp. 538–548. [CrossRef]
Tøndel, P. , and Johansen, T. A. , 2005, “ Control Allocation for Yaw Stabilization in Automotive Vehicles Using Multiparametric Nonlinear Programming,” American Control Conference (ACC), Portland, OR, June 8–10, pp. 453–458.
Xydas, E. , Marmaras, C. , Cipcigan, L. M. , Jenkins, N. , Carroll, S. , and Barker, M. , 2016, “ A Data-Driven Approach for Characterising the Charging Demand of Electric Vehicles: A UK Case Study,” Appl. Energy, 162, pp. 763–771. [CrossRef]
Dimitrova, Z. , and Maréchal, F. , 2016, “ Techno–Economic Design of Hybrid Electric Vehicles and Possibilities of the Multi-Objective Optimization Structure,” Appl. Energy, 161, pp. 746–759. [CrossRef]
Shabbir, W. , and Evangelou, S. A. , 2014, “ Real-Time Control Strategy to Maximize Hybrid Electric Vehicle Powertrain Efficiency,” Appl. Energy, 135, pp. 512–522. [CrossRef]
Hou, C. , Ouyang, M. , Xu, L. , and Wang, H. , 2014, “ Approximate Pontryagin's Minimum Principle Applied to the Energy Management of Plug-In Hybrid Electric Vehicles,” Appl. Energy, 115, pp. 174–189. [CrossRef]
Torres, J. L. , Gonzalez, R. , Gimenez, A. , and Lopez, J. , 2014, “ Energy Management Strategy for Plug-In Hybrid Electric Vehicles: A Comparative Study,” Appl. Energy, 113, pp. 816–824. [CrossRef]
Wang, R. , Chen, Y. , Feng, D. , Huang, X. , and Wang, J. , 2011, “ Development and Performance Characterization of an Electric Ground Vehicle With Independently Actuated In-Wheel Motors,” J. Power Sources, 196(8), pp. 3962–3971. [CrossRef]
Kohler, S. , Viehl, A. , Bringmann, O. , and Rosenstiel, W. , 2014, “ Energy-Efficient Torque Distribution for Axle-Individually Propelled Electric Vehicles,” IEEE Intelligent Vehicles Symposium (IVS), Dearborn, MI, June 8–11, pp. 1109–1114.
Dizqah, A. M. , Lenzo, B. , Sorniotti, A. , Gruber, P. , Fallah, S. , and De Smet, J. , 2016, “ A Fast and Parametric Torque Distribution Strategy for Four-Wheel-Drive Energy-Efficient Electric Vehicles,” IEEE Trans. Ind. Electron., 63(7), pp. 4367–4376. [CrossRef]
Tang, Y. , 2013, “ Method of Operating a Dual Motor Drive and Control System for an Electric Vehicle,” Tesla Motors, Inc., Palo Alto, CA, U.S. Patent No. US20130241445 A1. http://www.google.com/patents/US20130241445
iCOMPOSE, 2013, “ Integrated Control of Multiple-Motor and Multiple-Storage Fully Electric Vehicles,” accessed July 7, 2016, http://www.i-compose.eu/iCompose/
Genta, G. , 1997, Motor Vehicle Dynamics: Modeling and Simulation, World Scientific, Singapore. [CrossRef]
Di Nicola, F. , Sorniotti, A. , Holdstock, T. , Viotto, F. , and Bertolotto, S. , 2012, “ Optimization of a Multiple-Speed Transmission for Downsizing the Motor of a Fully Electric Vehicle,” SAE Int. J. Altern. Powertrains, 1(1), pp. 134–143. [CrossRef]
Domínguez, L. F. , Narciso, D. A. , and Pistikopoulos, E. N. , 2010, “ Recent Advances in Multiparametric Nonlinear Programming,” Comput. Chem. Eng., 34(5), pp. 707–716. [CrossRef]
Grancharova, A. , and Johansen, T. A. , 2012, “ Multi-Parametric Programming,” Explicit Nonlinear Model Predictive Control—Theory and Applications, Springer, Berlin, pp. 1–37. [CrossRef]
de Boor, C. , 1978, A Practical Guide to Splines, Springer-Verlag, New York. [CrossRef]


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Fig. 1

Simplified schematic of the vehicle control system

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Fig. 2

The vehicle demonstrator setup on the rolling road facility

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Fig. 3

Experimental power loss characteristics for the left front electric drivetrain for different vehicle speeds

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Fig. 4

Vehicle schematic with some of the geometric parameters affecting the vertical load transfer caused by longitudinal and lateral acceleration

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Fig. 5

Power loss characteristics at each vehicle corner (i=1…4) at 90 km/h with ax=6 m/s2 and ay=2.5 m/s2

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Fig. 6

Power loss characteristics of the original drivetrains at the front axle (1,2) and the drivetrains scaled with β=0.5 at the rear axle (3,4) at 90 km/h

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Fig. 7

Overlap of the experimentally measured power loss characteristic of the left front drivetrain at 90 km/h and the three investigated fitting functions

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Fig. 8

I-CA: map of {r}* as a function of vehicle speed and demanded drivetrain output torque on the vehicle side; the white star represents the point experimentally investigated in steady-state conditions in Sec. 6

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Fig. 9

E-CA at 90 km/h with ax=6 m/s2 and ay=2.5 m/s2: (a) optimal front-to-total torque ratio {r}*, (b) optimal torque shift {ε}*, and (c) optimal torque shift {εw}*

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Fig. 10

E-CA: optimal front-to-total torque ratio (in percentage, {r}*) as a function of the demanded drivetrain output torque on a vehicle side (τd,s), at 90 km/h with β=0.5

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Fig. 11

Estimated power losses on a vehicle side at 90 km/h for different torque allocation strategies: single axle (SA), even distribution (ED) and I-CA

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Fig. 12

Estimated power losses on a vehicle side at 90 km/h for different torque allocation strategies: I-CA, E-CA, and H-CA

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Fig. 13

Speed profile of the Surrey Designed Driving Cycle (SDDC)

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Fig. 14

Experimental points of the SDDC and switching torques for E-CA and H-CA



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