Minimum-time optimal control for battery electric vehicles with four wheel-independent drives considering electrical overloading

References

• Hendershot JR, Miller TJE. Design of brushless permanent-magnet machines. Venice (FL): Motor Design Books LLC; 2010.
   Google Scholar
• Kampanakis A, Siampis E, Velenis E, et al. A torque vectoring optimal control strategy for combined vehicle dynamics performance enhancement and electric motor ageing minimisation. IFAC PapersOnLine. 2016;49:412–417. doi: https://doi.org/10.1016/j.ifacol.2016.08.061
   Google Scholar
• Ebbesen S. Optimal sizing and control of hybrid electric vehicles [Ph.D. dissertation]. ETH Zürich; 2012.
   Google Scholar
• Sundström O, Guzzella L, Soltic P. Optimal hybridisation in two parallel hybrid electric vehicles using dynamic programming. IFAC. 2008;41(2):4642–4647.
   Google Scholar
• Wang X, He H, Sun F, et al. Application study on the dynamic programming algorithm for energy management of plug-in hybrid electric vehicles. Energies. 2015;8:3225–3244. doi: https://doi.org/10.3390/en8043225
   Web of Science ®Google Scholar
• Elbert P, Widmer M, Gisler HJ, et al. Stochastic dynamic programming for the energy management of a serial hybrid electric bus. Int J Veh Des. 2015;69:88–112. doi: https://doi.org/10.1504/IJVD.2015.073115
   Web of Science ®Google Scholar
• Salazar M, Elbert P, Ebbesen S, et al. Time-optimal control policy for a hybrid electric race car. IEEE Trans Veh Technol. 2017;66:1921–1934. doi: https://doi.org/10.1109/TVT.2017.2729623
   Web of Science ®Google Scholar
• Bertolazzi E, Biral F, Da Lio M. Symbolic numeric indirect method for solving optimal control problems for large multibody systems. Multibody Syst Dyn. 2005;13:233–252. doi: https://doi.org/10.1007/s11044-005-3987-4
   Web of Science ®Google Scholar
• Hendrikx JPM, Imeljlink TJJ, Kriens RFC. Application of optimal control theory to inverse simulation of car handling. Veh Syst Dyn. 1996;26:449–461. doi: https://doi.org/10.1080/00423119608969319
   Web of Science ®Google Scholar
• Cossalter V, Da Lio M, Lot R, et al. A general method for the evaluation of vehicle manoeuvrability with special emphasis on motorcycles. Veh Syst Dyn. 1999;31:113–135. doi: https://doi.org/10.1076/vesd.31.2.113.2094
   Web of Science ®Google Scholar
• Lot R, Dal Bianco N. The significance of high-order dynamics in lap time simulations. Proceedings of the 24th Symposium of the International Association for Vehicle System Dynamics, Graz, Austria, 2015 Aug 17–21. IAVSD; 2015.
   Google Scholar
• Dal Bianco N, Lot R, Gadola M. Minimum time optimal control simulation of a GP2 race car. Proc Inst Mech Eng Part D J Automob Eng. 2018;232:1180–1195. doi: https://doi.org/10.1177/0954407017728158
   Web of Science ®Google Scholar
• Dal Bianco N, Bertolazzi E, Biral F, et al. Comparison of direct and indirect methods for minimum lap time optimal control problems. Veh Syst Dyn. 2018;57:665–696. doi: https://doi.org/10.1080/00423114.2018.1480048
   Web of Science ®Google Scholar
• Lot R, Evangelou SA. Lap time optimization of a sports series hybrid electric vehicle. Proceedings of the World Congress on Engineering III; 2013 Jul 3–5; Vol III. London, UK: WCE; 2013.
   Google Scholar
• Limebeer DJN, Perantoni G, Rao AV. Optimal control of formula one car energy recovery systems. Int J Control. 2014;87:2065–2080.
   Web of Science ®Google Scholar
• Limebeer DJN, Rao AV. Faster, higher and greener – vehicular optimal control. IEEE Control Syst Mag. 2015;35:36–56.
   Web of Science ®Google Scholar
• Ebbesen S, Salazar M, Elbert P, et al. Time-optimal control strategies for a hybrid electric race car. IEEE Trans Control Syst Technol. 2018;26:233–247. doi: https://doi.org/10.1109/TCST.2017.2661824
   Web of Science ®Google Scholar
• Casanova D, Sharp RS, Symonds P. Minimum time manoeuvring: the significance of yaw inertia. Veh Syst Dyn. 2000;34:77–115. doi: https://doi.org/10.1076/0042-3114(200008)34:2;1-G;FT077
   Web of Science ®Google Scholar
• Casanova PT. On minimum time vehicle manoeuvring: the theoretical optimal lap [Ph.D. dissertation]. Cranfield University; 2000.
   Google Scholar
• Kelly DP. Lap time simulation with transient vehicle and tyre dynamics [Ph.D. dissertation]. Cranfield University; 2008.
   Google Scholar
• Robuschi N, Zeile C, Sager S, et al. Multiphase mixed-integer nonlinear optimal control of hybrid electric vehicles. Preprint at http://www.optimization-online.org/DB_HTML/2019/05/7223.html; 2019.
   Google Scholar
• Sedlacek T, Odenthal D, Wollherr D. Minimum-time optimal control for vehicles with active rear-axle steering, transfer case and variable parameters. Veh Syst Dyn. 2020.
   Google Scholar
• Pakniyat A, Caines PE. Time optimal hybrid minimum principle and the gear changing problem for electric vehicles. IFAC. 2015;48:187–192.
   Google Scholar
• Elbert P, Nueesch T, Ritter A, et al. Engine on/off control for the energy management of a serial hybrid electric bus via convex optimization. IEEE Trans Veh Technol. 2014;63:3549–3559. doi: https://doi.org/10.1109/TVT.2014.2304137
   Web of Science ®Google Scholar
• Schmid R, Buerger J, Bajcinca N. Efficient optimal control of plug-in-hybrid electric vehicles including explicit engine on/off decisions. IEEE European Control Conference; Limassol; ECC; 2018.
   Google Scholar
• Salazar M, Balerna C, Elbert P, Grando FP, Onder CH. Real-time control algorithms for a hybrid electric race car using a two-level model predictive control scheme. IEEE Trans Veh Technol. 2017;66:10911–10922. doi: https://doi.org/10.1109/TVT.2017.2729623
   Web of Science ®Google Scholar
• Liniger A, Domahidi A, Morari M. Optimization-based autonomous racing of 1:43 scale RC cars. Optim Control Appl Methods. 2015;36:628–647. doi: https://doi.org/10.1002/oca.2123
   Web of Science ®Google Scholar
• Keen SD, Cole DJ. Application of time-variant predictive control to modelling driver steering skill. Veh Syst Dyn. 2011;49:527–559. doi: https://doi.org/10.1080/00423110903551626
   Web of Science ®Google Scholar
• Timings JP, Cole DJ. Vehicle trajectory linearisation to enable efficient optimisation of the constant speed racing line. Veh Syst Dyn. 2012;50:883–901. doi: https://doi.org/10.1080/00423114.2012.671946
   Web of Science ®Google Scholar
• Kapania NR, Subosits J, Gerdes JC. A sequential two-step algorithm for fast generation of vehicle racing trajectories. J Dyn Syst Meas Control. 2016;138:091005. doi: https://doi.org/10.1115/1.4033311
   Web of Science ®Google Scholar
• Salazar M, Bussi C, Grando FP, et al. Optimal control policy tuning and implementation for a hybrid electric race car. IFAC OnLine. 2016;49:147–152.
   Google Scholar
• de Castro R, Tanelli M, Araujo RE, et al. Torque allocation in electric vehicles with in-wheel motors: a performance-oriented approach. 52nd IEEE Conf Decis Control; Florence. 2013;1538–1543. doi: https://doi.org/10.1109/CDC.2013.6760101
   Google Scholar
• de Castro R, Tanelli M, Araujo RE, et al. Minimum-time path-following for highly redundant electric vehicles. IEEE Trans Control Syst Technol. 2016;24:487–501. doi: https://doi.org/10.1109/TCST.2015.2458773
   Web of Science ®Google Scholar
• Eckert M. Energieoptimale fahrdynamikregelung mehrmotoriger elektrofahrzeuge [Ph.D. dissertation]. Karlsruhe Institute of Technology; 2015.
   Google Scholar
• Dunning I, Huchette J, Lubin M. JuMP: a modeling language for mathematical optimization. SIAM Rev. 2017;59:295–320. doi: https://doi.org/10.1137/15M1020575
   Web of Science ®Google Scholar
• Wächter A, Biegler LT. On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math Program. 2005;1:25–57.
   Google Scholar
• Schramm D, Hiller M, Bardini R. Vehicle dynamics – modeling and simulation. Berlin: Springer-Verlag; 2014.
   Google Scholar
• Salameh ZM, Casacca MA, Lynch WA. A mathematical model for lead-acid batteries. IEEE Trans Energy Convers. 1992;7:93–98. doi: https://doi.org/10.1109/60.124547
   Web of Science ®Google Scholar
• Lupberger S, Degel W, Odenthal D, et al. Control allocation concept for hybrid braking considering dynamic battery behaviour. IFAC World Congress. 2020;21: Manuscript accepted for publication.
   Google Scholar
• Chen Z, Fu Y, Mi CC. State of charge estimation of lithium-ion batteries in electric drive vehicles using extended Kalman filtering. IEEE Trans Veh Technol. 2013;62:1020–1030. doi: https://doi.org/10.1109/TVT.2012.2235474
   Web of Science ®Google Scholar
• Kim J, Oh and H. Lee J. Review on battery thermal management system for electric vehicles. Appl Therm Eng. 2019;149:192–212. doi: https://doi.org/10.1016/j.applthermaleng.2018.12.020
   Web of Science ®Google Scholar
• Kirchhoff S. Ueber den durchgang eines elektrischen stromes durch eine ebene, insbesondere durch eine kreisfoermige. Ann Phys Chem. 1845;4:497–514. doi: https://doi.org/10.1002/andp.18451400402
   Google Scholar
• Mahmoudi A, Soong WL, Pellegrino G, et al. Efficiency maps of electrical machines. IEEE Energy Convers Congr Exposition. Montreal, QC: ECCE. 2015;2791–2799.
   Google Scholar
• Mahmoudi A, Soong WL, Pellegrino G, et al. Loss function modeling of efficiency maps of electrical machines. IEEE Trans Ind Appl. 2017;53:4221–4231. doi: https://doi.org/10.1109/TIA.2017.2695443
   Web of Science ®Google Scholar
• Bezanson J, Edelman A, Karpinski S, et al. Julia: a fresh approach to numerical computing. SIAM Rev. 2017;59:65–98. doi: https://doi.org/10.1137/141000671
   Web of Science ®Google Scholar
• Revels J, Lubin M, Papamarkou T. Forward-mode automatic differentiation in julia. arXiv:1607.07892[cs.MS]; 2016.
   Google Scholar
• Perantoni G, Limebeer DJN. Optimal control for a formula one car with variable parameters. Veh Syst Dyn. 2014;52:653–678. doi: https://doi.org/10.1080/00423114.2014.889315
   Web of Science ®Google Scholar
• Betts J. Practical methods for optimal control and estimation using nonlinear programming – second edition. Philadelphia: SIAM; 2010.
   Google Scholar
• Albrecht S. Modeling and numerical solution of inverse optimal control problems for the analysis of human motions [Ph.D. dissertation]. Technical University of Munich; 2014.
   Google Scholar
• Kelly M. An introduction to trajectory optimization: how to do your own direct collocation. SIAM Rev. 2017;59:849–904. doi: https://doi.org/10.1137/16M1062569
   Web of Science ®Google Scholar
• Masouleh MI, Limebeer DJN. Optimizing the aero-suspension interactions in a formula one car. IEEE Trans Control Syst Technol. 2016;24:912–927. doi: https://doi.org/10.1109/TCST.2015.2475396
   Web of Science ®Google Scholar
• Limebeer DJN, Perantoni G. Optimal control of a formula one car on a three-dimensional track-part 2: optimal control. J Dyn Syst Meas Control. 2015;137:051019. doi: https://doi.org/10.1115/1.4029466
   Web of Science ®Google Scholar