Abstract：A two-speed, automatic mechanical transmission (AMT) is developed for electric vehicles with a planetary gear system, a centrifugal clutch and a belt brake. The transmission shifts seamlessly between the two gears to eliminate the power interruption problem during gear shifting in conventional AMT. The electric vehicle driveline is modeled to get the optimal control method using dynamic programming and convex optimization. The optimal control variables and optimal control system minimize vehicle jerk and frictional losses. A normal sectional control method is also used during gear shifting for comparison in simulations. The simulations indicate that the optimal control method significantly improves the gear shift comfort while maintaining the dynamic performance as well as vehicle acceleration with decreases of frictional losses in the clutch and brake.
方圣楠, 宋健, 宋海军, 台玉琢, TRUONG Sinh Nguyen. 基于最优控制理论的电动汽车机械式自动变速器换档控制[J]. 清华大学学报（自然科学版）, 2016, 56(6): 580-586.
FANG Shengnan, SONG Jian, SONG Haijun, TAI Yuzhuo, TRUONG Sinh Nguyen. Shifting control of automatic mechanical transmissions for electric vehicles based on optimal control theory. Journal of Tsinghua University(Science and Technology), 2016, 56(6): 580-586.
 Chan C C, Bouscayrol A, Chen K. Electric, hybrid, and fuel-cell vehicles: Architectures and modeling [J]. IEEE Transactions on Vehicular Technology, 2010, 59(2): 589-598.
 Emadi A, Williamson S S, Khaligh A. Power electronics intensive solutions for advanced electric, hybrid electric, and fuel cell vehicular power systems [J]. IEEE Transactions on Power Electronics, 2006, 21(3): 567-577.
 Welchko B A, Nagashima J M. The influence of topology selection on the design of EV/HEV propulsion systems [J]. IEEE Power Electronics Letters, 2003, 1(2): 36-40.
 Hofman T, Dai C H. Energy efficiency analysis and comparison of transmission technologies for an electric vehicle [C]// IEEE Vehicle Power and Propulsion Conference. Lille, 2010: 1-6.
 Ren Q, Crolla D A, Morris A. Effect of transmission design on electric vehicle (EV) performance [C]// IEEE Vehicle Power and Propulsion Conference. Dearborn, MI, 2009: 1260-1265.
 Koneda P T, Stockton T R. Design of a Two-Speed Automatic Transaxle for an Electric Vehicle [R]. SAE 850198, 1985.
 Wu G, Zhang X, Dong Z. Impacts of Two-Speed gearbox on Electric Vehicle's Fuel Economy and Performance [R]. SAE 2013-01-0349, 2013.
 Gu Q, Cheng X. Study on double clutch transmission gear shift control based on optimal control theory [C]// IEEE International Conference on Industrial Engineering and Engineering Management. Changchun, 2011: 629-634.
 Sorniotti A, Holdstock T, Pilone G L, et al. Analysis and simulation of the gearshift methodology for a novel two-speed transmission system for electric powertrains with a central motor [J]. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 2012, 226(7): 915-929.
 Sorniotti A, Pilone G L, Viotto F, et al. A Novel Seamless 2-Speed Transmission System for Electric Vehicles: Principles and Simulation Results [R]. SAE 2011-37-0022, 2011.
 Haj-Fraj A, Pfeiffer F. Optimal control of gear shift operations in automatic transmissions [J]. Journal of the Franklin Institute, 2001, 338(2/3): 371-390.
 Glielmo L, Vasca F. Optimal Control of Dry Clutch Engagement [R]. SAE 2000-01-0837, 2000.
 Sun C, Zhang J. Optimal control applied in automatic clutch engagements of vehicles [J]. Chinese Journal of Mechanical Engineering, 2004, 17(2): 280-283.
 严忆泉, 宋健, 李亮. 干式双离合器自动变速器自适应起步控制 [J]. 清华大学学报: 自然科学版, 2014, 54(6): 734-737.YAN Yiquan, SONG Jian, LI Liang. Self-adaption initial acceleration control strategies of a dry dual clutch transmission [J]. J Tsinghua Univ: Sci and Tech, 2014, 54(6): 734-737. (in Chinese)