Mixed-Integer Optimal Design and Energy Management of Hybrid Electric Vehicles with Automated Manual Transmissions

The energy efficiency improvement problems of hybrid electric vehicles (HEVs) with automated manual transmissions are investigated from both the design and control aspects for extended searching space in this work. To optimize the transmission, the gearshift commands and power distribution simultaneously, a combined mixed-integer optimal design and control problem (MIOCP) is formulated. The challenging MIOCP is then reformulated by introducing augmented terms in both objective function and the dynamic model to handle the integer control variables. The reformulated problem is solved with an optimal control software package developed by the authors, the performance of which is validated with dynamic programming and equivalent consumption minimization strategy. Optimal design and mixed-integer control results of the HEV are obtained for different cases, some existing confusions of transmission selection for the HEVs are clarified quantitatively. Results show that transmissions with fewer gear ratios can achieve competitive performances compared with the original one by using the proposed approach.