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In this paper, the pulse and glide (PnG) operation for parallel hybrid electric vehicles (HEVs) with step-gear transmission in cruising scenario is considered. The PnG operation is an eco-driving technique that alternately turns on and off the engine to achieve better fuel economy. For HEVs, the batteries can serve as yet another energy buffer in addition to the vehicle body. However, due to the power loss during battery charging and discharging, the fuel saving performance of PnG using only battery is much degraded, even though it can lead to better ride comfort. Therefore, in this work, we introduce speed oscillation to SOC-PnG that originally only oscillates the state-of-charge (SOC) of the battery. Meanwhile, desired ride comfort and SOC sustenance requirements need to be fulfilled. To achieve this goal, two optimal control problems are formulated, one for the gliding phase and the other for the pulsing phase. By linearizing the vehicle dynamics and applying the McCommick envelop approach, the problems can be transcribed into quadratic programming (QP) problems using the Legendre pseudo-spectral (PS) method. The resultant QP problems can be solved efficiently. Therefore, this framework is suitable for real-time on-line implementation. Numerical simulations are conducted to show the ability of the proposed method to improve fuel economy, while maintaining desired ride comfort and sustaining the battery SOC.
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Shieh et al. (2019) studied this question.