Online optimization of Pontryagin’s minimum principle for a series hydraulic hybrid wheel loader

The hydraulic hybrid powertrain has great potential for reducing fuel consumption and emission of off-road vehicles. The energy management strategy is the key to hybrid powertrain and currently there are many well-developed strategies. Of which the Pontryagin’s minimum principle is of research interest since it is a global optimization method while less computational burden than dynamic programming. However, it requires full cycle information to calculate co-state value in the principle, making it not implementable. Therefore in this study an implementable Pontryagin’s minimum principle is proposed for a series hybrid wheel loader, where the optimal co-state value in the principle is trained through repetitive wheel loader duty cycle. The Pontryagin’s minimum principle formulations of hybrid wheel loader are developed. The online co-state training algorithm is presented. A dynamic simulation model of hybrid wheel loader is developed. The fuel consumption of hybrid wheel loader with proposed strategy is compared with dynamic programming strategy and rule-based strategy in wheel loader long and short loading cycles. Results show the fuel consumption with proposed strategy is close to dynamic programming result and is lower than rule-based strategy. Finally, the influence of pressure level of hybrid powertrain on vehicle fuel consumption is studied.