Numerical Methods for Optimal Control of Hybrid Electric Agricultural Tractors

Electrification of agricultural machinery offers substantial benefits and has drawn attentions from manufacturers, so different types of hybrid electric agricultural tractors (HEATs) have been conceptually designed. In HEATs, energy management strategies play an important role to improve the performance of fuel economy. The previous studies are dominated by rule-based strategies. This work proposes optimization-based energy management strategies for HEATs to minimize the fuel consumption in typical working cycles. Based on the optimal control principles, dynamic programming, indirect method, and direct method are used to solve the formulated optimal control problem (OCP) and obtain three different optimal energy management strategies. All the three strategies achieve good performance in solving the OCP. Moreover, compared with the typical rule-based benchmarking strategy, these optimal EMSs show significant improvements in fuel efficiency (up to 5%). At last, the advantages and disadvantages of each method are illustrated and discussed by numerical simulations.