To further improve the energy-saving potential and robustness of the energy management strategy (EMS) for plug-in hybrid electric vehicles (PHEVs) in a real-time application, this paper proposes a modified model-free-adaptivecontrol-based (MFAC-based) EMS to overcome the disadvantages in our previous MFAC-based EMS. First, the influence of external disturbance on MFAC-based EMS is discussed, and the results show that both the vehicle velocity and load change have a significant impact on its performance. Second, a modified MFAC-based real-time EMS is designed based on history driving data obtained from a repeated route in which a state-of-charge (SOC)constraint-based reference SOC planning method is firstly proposed to simultaneously consider the vehicle velocity and changing load. Then, global SOC constraints are incorporated in Pontryagin's minimum principle (PMP) to enhance the adaptive capability of the proposed method. Finally, the optimal solution of PMP (i.e., optimal constant) is deployed as a benchmark, and the performance of the modified MFAC-based EMS (namely MFAC-II and MFAC-III) is in contrast to the previous one (MFAC for short) under various real-world driving cycles. The results demonstrate that the MFAC-III has a remarkable improvement in both economic performance and robustness.

This paper proposes a robust design approach based on the Design for Six Sigma (DFSS), to promote the robustness of our previous model-free-adaptive-control-based (MFAC-based) energy management strategy (EMS) for the plug-in hybrid electric vehicles (PHEVs) in real-time application. First, the multi-island genetic algorithm (MIGA) is employed for a deterministic design of the MFAC-based EMS, and the Monte Carlo simulation (MCS) is utilized to evaluate the sigma level of the strategy with the deterministic design results. Second, a DFSS framework is formulated to reinforce the robustness of the MFAC-based EMS, in which the velocity and the vehicle mass are considered external disturbances whilst the terminal state of charge (SOC) of the battery and the fuel consumption (FC) are conducted as responses. In addition, real-time SOC constraints are incorporated into Pontryagin’s minimum principle (PMP) to confine the fluctuation of battery SOC in MFAC-based EMS to make it closer to the solution of the dynamic programming (DP). Finally, the effectiveness of the robust design results is assessed by contrasting with other strategies for various combined driving cycles (including velocity, vehicle mass, and road slope). The comparisons demonstrate the remarkable promotion of the robust design in terms of the energy-saving potential and the performance against external disturbance. The average improvement of the FCs can reach up to a considerable 19.66% and 9.79% in contrast to the charge-depleting and charge-sustaining (CD-CS) strategy as well as the deterministic design of MFAC-based EMS. In particular, the energy-saving performance is comparable to DP, where there is only a gap of −1.68%.