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.
WenQWangFXuB, et al. Improving the fuel efficiency of compact wheel loader with a series hydraulic hybrid powertrain. IEEE Trans Veh Technol2020; 69(1): 10700–10709.
9.
WangFZulkefliMAMSunZX, et al. Investigation on the energy management strategy for hydraulic hybrid wheel loaders. In: Proceedings of the ASME 2013 dynamic systems and control conference, Palo Alto, CA, USA, 2013.
10.
WuBLinCFilipiZ, et al. Optimal power management for a hydraulic hybrid delivery truck. Veh Syst Dyn2004; 42(1–2): 23–40.
11.
TranDDVafaeipourMBaghdadiME, et al. Thorough state-of-the-art analysis of electric and hybrid vehicle powertrains: topologies and integrated energy management strategies. Renew Sustain Energy Rev2020; 119: 109596.
12.
OnoriSSerraoLRizzoniG. Hybrid electric vehicles– energy management strategies. Springer: Springer-Verlag London, 2016.
13.
SalmasiFR. Control strategies for hybrid electric vehicles: evolution, classification, comparison, and future trends. IEEE Trans Veh Technol2007; 56(5): 2393–2404.
14.
WangBWangWZhangJ, et al. Comparison research of different control strategies on parallel hybrid electric vehicle. J Syst Simul2006; 18: 401–404.
15.
ShabbirWEvangelouSA. Threshold-changing control strategy for series hybrid electric vehicles. Appl Energy2019; 235: 761–775.
16.
PengJHeHWXiongR. Rule based energy management strategy for a series–parallel plug-in hybrid electric bus optimized by dynamic programming. Appl Energy2017; 185: 1633–1643.
17.
KimNWLeeDHZhengC, et al. Realization of PMP-based control for hybrid electric vehicles in a backward-looking simulation. Int J Automot Technol2014; 15(4): 625–635.
18.
OnoriSTribioliL. Adaptive Pontryagin’s Minimum Principle supervisory controller design for the plug-in hybrid GM Chevrolet Volt. Appl Energy2015; 147: 224–234.
19.
VafaeipourMBaghdadiMEMierloJV, et al. An ECMS-based approach for energy management of a HEV equipped with an electrical variable transmission. In: 14th international conference on ecological vehicles and renewable energies, Monte-Carlo, Monaco, 2019. New York, NY: IEEE.
20.
MusardoCRizzoniG. A-ECMS: an adaptive algorithm for hybrid electric vehicle energy management. In: Proceedings of the 44th IEEE conference on decision and control and the European control conference 2005, Seville, Spain, 2005.
21.
SunCSunFHeH. Investigating adaptive-ECMS with velocity forecast ability for hybrid electric vehicles. Appl Energy2017; 185: 1644–1653.
22.
YuanZTengLFengchunS, et al. Comparative study of dynamic programming and Pontryagin’s minimum principle on energy management for a parallel hybrid electric vehicle. Energies2013; 6: 2305–2318.
23.
YangYPeiHHuX, et al. Fuel economy optimization of power split hybrid vehicles: a rapid dynamic programming approach. Energy2019; 166: 929–938.
24.
MouraSJFathyHKCallawayDS, et al. A stochastic optimal control approach for power management in plug-in hybrid electric vehicles. IEEE Trans Control Syst Technol2011; 19(6): 545–555.
25.
WangDLinXZhangY. Fuzzy logic control for a parallel hydraulic hybrid excavator using genetic algorithm. Autom Constr2011; 20: 581–587.
26.
SunH. Multi-objective optimization for hydraulic hybrid vehicle based on adaptive simulated annealing genetic algorithm. Eng Appl Artif Intell2010; 23: 27–33.
27.
GeeringHP. Optimal control with engineering applications. Berlin-Heidelberg: Springer-Verlag, 2007.
28.
WangYWuZChenY, et al. Research on energy optimization control strategy of the hybrid electric vehicle based on Pontryagin’s minimum principle. Comput Electr Eng2018; 72: 203–213.
29.
KimNChaSPengH. Optimal control of hybrid electric vehicles based on Pontryagin’s minimum principle. IEEE Trans Control Syst Technol2011; 19(5): 1279–1287.
30.
SongKWangXLiF, et al. Pontryagin’s minimum principle-based real-time energy management strategy for fuel cell hybrid electric vehicle considering both fuel economy and power source durability. Energy2020; 205: 118064.
31.
LiXWangYYangD, et al. Adaptive energy management strategy for fuel cell/battery hybrid vehicles using Pontryagin’s minimal principle. J Power Sources2019; 440: 227105.
32.
OuddahNAdouaneLAbdrakhmanovR. From offline to adaptive online energy management strategy of hybrid vehicle using Pontryagin’s minimum principle. Int J Automot Technol2018; 19(3): 571–584.
33.
ZhangQWangFXuB, et al. Influence of hydraulic accumulator performance on the hydraulic hybrid powertrain. In: Proceedings of the ASME/BATH 2019 symposium on fluid power & motion control, Sarasota, US, 2019.
34.
NilssonTFröbergAÅslundJ. Predictive control of a diesel electric wheel loader powertrain. Control Eng Pract2015; 41: 47–56.
