Pontryagin’s Minimum Principle based model predictive control of energy management for a plug-in hybrid electric bus

Xie, Shaobo; Hu, Xiaosong; Xin, Zongke; Brighton, James

doi:10.1016/j.apenergy.2018.12.032

Cited by 306 publications

(117 citation statements)

References 54 publications

Supporting

Mentioning

102

Contrasting

Order By: Relevance

“…Currently, Pontryagin's minimum principle (PMP) has been widely adopted for the energy management of PHEBs [25,49]. However, it is still a great challenge to apply the PMP to the EMS in real time for unknown driving cycles.…”

Section: Real-time Application Of the Energy Management Strategymentioning

confidence: 99%

Integrated Component Optimization and Energy Management for Plug-In Hybrid Electric Buses

Liu

Zhao

et al. 2019

Processes

View full text Add to dashboard Cite

The complicated coupling of component design together with energy management has brought a significant challenge to the design, optimization, and control of plug-in hybrid electric buses (PHEBs). This paper proposes an integrated optimization methodology to ensure the optimum performance of a PHEB with a view toward designing and applications. First, a novel co-optimization method is proposed for redesigning the driveline parameters offline, which combines a nondominated sorting genetic algorithm-II (NSGA-II) with dynamic programming to eliminate the impact of the coupling between the component design and energy management. Within the new method, the driveline parameters are optimally designed based on a global optimal energy management strategy, and fuel consumption and acceleration time can be respectively reduced by 4.71% and 4.59%. Second, a model-free adaptive control (MFAC) method is employed to realize the online optimal control of energy management on the basis of Pontryagin's minimum principle (PMP). Particularly, an MFAC controller is used to track the predesigned linear state-of-charge (SOC), and its control variable is regarded as the co-state of the PMP. The main finding is that the co-state generated by the MFAC controller gradually converges on the optimal one derived according to the prior known driving cycles. This implies that the MFAC controller can realize a real-time application of the PMP strategy without acquiring the optimal co-state by offline calculation. Finally, the verification results demonstrated that the proposed MFAC-based method is applicable to both the typical and unknown stochastic driving cycles, meanwhile, and can further improve fuel economy compared to a conventional proportional-integral-differential (PID) controller.Processes 2019, 7, 477 2 of 23 on a single-objective (or multiobjective) optimization problem of driveline matching, component sizing, topology design, or the EMS [8][9][10][11]. For the predefined single-shaft coaxial parallel plug-in hybrid electric bus (PHEB) in our research, component sizing and the energy management control are extremely significant to fuel economy. To guarantee the optimality of dynamic performance and fuel economy, the driveline design and the EMS should be simultaneously considered, as they are strongly coupled [12]. Previous work has disposed of the combined optimization problem in a bilevel manner, where the outer loop is for the former and the inner loop is for the latter [8,13]. Many optimization algorithms have also been extensively applied to solve this problem, such as a genetic algorithm (GA) [4,14], particle swarm optimization (PSO) [11,15], and simulated annealing (SA) [9,16]. Most of them have been utilized to optimally design the component parameters for an outer loop, while a rule-based EMS is nested in an inner loop. However, the optimization results were suboptimal and influenced by the established rules due to the coupling relationship between the component design and EMS [3,7]. To overcome this drawback, another categ...

show abstract

Section: Real-time Application Of the Energy Management Strategymentioning

confidence: 99%

Integrated Component Optimization and Energy Management for Plug-In Hybrid Electric Buses

Liu

Zhao

et al. 2019

Processes

View full text Add to dashboard Cite

show abstract

“…References and proposed two different nonlinear MPC (NMPC)‐based strategies by combining particle swarm optimization method. Reference proposed a MPC‐based strategy by deploying a PMP algorithm. In practice, MPC‐based strategies have high robustness and adaptability.…”

Section: Introductionmentioning

confidence: 99%

Self‐learning energy management for plug‐in hybrid electric bus considering expert experience and generalization performance

Guo¹,

Zhao²,

Guo³

et al. 2020

Int J Energy Res

View full text Add to dashboard Cite

A self-learning energy management is proposed for plug-in hybrid electric bus, by combining Q-Learning (QL) and Pontryagin's minimum principle algorithms. Different from the existing strategies, the expert experience and generalization performance are focused in the proposed strategy. The expert experience is designed as the approximately optimal reference state-of-charge (SOC) trajectories, and the generalization performance is enhanced by a multiply driving cycle training method. In specific, an efficient zone of SOC is firstly designed based on the approximately optimal reference SOC trajectories. Then, the agent of the QL is trained off-line by taking the expert experience as reference SOC trajectories.Finally, an adaptive strategy is proposed based on the well-trained agent. Specially, two different reward functions are defined. That is, the reward function in the off-line training mainly considers the tracking performance between the expert experience and the SOC, while mainly considering the punishment in the adaptive strategy. Simulation results show that the proposed strategy has good generalization performance and can improve the fuel economy by 22.49%, compared to a charge depleting-charge sustaining (CDCS) strategy. K E Y W O R D Senergy management, expert experience, generalization performance, plug-in hybrid electric bus, Q-learning

show abstract

“…In [3], the CD/CS operation-like SoC reference trajectory generation is proposed for driving cycles including LEZs, where the battery charge is sustained in hybrid driving outside of LEZ, while using pure electric driving within LEZ. Model predictive control (MPC)-based energy management strategies are becoming a research topic of many recent papers, where on-line optimizations of PHEV control variables are performed on a receding horizon [10][11][12]. A Monte Carlo approach is applied in [13] to reconstruct the optimal SoC reference trajectory over an MPC strategy prediction horizon.…”

Section: Introductionmentioning

confidence: 99%

“…A Monte Carlo approach is applied in [13] to reconstruct the optimal SoC reference trajectory over an MPC strategy prediction horizon. In [12] and [14], SoC reference is provided to MPC control strategy in the form of terminal condition at the end of MPC optimization time horizon, which is calculated based on real-time traffic flow data in [14], and based on prediction of travelled distance within the following optimization time horizon in [12].…”

Section: Introductionmentioning

confidence: 99%

Synthesis of Optimal Battery State-of-Charge Trajectory for Blended Regime of Plug-in Hybrid Electric Vehicles in the Presence of Low-Emission Zones and Varying Road Grades

2019

View full text Add to dashboard Cite

The powertrain efficiency for plug-in hybrid electric vehicles (PHEV) can be maximized by gradually discharging the battery in a blended regime, where the engine is regularly used all over the driving cycle. A key step in designing an optimal PHEV control strategy for the blended regime corresponds to synthesis of battery state-of-charge (SoC) reference trajectory. The paper first demonstrates that the optimal SoC trajectory can significantly differ from a typical linear-like shape in the case of varying road grade and presence of low-emission zones (LEZ). Next, dynamic programming (DP)-based optimizations of PHEV control variables are conducted for the purpose of extracting and analyzing optimal SoC trajectory patterns. It is shown that the optimality is closely related to the minimization of SoC trajectory length with respect to travelled distance. This finding is used for SoC reference trajectory synthesis in the presence of LEZ and varying road grades. Finally, the overall PHEV control strategy is applied to a PHEV-type city bus and verified by means of computer simulations in comparison with the DP optimization benchmark.

show abstract

Pontryagin’s Minimum Principle based model predictive control of energy management for a plug-in hybrid electric bus

Cited by 306 publications

References 54 publications

Integrated Component Optimization and Energy Management for Plug-In Hybrid Electric Buses

Integrated Component Optimization and Energy Management for Plug-In Hybrid Electric Buses

Self‐learning energy management for plug‐in hybrid electric bus considering expert experience and generalization performance

Synthesis of Optimal Battery State-of-Charge Trajectory for Blended Regime of Plug-in Hybrid Electric Vehicles in the Presence of Low-Emission Zones and Varying Road Grades

Contact Info

Product

Resources

About