融合动态规划与模型预测控制的燃料电池无人机能量管理策略

doi:10.19595/j.cnki.1000-6753.tces.251126

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摘要为了降低燃料电池无人机的运行成本,延长其续航时间,该文提出一种融合动态规划（DP）与模型预测控制（MPC）的实时优化能量管理策略（EMS）,对燃料电池无人机混合动力系统进行能量管理。通过马尔科夫链（MC）模型对飞行需求功率进行精确预测,构建了包含等效氢气消耗、锂电池衰减成本和燃料电池衰减成本的多目标优化代价函数,使用DP算法求解出预测时域内的最优功率分配序列,并且利用MPC的滚动优化机制实现全局实时优化。研究表明：在相同的锂电池初始荷电状态（SOC）和给定飞行工况条件下,基于DP-MPC的氢气消耗量为11.72 g,与MPC、等效消耗最小策略（ECMS）和状态机控制（SMC）相比,续航时间分别提高了5.39%、13.62%和3.05%;总运行成本分别降低了0.71%、6.12%和1.01%;混合动力系统的总效率分别提高了13.41%、16.74%和12.23%。此外,所提出的DP-MPC策略在面对负载功率波动时,直流总线电压平均波动低于0.01 V,为提高燃料电池无人机的经济性和耐久性提供了方法指导。

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关键词 ：燃料电池无人机, 动态规划, 模型预测控制, 马尔科夫链, 运行成本

Abstract：With the low altitude economy being incorporated into the national strategic emerging industry system, fuel cell unmanned aerial vehicles (UAVs) have become the core technology direction to break through the bottleneck of lithium battery range due to their high energy density, zero carbon emission, and long-rangecharacteristics. However, the existing energy management strategies (EMSs) have contradictions between real-time and global optimization performance: rule-based methods (e.g., PID) are difficult to adapt to dynamic working conditions, the UAV′s arithmetic resources limit deep reinforcement learning strategies, and optimization-based methods (e.g., dynamic programming) are globally optimal, but with high computational complexity, and cannot be applied in real-time. There is an urgent need for an EMSs that strike a balance between real-time performance and economic efficiency. Aiming at the challenge of fuel cell UAVs, such as high running cost and short fuel cell life, a real-time EMS integrating dynamic programming (DP) and model predictive control (MPC) is proposed, which aims to reduce the equivalent hydrogen consumption, extend the life of the powertrain system, and improve the operation time through multi-objective optimization.
Firstly, a Markov predictor that can predict the future demand power is formed by cyclic indexing and updating the constructed state transfer matrix (STM) row by row, using data from typical flight conditions of the UAV. Then, it predicts the UAV demand power in real time according to the constructed Markov predictor and rationally allocates the energy of the lithium battery and fuel cell in combination with the powertrain configuration of the hydrogen-energy UAV. During system operation, the proposedcost function is used to quantify the running cost of each time step within the prediction step. The DP algorithm is used to obtain the short-term optimal power allocation sequence, and then the first element is applied to the fuel cell UAV powertrain. Rolling optimization is carried out according to the same method within the next prediction step, aimingto achieve the lowest running cost in the entire operation process.The following conclusions can be drawn from the results:
(1) After comparing the state transfer probability distribution characteristics of different step lengths, it is found that with the increase of the prediction step length, when the prediction step length is less than 3, the state probability distribution shows more obvious diagonal distribution characteristics, when the prediction step length is more than 5, the probability distribution under the state transfer matrix no longer shows obvious diagonal aggregation characteristics, and finally N_p = 5 is selected as the prediction step length.
(2) By analyzing the probability distribution of fuel cell output power, the DP-MPC strategy has the highest percentage of operating points in the efficient interval of the fuel cell of 85.43%, which is 11.2%, 61.5% and 49.9% higher than MPC, ECMS, and SMC. Meanwhile, the DP-MPC strategy has the highest entire efficiency of 83.46%, which is improved by 13.41%, 16.74% and 12.23% compared to MPC, ECMS, and SMC, respectively.
(3) Based on the cost analysis, it is found that the DP-MPC-based EMS proposed in this paper can effectively reduce the total running cost of the UAV by 0.71%, 6.12% and 1.01% compared to MPC, ECMS, and SMC, respectively, and the operation time is improved by 5.39%, 13.62% and 3.05%.

Key words： Fuel cell unamed aerial vehicles (UAVs) dynamic programming model predictive control Markov chain running cost

收稿日期: 2025-06-30

PACS:

TM911

基金资助:国家自然科学基金（51977061, 51407063）和武汉市东湖高新区揭榜挂帅项目（2024KJB336）资助

通讯作者: 章国光男,1964年生,教授,硕士生导师,研究方向为汽车电动化。E-mail：zhangguoguang@hbut.edu.cn

作者简介: 全睿男,1984年生,教授,博士生导师,研究方向为氢能与燃料电池。E-mail：quan_rui@126.com

引用本文:

全睿, 刘大志, 管鑫, 章国光, 全琎. 融合动态规划与模型预测控制的燃料电池无人机能量管理策略[J]. 电工技术学报, 2026, 41(14): 5003-5016. Quan Rui, Liu Dazhi, Guan Xin, Zhang Guoguang, Quan Jin. Energy Management Strategy for Fuel Cell Unmanned Aerial Vehicles Integrating Dynamic Programming with Model Predictive Control. Transactions of China Electrotechnical Society, 2026, 41(14): 5003-5016.

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