混合整数与连续模型预测控制在二进制推进器中的应用：一种比较研究
Mixed-Integer vs. Continuous Model Predictive Control for Binary Thrusters: A Comparative Study
AI总结：
本文比较了连续MPC与Delta-Sigma调制方法与直接混合整数MPC在二进制推进器控制中的性能，发现MIMPC在低推力条件下更高效，而结合调制器动态的二进制MPC提高了鲁棒性。
摘要：
二进制开/关推进器常用于航天器在近轨操作中的姿态和位置控制。然而，其离散性质对传统连续控制方法提出了挑战。这些离散执行器的控制要么明确地建模为混合整数优化问题，要么通过两层方法处理，其中连续控制器的输出通过模拟-数字调制技术如Delta-Sigma调制转换为二进制命令。本文提供了二进制推进器控制中两种范式的第一系统比较，对比连续模型预测控制（MPC）与Delta-Sigma调制与直接混合整数MPC（MIMPC）方法。此外，我们提出了一种新的MPC变体用于二进制执行器系统，该变体基于Delta-Sigma调制器的状态。两种连续MPC变体和MIMPC通过使用ESA的REACSA平台进行广泛模拟进行了评估。结果表明，尽管所有方法在高推力条件下表现相似，但MIMPC在低推力条件下实现了更优的燃料效率。连续MPC与调制在高推力水平下表现出不稳定性，而结合调制器动态的二进制MPC提高了鲁棒性，并将效率差距缩小到MIMPC。从模拟和实际系统实验可以看出，MIMPC为资源受限任务提供了完整的稳定性和燃料效率优势，而连续控制方法在计算受限应用中仍然具有吸引力。
英文摘要：
Binary on/off thrusters are commonly used for spacecraft attitude and position control during proximity operations. However, their discrete nature poses challenges for conventional continuous control methods. The control of these discrete actuators is either explicitly formulated as a mixed-integer optimization problem or handled in a two-layer approach, where a continuous controller's output is converted to binary commands using analog-to digital modulation techniques such as Delta-Sigma-modulation. This paper provides the first systematic comparison between these two paradigms for binary thruster control, contrasting continuous Model Predictive Control (MPC) with Delta-Sigma modulation against direct Mixed-Integer MPC (MIMPC) approaches. Furthermore, we propose a new variant of MPC for binary actuated systems, which is informed using the state of the Delta-Sigma Modulator. The two variations for the continuous MPC along with the MIMPC are evaluated through extensive simulations using ESA's REACSA platform. Results demonstrate that while all approaches perform similarly in high-thrust regimes, MIMPC achieves superior fuel efficiency in low-thrust conditions. Continuous MPC with modulation shows instabilities at higher thrust levels, while binary informed MPC, which incorporates modulator dynamics, improves robustness and reduces the efficiency gap to the MIMPC. It can be seen from the simulated and real-system experiments that MIMPC offers complete stability and fuel efficiency benefits, particularly for resource-constrained missions, while continuous control methods remain attractive for computationally limited applications.
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