用最优控制抑制转子不平衡
Rotor imbalance suppression by optimal control
摘要：
考虑了不平衡转子。给出了一个移动平衡质量系统。我们确定平衡质量的最佳运动，以尽量减少转子上的不平衡。最佳运动由开环控制给出，解决了无限时间内的最优控制问题。利用变分法证明了最优解的存在性，并推导出相应的最优性条件。严格研究了控制系统的渐近行为。通过构造一个新的最优解，证明了最优解随时间$t\to +\infty$收敛到稳定构形.给出了算法的收敛速度的显式估计。这保证了最优控制使系统稳定。在不平衡低于计算阈值的情况下，收敛以指数方式快速发生。这是证明了稳定流形定理适用于庞特里亚金最优性系统。提出了一种基于强化学习的闭环控制策略。进行了数值模拟，验证了理论结果。
英文摘要：
An imbalanced rotor is considered. A system of moving balancing masses is given. We determine the optimal movement of the balancing masses to minimize the imbalance on the rotor. The optimal movement is given by an open-loop control solving an optimal control problem posed in infinite time. By methods of the Calculus of Variations, the existence of the optimum is proved and the corresponding optimality conditions have been derived. Asymptotic behavior of the control system is studied rigorously. By Łojasiewicz inequality, convergence of the optima as time $t\to +\infty$ towards a steady configuration is ensured. An explicit estimate of the convergence rate is given. This guarantees that the optimal control stabilizes the system. In case the imbalance is below a computed threshold, the convergence occurs exponentially fast. This is proved by the Stable Manifold Theorem applied to the Pontryagin optimality system. Moreover, a closed-loop control strategy based on Reinforcement Learning is proposed. Numerical simulations have been performed, validating the theoretical results.
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