微通道中液滴输运的最优控制与闭环稳定性
Optimal Control and Closed-Loop Stability of Droplet Transport in a Microchannel
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中文总结 AI 辅助
本研究基于润滑理论，通过ODE和PDE两种模型优化微通道液滴输运，发现短距“平移-松弛”和长距“紧凑-平移-松弛”两种最优策略，并证明CLF反馈实现闭环指数稳定。
中文摘要 AI 辅助
理解受限几何结构中流体液滴的高效输运近期已成为工业应用关注的一个领域。在本工作中，我们专注于设计能够最优地引导液滴运动的控制策略。这里，我们将最优控制框架应用于基于润滑理论的微通道液滴输运问题，该理论最小化粘性耗散。我们采用了两种互补的建模路径：一种是通过庞特里亚金极大值原理优化的降阶常微分方程（ODE）模型，以及一种使用协方差矩阵自适应进化策略优化的全非线性偏微分方程（PDE）模型。通过参数化目标位移、液滴尺寸和毛细数，我们发现了两种不同的最优输运机制：针对短距离的“平移-松弛”策略和针对较长目标的“紧凑-平移-松弛”策略。在连续介质力学中，表面力与累积粘性耗散之间的竞争决定了最优输运策略。我们进一步表明，降阶控制器向连续介质模型转移的位移范围由毛细刚度控制。最后，我们通过将控制李雅普诺夫函数（CLF）框架适配到降阶动力学来解决闭环稳定性问题。我们证明了惩罚偏离目标的终端代价在物理域上充当一个代价兼容的CLF，并证明了CLF兼容的反馈指数稳定目标状态。
英文摘要
Understanding the efficient transport of fluid droplets in confined geometries has been a domain of interest for industrial applications in recent times. In the present work, we focus on designing control strategies that optimally steer droplet motion. Here, we apply optimal control framework to the droplet transport problem in a microchannel based on lubrication theory that minimizes viscous dissipation. Two complementary modeling routes are adopted: a reduced-order ordinary differential equation (ODE) model optimized via Pontryagin's Maximum Principle, and a full nonlinear partial differential equation (PDE) model optimized using a Covariance Matrix Adaptation-Evolutionary Strategy. By parameterizing target displacement, droplet size, and capillary number, we uncover two distinct optimal transport regimes: a "translate-relax" strategy for short distances and a "compact-translate-relax" strategy for longer targets. In continuum mechanics, the competition between surface forces and cumulative viscous dissipation decides the optimal transport strategies. We further show that the displacement range over which the reduced-order controller transfers to the continuum model is governed by capillary stiffness. We finally address closed-loop stability by adapting a control Lyapunov function (CLF) framework to the reduced-order dynamics. We demonstrate that the terminal cost which penalizes deviation from the target, serves as a cost-compatible CLF on the physical domain, and prove that the CLF-compatible feedback exponentially stabilizes the target state.
发表机构
- Lehigh University（利哈伊大学）
机构由 AI 辅助整理，请以论文原文为准。
