带表面张力的线性化粘性液槽系统的控制

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization Pub Date : 2024-03-21 DOI:10.1137/23m158749x

Iasson Karafyllis, Miroslav Krstic

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引用次数: 0

摘要

SIAM 控制与优化期刊》第 62 卷第 2 期第 1034-1059 页，2024 年 4 月。摘要本文研究了粘性槽液系统的线性化问题。油箱-液体系统的线性化给出了一个高阶偏微分方程，它是带有 Kelvin-Voigt 阻尼的波方程和 Euler-Bernoulli 梁方程的组合。单一输入出现在两个边界条件（边界输入）中。论文提供了开环系统的结果（解的存在性/唯一性和开环系统的稳定性）以及反馈稳定器的构造结果。更具体地说，反馈设计方法基于控制 Lyapunov 函数（CLF）。提出的 CLF 是对水箱-液体系统总能量函数的修改和增强，从而捕捉到粘度、摩擦力和表面张力的耗散效应。通过关注线性化的水箱系统，我们能够提供非线性情况下无法提供的结果：(1) 解的存在性和唯一性，(2) 摩擦力和表面张力的同时存在，以及 (3) 使用不同的 CLF 在更强规范下的稳定性。

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Control of a Linearized Viscous Liquid–Tank System with Surface Tension

SIAM Journal on Control and Optimization, Volume 62, Issue 2, Page 1034-1059, April 2024.
Abstract. This paper studies the linearization of the viscous tank–liquid system. The linearization of the tank–liquid system gives a high-order partial differential equation, which is a combination of a wave equation with Kelvin–Voigt damping and a Euler–Bernoulli beam equation. The single input appears in two of the boundary conditions (boundary input). The paper provides results both for the open-loop system (existence/uniqueness of solutions and stability properties of the open-loop system) as well as results for the construction of feedback stabilizers. More specifically, the feedback design methodology is based on control Lyapunov functionals (CLFs). The proposed CLFs are modifications and augmentations of the total energy functionals for the tank–liquid system so that the dissipative effects of viscosity, friction, and surface tension are captured. By focusing on the linearized water–tank system, we are able to provide results that are not provided in the nonlinear case: (1) existence and uniqueness of solutions, (2) simultaneous presence of friction and surface tension, and (3) stabilization in a stronger norm, using a different CLF.

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来源期刊

SIAM Journal on Control and Optimization 数学-应用数学

CiteScore

4.00

自引率

4.50%

发文量

143

审稿时长

12 months

期刊介绍： SIAM Journal on Control and Optimization (SICON) publishes original research articles on the mathematics and applications of control theory and certain parts of optimization theory. Papers considered for publication must be significant at both the mathematical level and the level of applications or potential applications. Papers containing mostly routine mathematics or those with no discernible connection to control and systems theory or optimization will not be considered for publication. From time to time, the journal will also publish authoritative surveys of important subject areas in control theory and optimization whose level of maturity permits a clear and unified exposition. The broad areas mentioned above are intended to encompass a wide range of mathematical techniques and scientific, engineering, economic, and industrial applications. These include stochastic and deterministic methods in control, estimation, and identification of systems; modeling and realization of complex control systems; the numerical analysis and related computational methodology of control processes and allied issues; and the development of mathematical theories and techniques that give new insights into old problems or provide the basis for further progress in control theory and optimization. Within the field of optimization, the journal focuses on the parts that are relevant to dynamic and control systems. Contributions to numerical methodology are also welcome in accordance with these aims, especially as related to large-scale problems and decomposition as well as to fundamental questions of convergence and approximation.