Feedback Stabilization of Tank-Liquid System with Robustness to Surface Tension
Abstract
We construct a robust stabilizing feedback law for the viscous Saint-Venant system of Partial Differential Equations (PDEs) with surface tension and without wall friction. The Saint-Venant system describes the movement of a tank which contains a viscous liquid. We assume constant contact angles between the liquid and the walls of the tank and we achieve a spill-free exponential stabilization with robustness to surface tension by using a Control Lyapunov Functional (CLF). The proposed CLF provides a parameterized family of sets which approximate the state space from the interior. Based on the CLF, we construct a nonlinear stabilizing feedback law which ensures that the closed-loop system converges exponentially to the desired equilibrium point in the sense of an appropriate norm.
Keywords
Cite
@article{arxiv.2301.01688,
title = {Feedback Stabilization of Tank-Liquid System with Robustness to Surface Tension},
author = {Iasson Karafyllis and Filippos Vokos and Miroslav Krstic},
journal= {arXiv preprint arXiv:2301.01688},
year = {2023}
}
Comments
24 pages, submitted to Systems & Control Letters for possible publication. arXiv admin note: text overlap with arXiv:2206.01385