PI Control for the Cascade Channels Modeled by General Saint-Venant Equations

• 成果类型: Article
• 署名作者: Hayat, Amaury; Hu, Yating; Shang, Peipei
• 署名单位: Institut Polytechnique de Paris; Ecole des Ponts ParisTech; Tongji University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3341767
• 发表日期: 2024
• 页码: 4974-4987
• 关键词: mathematical models; friction; steady-state; regulation; irrigation; control theory; Numerical stability; feedback stabilization; hyperbolic systems; Lyapunov approach; Saint-Venant equations

摘要

The input-to-state stability of the nonhorizontal cascade channels with different arbitrary cross section, slope, and friction modeled by Saint-Venant equations is addressed in this article. The control input and measured output are both on the collocated boundary. The proportional-integral (PI) control is proposed to study both the exponential stability and the output regulation of closed-loop systems with the aid of the Lyapunov approach. An explicit quadratic Lyapunov function as a weighted function of a small perturbation of the nonuniform steady-states of different channels is constructed. We show that by a suitable choice of the boundary feedback controls, the local exponential stability and the input-to-state stability of the nonlinear Saint-Venant equations for the H(2 )norm are guaranteed, then validated with numerical simulations. Meanwhile, the output regulation and the rejection of constant disturbances are realized as well.