Single-boundary control of the two-phase Stefan system
Single-boundary control of the two-phase Stefan system
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DOI：
10.1016/j.sysconle.2019.104573
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发表时间：
2020-01-01
影响因子：
2.6
通讯作者：
Krstic, Miroslav
中科院分区：
文献类型：
--
作者：
Koga, Shumon;Krstic, Miroslav
本文介绍了两相斯蒂芬问题的控制设计。两相Stefan问题是一种典型的液固相变模型，它描述了温度分布的时间演变，温度分布被液固两相的子域划分为液固两相的移动界面位置。由两个扩散偏微分方程（PDEs）定义在一个时变空间域中，由两个状态的诺依曼边值驱动的常微分方程（ODE）描述，从而得到一个非线性耦合的PDE-ODE-PDE系统。利用单边界热输入，设计了一种状态反馈控制律，通过能量整形将界面位置稳定在期望的设定值上。我们证明了控制律下的闭环系统保证了模型有效性的一些条件，并在空间L-2范数上给出了全局指数稳定性估计。进一步证明了闭环稳定性对物理参数不确定性的鲁棒性。通过数值仿真，将所提出的控制律与单相斯特芬问题的控制设计相比较，说明了所提出的控制律的理想性能。(C) 2019 Elsevier B.V.版权所有
This paper presents the control design of the two-phase Stefan problem. The two-phase Stefan problem is a representative model of liquid-solid phase transition by describing the time evolutions of the temperature profile, which is divided by subdomains of liquid and solid phases as the liquid-solid moving interface position. The mathematical formulation is given by two diffusion partial differential equations (PDEs) defined on a time-varying spatial domain described by an ordinary differential equation (ODE) driven by the Neumann boundary values of both PDE states, resulting in a nonlinear coupled PDE-ODE-PDE system. We design a state feedback control law by means of energy-shaping to stabilize the interface position to a desired setpoint by using single boundary heat input. We prove that the closed-loop system under the control law ensures some conditions for model validity, and the global exponential stability estimate is shown in the spatial L-2 norm. Furthermore, the robustness of the closed-loop stability with respect to the uncertainties of the physical parameters is shown. Numerical simulation is provided to illustrate the desired performance of the proposed control law in comparison to the control design for the one-phase Stefan problem. (C) 2019 Elsevier B.V. All rights reserved.