Control of Two-Phase Stefan Problem via Single Boundary Heat Input

被引:0
|
作者
Koga, Shumon [1 ]
Krstic, Miroslav [1 ]
机构
[1] Univ Calif San Diego, Dept Mech & Aerosp Engn, 9500 Gilman Dr, La Jolla, CA 92093 USA
关键词
NUMERICAL-SOLUTION;
D O I
暂无
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
This paper presents the control design of the two-phase Stefan problem via a single boundary heat input. 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. As an extension from our previous study on the one-phase Stefan problem, we design a state feedback control law to stabilize the interface position to a desired setpoint by employing the backstepping method. 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 L-2 norm. Numerical simulation is provided to illustrate the good performance of the proposed control law.
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页码:2914 / 2919
页数:6
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