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Delay compensated control of the Stefan problem and robustness to delay mismatch
Author(s) -
Koga Shumon,
BreschPietri Delphine,
Krstic Miroslav
Publication year - 2020
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.4909
Subject(s) - setpoint , control theory (sociology) , backstepping , robustness (evolution) , stefan problem , nonlinear system , actuator , ode , mathematics , computer science , adaptive control , mathematical analysis , physics , boundary (topology) , control (management) , biochemistry , chemistry , quantum mechanics , artificial intelligence , gene
Summary This paper presents a control design for the one‐phase Stefan problem under actuator delay via a backstepping method. The Stefan problem represents a liquid‐solid phase change phenomenon which describes the time evolution of a material's temperature profile and the interface position. The actuator delay is modeled by a first‐order hyperbolic partial differential equation (PDE), resulting in a cascaded transport‐diffusion PDE system defined on a time‐varying spatial domain described by an ordinary differential equation (ODE). Two nonlinear backstepping transformations are utilized for the control design. The setpoint restriction is given to guarantee a physical constraint on the proposed controller for the melting process. This constraint ensures the exponential convergence of the moving interface to a setpoint and the exponential stability of the temperature equilibrium profile and the delayed controller in theℋ 1norm. Furthermore, robustness analysis with respect to the delay mismatch between the plant and the controller is studied, which provides analogous results to the exact compensation by restricting the control gain.