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Delay compensated control of the Stefan problem and robustness to delay mismatch

Abstract : 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 the  1 norm. 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.
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Submitted on : Wednesday, October 28, 2020 - 5:00:40 PM
Last modification on : Thursday, August 26, 2021 - 1:34:02 PM
Long-term archiving on: : Friday, January 29, 2021 - 7:26:33 PM

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Shumon Koga, Delphine Bresch-Pietri, Miroslav Krstic. Delay compensated control of the Stefan problem and robustness to delay mismatch. International Journal of Robust and Nonlinear Control, Wiley, 2020, 30 (6), pp.2304-2334. ⟨10.1002/rnc.4909⟩. ⟨hal-02982645⟩

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