Enthalpy-based feedback control algorithms for the Stefan problem

A control law is derived for full-state feedback control of the single-phase Stefan problem, used as a model of industrial casting processes. A conceptually novel controller design approach is proposed for this problem, with the control law chosen to ensure exponential stability of the average enthalpy, and proven to guarantee asymptotic convergence of both the temperature field and the solidification front position to a desired reference. A plausible output feedback control algorithm is also given that demonstrates good behavior in simulation.

[1]  M. Krstić Boundary Control of PDEs: A Course on Backstepping Designs , 2008 .

[2]  Michael Hinze,et al.  Optimal control of the free boundary in a two-phase Stefan problem , 2007, J. Comput. Phys..

[3]  Nicholas Zabaras,et al.  Control of the freezing interface motion in two‐dimensional solidification processes using the adjoint method , 1995 .

[4]  Jürgen Sprekels,et al.  Automatic Control via Thermostats of a Hyperbolic Stefan Problem with Memory , 1999 .

[5]  B. Furenes,et al.  Solidification and control of a liquid metal column , 2006, Simul. Model. Pract. Theory.

[6]  Bryan Petrus,et al.  Feedback control of the two-phase Stefan problem, with an application to the continuous casting of steel , 2010, 49th IEEE Conference on Decision and Control (CDC).

[7]  Philippe Martin,et al.  Boundary control of a nonlinear Stefan problem , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[8]  Xiaoxu Zhou,et al.  Real-Time, Model-Based Spray-Cooling Control System for Steel Continuous Casting , 2011 .

[9]  J. A. Walker,et al.  Dynamical Systems and Evolution Equations , 1980 .

[10]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[11]  P. Neittaanmäki,et al.  Optimal Control of Nonlinear Parabolic Systems: Theory: Algorithms and Applications , 1994 .

[12]  Y. Meng,et al.  Heat-transfer and solidification model of continuous slab casting: CON1D , 2003 .

[13]  O. Ladyženskaja Linear and Quasilinear Equations of Parabolic Type , 1968 .

[14]  M. Krstić,et al.  Boundary Control of PDEs , 2008 .

[15]  Xiaoxu Zhou,et al.  IMPLEMENTATION OF A REAL-TIME MODEL-BASED SPRAY- COOLING CONTROL SYSTEM FOR STEEL CONTINUOUS CASTING , 2011 .

[16]  W. Marsden I and J , 2012 .

[17]  C. Saguez Optimal control of free boundary problems , 1986 .

[18]  T. K. Caughey,et al.  Dynamical Systems and Evolution Equations: Theory and Applications , 1980 .