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A semi‐discrete approach to modelling and control of the continuous casting process
Author(s) -
Guo Baozhu,
Xia Xiaohua,
CamisaniCalzolari Ferdinando Roux,
Craig Ian K.
Publication year - 2000
Publication title -
steel research
Language(s) - English
Resource type - Journals
eISSN - 1869-344X
pISSN - 0177-4832
DOI - 10.1002/srin.200001220
Subject(s) - controllability , partial differential equation , linearization , mathematics , heat equation , heat transfer , ordinary differential equation , nonlinear system , boundary (topology) , transformation (genetics) , continuous casting , distributed parameter system , boundary value problem , mathematical analysis , parabolic partial differential equation , control theory (sociology) , differential equation , control (management) , computer science , mechanics , physics , materials science , biochemistry , chemistry , quantum mechanics , artificial intelligence , composite material , gene
Starting from a partial differential equation describing the heat transfer in the continuous casting of steel, the Kirchhoff transformation is used to obtain a more simplified governing heat equation. A boundary state and control transformation is then introduced to obtain a nonlinear heat equation with boundary control. The semi‐discrete approximation is applied in the investigation to obtain an ordinary differential equation model. The derived lumped parameter control model can be used to get an approximate solution for the system as well as for finite dimensional system control studies. Finally, local controllability is proved for the system using a linearization technique.