Abstract
A mathematical model for the continuous casting of mild steel was developed and compared with experimental data. This model was then used as a basis for a nonlinear state estimation algorithm which provides on-line estimates of the solidified crust thickness and solid temperature distribution based only on noisy steel surface measurements. The computational algorithm, which makes use of eigenfunction decomposition methods, was found to be computationally efficient, and the filter performed well under simulation, even in the face of large temperature measurement errors.
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Abbreviations
- A,B,c,E,D,a:
-
Eigen-coefficients
- b′:
-
Solid crust thickness
- b:
-
Dimensionless solid crust thickness
- h:
-
Heat transfer coefficient at mould wall
- hℓ :
-
Heat transfer coefficient at liquid surface
- H:
-
Dimensionless heat transfer coefficient
- k:
-
Thermal conductivity
- L :
-
Latent heat of solidification
- ℓ:
-
Distance from mould surface to liquidus line
- L:
-
Distance from the mould surface to its center
- Puu,Pub,Pbu,Pbb :
-
Differential sensitivities
- R−1,R+,R −10 ,Q:
-
Weighting factors
- r:
-
Normalized distance from the mould surface
- t:
-
Time
- T:
-
Temperature
- uS :
-
Dimensionless temperature
- uC :
-
Casting speed
- x:
-
Distance below meniscus
- z:
-
Distance from the mould surface
- α:
-
Thermal diffusivity
- λ:
-
Eigenvalue
- φ:
-
Eigenfunction
- ρ:
-
Density
- τ:
-
Scaled time
- ψ:
-
Initial condition
- ℓ:
-
Liquid region
- m:
-
Mushy region
- Liq:
-
Liquidus line
- S:
-
Solid region
- Sol:
-
Solidus line
References
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Greiss, F.K., Ray, W.H. (1977). The application of distributed parameter state estimation theory to a metallurgical casting operation. In: Bensoussan, A., Lions, J.L. (eds) New Trends in Systems Analysis. Lecture Notes in Control and Information Sciences, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0041111
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DOI: https://doi.org/10.1007/BFb0041111
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