Method for controlling furnace temperature

Claim 1

A method of controlling furnace temperature for use with a slab heating furnace having a zone with controllable heating means, including the steps of: (a) calculating a desired temperature profile of a slab as it progresses through a furnace divided into sub-zones along its length, said calculation minimizing total fuel flow and based on shape information of said slab, slab temperature at a prior position within said furnace, and the predetermined slab temperature at a discharge position of the furnace; (b) predicting the distribution of the gas temperature at each said subzone along the length of the furnace; (c) calculating the present slab temperature distribution by using said distribution of said gas temperature predicted in step (b); (d) comparing said slab temperature calculated in step (c) at the present time with said desired slab temperature calculated in step (a) to produce a difference between them; and (e) adjusting the output of said heating means according to said temperature deviation produced in step (d); wherein said desired temperature curve is predicted based on the T si which minimizes W T and said T si is calculated according to the equation ##EQU17## where W T is the total injected fuel flow, H g is the heat produced per unit of fuel flow, T si is the slab temperature in the ith subzone, T gi is the temperature at the center of the ith subzone, C pg is the specific heat of the exhausted gas, C is a constant relating the volume of exhausted gas to the fuel flow, A i and B i are constants depending on the structure of the furnace, T si is the slab temperature in the ith subzone, C p is the specific heat of the slab, E i is equal to (C p ·γ·H·v)/(D i ·l i ·2) where γ is the specific gravity of the slab; H is the thickness of the slab, D i is the radiative heat conversion coefficient, l i is the length of the ith subzone, and v is the velocity of the moving slab.

Claim 2

A method of controlling furnace temperature for use with a slab heating furnace having a zone with controllable heating means, including the steps of: (a) calculating a desired temperature profile of a slab as it progresses through a furnace divided into sub-zones along its length, said calculation minimizing total fuel flow and based on shape information of said slab, slab temperature at a prior position within said furnace, and the predetermined slab temperature at a discharge position of the furnace; (b) predicting the distribution of the gas temperature at each said subzone along the length of the furnace; (c) calculating the present slab temperature distribution by using said distribution of said gas temperature predicted in step (b); (d) comparing said slab temperature calculated in step (c) at the present time with said desired slab temperature calculated in step (a) to produce a difference between them; and (e) adjusting the output of said heating means according to said temperature deviation produced in step (d); wherein said desired temperature curve is predicted based on the T si which minimizes W T and said T si is calculated according to the equation ##EQU17## where W T is the total injected fuel flow, H g is the heat produced per unit of fuel flow, T si is the slab temperature in the ith subzone, T gi is the temperature at the center of the ith subzone, C pg is the specific heat of the exhausted gas, C is a constant relating the volume of exhausted gas to the fuel flow, A i and B i are constants depending on the structure of the furnace, T si is the slab temperature in the ith subzone, C p is the specific heat of the slab, E i is equal to (C p ·γ·H·v)/(D i ·l i ·2) where γ is the specific gravity of the slab; H is the thickness of the slab, D i is the radiative heat conversion coefficient, l i is the length of the ith subzone, and v is the velocity of the moving slab.