Method and apparatus for controlling a slab reheat furnace

Claim 2

For use with a slab reheat furnace having at least one zone with a controllable heating means, a method of controlling the heating means including the steps of: a. predicting the average temperature of each slab in the zone as a function of the gas temperature in the zone and the thermal properties, dimensions, location, velocity and past thermal history of each slab; b. establishing a deviation between the predicted average temperature of each slab and a desired average temperature at the location of the slab; c. establishing a performance index as a function of the combined deviations of all slabs in the zone; and d. adjusting the output of the heating means as a function of the established performance index.

Claim 3

A method of the type recited in claim 1 wherein the steps of said method are repeated following each change in the number or location of slabs in the zone or after an interval of predetermined length if no change in number or location has occurred during the interval.

Claim 4

A method as recited in claim 2 wherein the step of predicting the average temperature of each slab includes the steps of: a. predicting the temperature at surface and center slices in each slab as a function of the temperatures in the zone and the thermal properties, dimensions, location, velocity and past thermal history of the slab; and b. combining the predicted surface and center temperatures according to an assumed temperature distribution through the thickness of the slab to establish an average temperature.

Claim 5

A method as recited in claim 2 wherein the performance index is established by: a. weighting the calculated deviation of each slab as a function of the slab location within the zone whereby the deviation of a slab near the exit from the zone is given greater weight than the deviation of a slab nearer the entrance to the zone; and b. adding the weighted deviation of all slabs in the zone to establish the performance index.

Claim 6

A method as recited in claim 2 including the further step of revising the value given a thermal property of a slab by: a. measuring the surface temperature of the slab in a particular location in the zone; b. calculating the surface temperature of the slab in that location; c. comparing the measured surface temperature with the calculated surface temperature to establish a temperature deviation; and d. adjusting the magnitude of the value given a thermal property for use during future calculations as a function of the established temperature deviation.

Claim 7

A method as recited in claim 2 including the further steps of revising the value given a thermal property of a slab by: a. measuring the surface temperature of a slab at a particular location in the milL after the slab is discharged from the furnace; b. calculating the surface temperature of the slab at the same location in the mill by calculating the surface temperature of the slab at the time of discharge from the furnace and by subtracting calculated temperature losses during the travel of the slab to the particular location; c. comparing the measured surface temperature with the calculated surface temperature to establish a temperature deviation; and d. adjusting the magnitude of a thermal property for use in future calculations as a function of the established temperature deviation.

Claim 8

A method as recited in claim 2 wherein the average temperature of each slab is predicted by: a. determining the temperatures in surface and center slices of a slab by integrating the following simultaneous, nonlinear differential equations wherein Ts is the predicted temperature in the surface slice, Tc is the predicted temperature in the center slice, Tg is the gas temperature in the zone at the slab location. K1, K2, K3, and K4 are constants dependent upon the properties of the slab, epsilon is the emissivity of the slab, and h is the thickness of the slab; and b. establishing an average temperature using the values of Ts and Tc and assuming a parabolic heat distribution through the thickness of the slab.

Claim 9

A method as recited in claim 2 including the further step of limiting the adjustment of the output of said heating means to a predetermined maximum to avoid washing of slab surfaces.

Claim 10

A method as recited in claim 3 wherein the temperatures in the zone are established by: a. measuring the gas temperatures in the zone in at least two different locations; and b. establishing a zone temperature profile conforming to a predetermined pattern and having magnitudes proportional to the measured ambient temperatures.

Claim 11

A method as recited in claim 3 wherein the performance index is established by: a. weighting the calculated deviation of each slab as a function of the location of the slab within the zone whereby the deviation of a slab near the exit from the zone is given greater weight than the deviation of a slab nearer the entrance to the zone; and b. adding the weighted deviations of all slabs in the zone to establish the performance index.

Claim 12

A method as recited in claim 14 including the further step of limiting the adjustment of the output of said heating means to a predetermined maximum to avoid washing of slab surfaces.

Claim 13

A method as recited in claim 9 wherein the performance index is established by: a. weighting the calculated deviation of each slab as a function of the location of the slab within the zone whereby the deviation of a slab near the exit from the zone is given greater weight than the deviation of a slab nearer the entrance to the zone; and b. adding the weighted deviations of all slabs in the zone to establish the performance index.

Claim 14

A control system for use with a slab reheat furnace having at least one zone with controllable heating means, said system including: a. means for predicting the temperatures in surface and center slices of each slab in the zone as a function of the temperatures in the zone and the thermal properties, dimensions, location, and past thermal history of each slab; b. means for establishing an average temperature in the slab; c. means for subtracting the established average temperature of each slab from a predetermined desired temperature of a slab in the same location to establish a temperature deviation for each slab; d. means for combining the established temperature deviations to establish a performance index for the zone; and e. means for adjusting the output of the heating means as a function of the established performance index.

Claim 15

A control system for use with a slab reheat furnace having at least one zone with controllable heating means, said system including: a. means for predicting the temperatures in surface and center slices of each slab in the zone as a function of the temperatures in the zone and the thermal properties, dimensions, location, and past thermal history of each slab; b. means for establishing an average temperature in the slab; c. means for subtracting the established average temperature of each slab from a predetermined desired temperature of a slab in the same location to establish a temperature deviation for each slab; d. means for combining the established temperature deviations to establish a performance index for the zone; and e. means for adjusting the output of the heating means as a function of the established performance index.

Claim 16

A control system as recitEd in claim 13 further including means for initiating operation of said system following each change in number or location of slabs within the zone or after an interval of predetermined length if no change in number or location has occurred during the interval.

Claim 17

A control system as recited in claim 13 further including: a. means for measuring the gas temperatures in at least two spaced locations in the zone; b. function-generating means for generating a zone temperature profile as a function of the measured ambient temperatures.

Claim 18

A control system as recited in claim 13 wherein said combining means further includes: a. means for weighting the established temperature of each slab in accordance with the location of the slab in the zone; and b. means for summing the weighted deviations of all slabs in the zone.

Claim 19

A control system as recited in claim 13 further including: a. means for measuring the surface temperature of a slab at a predetermined location in the zone; b. means for establishing the deviation between the measured surface temperature of the slab and the calculated surface temperature of the slab; and c. means for altering the values assigned a thermal property of all slabs as a function of the established temperature deviation.

Claim 20

A control system as recited in claim 13 further including: a. means for calculating the surface temperature of a slab at a time of discharge from the furnace; b. means for measuring the surface temperature of the slab at a predetermined location in the mill after the slab has been discharged from the furnace; c. means for calculating the temperature losses of the slab during the time required for the slab to travel from the furnace to the predetermined location of the measured means; d. means for comparing the measured surface temperature with the calculated discharge surface temperature minus the calculated temperature losses to establish a temperature deviation; and e. means for altering the values assigned a thermal property of all slabs as a function of the established temperature deviation.

Claim 21

A control system as recited in claim 13 further including means for limiting the adjustment performed by said adjusting means to predetermined maximum to avoid washing of slab surfaces.

Claim 22

A control system as recited in claim 14 wherein said combining means further includes: a. means for weighting the established temperature deviation of each slab in accordance with the location of the slab within the zone; and b. means for summing the weighted deviations of all slabs in the zone.

Claim 23

A control system as recited in claim 14 further including means for limiting the adjustment performed by said adjusting means to predetermined maximum to avoid washing of slab surfaces.

Claim 24

A control system as recited in claim 14 further including: a. means for measuring the surface temperature of a slab at a predetermined location in the zone; b. means for establishing the deviation between the measured surface temperature of a slab and the calculated surface temperature of the slab; and c. means for altering the values assigned a thermal property of all slabs as a function of the established temperature deviation.

Claim 25

A control system as recited in claim 14 further including: a. means for calculating the surface temperature of a slab at its time of discharge from the furnace; b. means for measuring the surface temperature of a slab at a predetermined location in the mill after the slab has been discharged from the furnace; c. means for calculating the temperature losses of the slab during the time required for the slab to travel from the furnace to the predetermined location of the measuring means; d. means for comparing the measured surface temperature with the calculated discharge surface temperature minus the calculated temperature losses to establish a temperature deviation; and e. means for altering the values asSigned a thermal property of all slabs as a function of the established temperature deviation.