Steel sheet temperature control device and temperature control method

Abstract

A steel sheet temperature control device including: a sheet temperature measurement unit; a furnace temperature measurement unit; an influence coefficient calculation unit; a control model setting unit that sets a control model; a state variable/disturbance estimation unit that estimates values of a state variable and a temperature disturbance variable of the control model at the same time; a furnace temperature change amount calculation unit that calculates a furnace temperature change amount of each of heating zones of a heating furnace under a constraint condition such that square sum of a deviation between a target value and the actual value of the temperature of the steel sheet at the outlet side of the heating furnace becomes minimum; and a furnace temperature control unit that controls a fuel flow rate used in each of the heating zones to achieve the calculated furnace temperature change amount.

Claims

1. A steel sheet temperature control device, comprising: a sheet temperature measurement unit that measures temperature of a steel sheet at an inlet side and an outlet side of a heating furnace including a plurality of heating zones disposed along a conveyance direction of the steel sheet; a furnace temperature measurement unit that measures furnace temperature of each of the heating zones; and a process computer configured to execute a process, the process including: calculating an influence coefficient representing temperature change of the steel sheet at the outlet side of the heating furnace in response to temperature change of the steel sheet at the inlet side of the heating furnace, and an influence coefficient representing temperature change of the steel sheet at the outlet side of the heating furnace in response to change in the furnace temperature of each of the heating zones, using a heating model equation capable of calculating the temperature of the steel sheet in the heating furnace, by inputting a set value of the temperature of the steel sheet at the inlet side of the heating furnace, and set values of the furnace temperature of each of the heating zones and sheet passing speed; setting a control model by inputting a furnace temperature change command value and outputting the furnace temperature of each of the heating zones and the temperature of the steel sheet at the outlet side of the heating furnace, by using the calculated influence coefficient, transfer time of the steel sheet until influence of furnace temperature change in each of the heating zones appears on the temperature of the steel sheet at the outlet side of the heating furnace, a time constant from when the furnace temperature change command value of each of the heating zones is output to when the furnace temperature is actually changed, and a variable representing unknown temperature disturbance to be applied to the temperature of the steel sheet at the outlet side of the heating furnace; estimating values of a state variable and a temperature disturbance variable of the control model at the same time, by inputting a deviation between an actual value of the temperature of the steel sheet at the inlet side of the heating furnace measured by the sheet temperature measurement unit and a set value, a deviation between an actual value of the temperature of the steel sheet at the outlet side of the heating furnace measured by the sheet temperature measurement unit and a set value, and a deviation between an actual value of the furnace temperature of each of the heating zones measured by the furnace temperature measurement unit and an initial set value; calculating a furnace temperature change amount of each of the heating zones under a constraint condition such that square sum of a deviation between a target value and the actual value of the temperature of the steel sheet at the outlet side of the heating furnace becomes minimum, by using the estimated values of the state variable and the temperature disturbance variable of the control model; and controlling a fuel flow rate used in each of the heating zones to achieve the calculated furnace temperature change amount.

2. The steel sheet temperature control device according to claim 1, wherein calculating the furnace temperature change amount includes at least one of constraint condition relating to upper and lower limit values of the furnace temperature, constraint condition relating to the furnace temperature change amount per unit time, constraint condition relating to upper and lower limit values of the fuel flow rate, and condition relating to the fuel flow rate change amount per unit time, as the constraint condition.

3. The steel sheet temperature control device according to claim 1, wherein the calculating of the influence coefficient, the setting, the estimating, and the calculating of the furnace temperature change amount are performed for each set value of a plurality of sheet passing speeds assumable during an actual operation, and the controlling includes controlling a fuel flow rate used in each of the heating zones to achieve the furnace temperature change amount calculated from the set value of the sheet passing speed close to actual sheet passing speed.

4. A steel sheet temperature control method, comprising: smeasuring temperature of a steel sheet at an inlet side and an outlet side of a heating furnace including a plurality of heating zones disposed along a conveyance direction of the steel sheet; measuring furnace temperature of each of the heating zones; calculating a first influence coefficient representing temperature change of the steel sheet at the outlet side of the heating furnace in response to temperature change of the steel sheet at the inlet side of the heating furnace, and a second influence coefficient representing temperature change of the steel sheet at the outlet side of the heating furnace in response to change in the furnace temperature of each of the heating zones, using a heating model equation capable of calculating the temperature of the steel sheet in the heating furnace, by inputting a set value of the temperature of the steel sheet at the inlet side of the heating furnace, and set values of the furnace temperature of each of the heating zones and sheet passing speed; setting a control model by inputting a furnace temperature change command value and outputting the furnace temperature of each of the heating zones and the temperature of the steel sheet at the outlet side of the heating furnace, by using the first influence coefficient and the second influence coefficient, transfer time of the steel sheet until influence of furnace temperature change in each of the heating zones appears on the temperature of the steel sheet at the outlet side of the heating furnace, a time constant from when the furnace temperature change command value of each of the heating zones is output to when the furnace temperature is actually changed, and a variable representing unknown temperature disturbance to be applied to the temperature of the steel sheet at the outlet side of the heating furnace; estimating values of a state variable and a temperature disturbance variable of the control model at the same time, by inputting a deviation between an actual value of the measured temperature of the steel sheet at the inlet side of the heating furnace and a set value, a deviation between an actual value of the measured temperature of the steel sheet at the outlet side of the heating furnace and a set value, and a deviation between an actual value of the measured furnace temperature of each of the heating zones and an initial set value; calculating a furnace temperature change amount of each of the heating zones under a constraint condition such that square sum of a deviation between a target value and the actual value of the temperature of the steel sheet at the outlet side of the heating furnace becomes minimum, by using the estimated values of the state variable and the temperature disturbance variable of the control model; and controlling a fuel flow rate used in each of the heating zones to achieve the calculated furnace temperature change amount.

5. The steel sheet temperature control device according to claim 2, wherein calculating of the influence coefficient, the setting, the estimating, and the calculating of the furnace temperature change amount are performed for each set value of a plurality of sheet passing speeds assumable during an actual operation, and the controlling includes controlling a fuel flow rate used in each of the heating zones to achieve the furnace temperature change amount calculated from the set value of the sheet passing speed close to actual sheet passing speed.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a block diagram illustrating a configuration of a steel sheet temperature control device according to an embodiment of the present invention.

(2) FIG. 2 is a block diagram illustrating a configuration of a conventional steel sheet temperature control device.

(3) FIG. 3 is a diagram illustrating a disturbance applied to the temperature of a steel sheet at the inlet side and the outlet side of a heating furnace.

(4) FIG. 4 is a diagram illustrating furnace temperature of each heating zone and temperature response of the steel sheet at the outlet side of the heating furnace in accordance with aspects of the present invention method.

(5) FIG. 5 is a diagram illustrating furnace temperature of each heating zone and temperature response of the steel sheet at the outlet side of the heating furnace in a conventional method.

(6) FIG. 6 is a diagram illustrating a disturbance applied to the temperature of the steel sheet at the outlet side of the heating furnace.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

(7) Hereinafter, a configuration of a steel sheet temperature control device according to an embodiment of the present invention and the operation thereof will be described in detail with reference to the accompanying drawings.

(8) FIG. 1 is a block diagram illustrating a configuration of a steel sheet temperature control device according to the embodiment of the present invention. As illustrated in FIG. 1, a steel sheet temperature control device 1 according to the embodiment of the present invention is a device that controls the temperature of a steel sheet in a heating furnace including n 1) pieces (five in the present embodiment) of heating zones disposed along a conveyance direction of the steel sheet.

(9) The steel sheet temperature control device 1 according to the embodiment of the present invention includes a sheet temperature measurement unit 11, a furnace temperature measurement unit 12, an influence coefficient calculation unit 13, a control model setting unit 14, a state variable/disturbance estimation unit 15, a furnace temperature change amount calculation unit 16, and a furnace temperature control unit 17 as main components.

(10) The sheet temperature measurement unit 11 measures the temperature (sheet temperature) of a steel sheet at the inlet side and the outlet side of the heating furnace at each predetermined period, and outputs an electric signal representing the sheet temperature to the state variable/disturbance estimation unit 15.

(11) The furnace temperature measurement unit 12 measures the actual value of the temperature (furnace temperature) of each heating zone in the heating furnace at each predetermined period, and outputs an electric signal representing the measured furnace temperature of each heating zone, to the state variable/disturbance estimation unit 15, the furnace temperature change amount calculation unit 16, and the furnace temperature control unit 17.

(12) The influence coefficient calculation unit 13 obtains a set value of the temperature of the steel sheet at the inlet side of the heating furnace, a furnace temperature set value and a sheet passing speed set value of each heating zone that are output from a process computer 21 in response to receiving an annealing command of the steel sheet. The influence coefficient calculation unit 13 calculates an influence coefficient representing the temperature change of the steel sheet at the outlet side of the heating furnace in response to the temperature change of the steel sheet at the inlet side of the heating furnace, and an influence coefficient representing the temperature change of the steel sheet at the outlet side of the heating furnace in response to the temperature change of the steel sheet in each heating zone, using the information obtained from the process computer 21. The influence coefficient calculation unit 13 then outputs electric signals representing the influence coefficients to the control model setting unit 14. A method for calculating the influence coefficients will now be described.

(13) When the set value of the temperature of the steel sheet at the inlet side of the heating furnace is T.sub.in, the set value of the sheet passing speed is V.sub.s, and the furnace temperature set value of each heating zone is T.sub.wi (i=1 to 5), the temperature T.sub.s of the steel sheet at the outlet side of the heating furnace is represented as T.sub.s=f (T.sub.in, V.sub.s, T.sub.w1, T.sub.w2, T.sub.w3, T.sub.w4, T.sub.w5). In this example, the function f is a heating model equation of a steel sheet in the heating furnace based on the following equation (1). In calculating a numerical value, the equation (1) calculates a difference by discretizing at a suitable time step Δt. In the equation (1), ρ represents specific heat [kcal/kg/K] of the steel sheet, C represents specific gravity [kg/m.sup.3] of the steel sheet, h represents sheet thickness [m] of the steel sheet, T.sub.s represents temperature [° C.] of the steel sheet, T.sub.w represents furnace temperature [° C.], ϕ.sub.cg represents the total heat transfer coefficient [−], σ represents a Stefan-Boltzmann constant (=1.3565e.sup.−11 [kcal/sec/m.sup.2/K.sup.4]), and t represents time [sec].

(14) $\begin{array}{cc}\rho .Math.C.Math.h.Math.\frac{\partial T_s\left(t\right)}{\partial t}=2{\varphi }_{\mathrm{cg}}\sigma \left({\left(T_w+273.15\right)}^4-{\left(T_s+273.15\right)}^4\right)& \left(1\right)\end{array}$

(15) The influence coefficient calculation unit 13 calculates an influence coefficient using the information obtained from the process computer 21, and using the following equations (2) to (7). In this example, the equation (2) represents an influence coefficient expressing the temperature change of the steel sheet at the outlet side of the heating furnace in response to the temperature change of the steel sheet at the inlet side of the heating furnace, and d.sub.1 in the equation (2) represents a variable representing the temperature variation of the steel sheet at the inlet side of the heating furnace. The equations (3) to (7) represent influence coefficients expressing the temperature change of the steel sheet at the outlet side of the heating furnace in response to the temperature change of the steel sheet in each heating zone.

(16) $\begin{array}{cc}\frac{\partial T_s}{\partial d_1}\cong \frac{\begin{array}{c}f\left(T_{\mathrm{in}}+\Delta d_1,V_s,T_{w_1},T_{w_2},T_{w_3},T_{w_4},T_{w_5}\right)-\\ f\left(T_{\mathrm{in}},V_s,T_{w_1},T_{w_2},T_{w_3},T_{w_4},T_{w_5}\right)\end{array}}{\Delta d_1}& \left(2\right)\\ \frac{\partial T_s}{\partial T_{w_1}}\cong \frac{\begin{array}{c}f\left(T_{\mathrm{in}},V_s,T_{w_1}+\Delta T,T_{w_2},T_{w_3},T_{w_4},T_{w_5}\right)-\\ f\left(T_{\mathrm{in}},V_s,T_{w_1},T_{w_2},T_{w_3},T_{w_4},T_{w_5}\right)\end{array}}{\Delta T}& \left(3\right)\\ \frac{\partial T_s}{\partial T_{w_2}}\cong \frac{\begin{array}{c}f\left(T_{\mathrm{in}},V_s,T_{w_1},T_{w_2}+\Delta T,T_{w_3},T_{w_4},T_{w_5}\right)-\\ f\left(T_{\mathrm{in}},V_s,T_{w_1},T_{w_2},T_{w_3},T_{w_4},T_{w_5}\right)\end{array}}{\Delta T}& \left(4\right)\\ \frac{\partial T_s}{\partial T_{w_3}}\cong \frac{\begin{array}{c}f\left(T_{\mathrm{in}},V_s,T_{w_1},T_{w_2},T_{w_3}+\Delta T,T_{w_4},T_{w_5}\right)-\\ f\left(T_{\mathrm{in}},V_s,T_{w_1},T_{w_2},T_{w_3},T_{w_4},T_{w_5}\right)\end{array}}{\Delta T}& \left(5\right)\\ \frac{\partial T_s}{\partial T_{w_4}}\cong \frac{\begin{array}{c}f\left(T_{\mathrm{in}},V_s,T_{w_1},T_{w_2},T_{w_3},T_{w_4}+\Delta T,T_{w_5}\right)-\\ f\left(T_{\mathrm{in}},V_s,T_{w_1},T_{w_2},T_{w_3},T_{w_4},T_{w_5}\right)\end{array}}{\Delta T}& \left(6\right)\\ \frac{\partial T_s}{\partial T_{w_5}}\cong \frac{\begin{array}{c}f\left(T_{\mathrm{in}},V_s,T_{w_1},T_{w_2},T_{w_3},T_{w_4},T_{w_5}+\Delta T\right)-\\ f\left(T_{\mathrm{in}},V_s,T_{w_1},T_{w_2},T_{w_3},T_{w_4},T_{w_5}\right)\end{array}}{\Delta T}& \left(7\right)\end{array}$

(17) The control model setting unit 14 obtains the sheet passing speed set value of each heating zone and the time constant of the furnace temperature from the process computer 21. The control model setting unit 14 calculates a control model equation required in the state variable/disturbance estimation unit 15 and the furnace temperature change amount calculation unit 16, using the information obtained from the process computer 21. The control model setting unit 14 then outputs an electric signal representing a parameter of the calculated control model equation to the state variable/disturbance estimation unit 15 and the furnace temperature change amount calculation unit 16. A method for calculating the control model equation will now be described.

(18) When transfer time L.sub.1[s] for transferring a steel sheet from the inlet position of the i-th heating zone to the outlet side position of the heating furnace (distance/sheet passing speed set value from the inlet side position of the i-th heating zone to the outlet side of the heating furnace) is required, the temperature T.sub.s of the steel sheet at the outlet side of the heating furnace is represented by the following equation (8) using the influence coefficients in the equations (2) to (7). In this example, ΔT.sub.wi in the equation (8) is a differential value between the furnace temperature actual value and the furnace temperature set value of each heating zone, and represents the furnace temperature variation. Moreover, s is a Laplace operator.

(19) $\begin{array}{cc}\begin{array}{c}{T}_s=\left(\frac{\partial T_s}{\partial T_{w_1}}\Delta T_{w_1}+\frac{\partial T_s}{\partial d_1}{d}_1\right)e^{-L_{1}s}+\frac{\partial T_s}{\partial T_{w_2}}\Delta T_{w_2}{e}^{-L_{2}s}+\\ \frac{\partial T_s}{\partial T_{w_3}}\Delta T_{w_3}{e}^{-L_{3}s}+\frac{\partial T_s}{\partial T_{w_4}}\Delta T_{w_4}{e}^{-L_{4}s}+\frac{\partial T_s}{\partial T_{w_5}}\Delta T_{w_5}{e}^{-L_{5}s}\end{array}\}& \left(8\right)\end{array}$

(20) It is assumed that a feedback control system is built from the furnace temperature command value to the furnace temperature actual value, and the furnace temperature control system can be approximated by the dynamic characteristic described in the following equation (9). In this example, ΔT.sub.wi.sup.ref in the equation (9) represents the furnace temperature target value of each heating zone, and T.sub.i represents the time constant from the furnace temperature command value to the furnace temperature actual value of each heating zone.

(21) $\begin{array}{cc}\frac{\Delta T_{w_1}}{\Delta T_{w_1}^{\mathrm{ref}}}=\frac{1}{T_{i}s+1},i=1,2,3,4,5& \left(9\right)\end{array}$

(22) It is also assumed that the transfer time element e.sup.−Lis in the equation (8) can be linearized by Pade approximation as illustrated in the following equation (10). The equation (10) is the third-order equation. However, the order of equation can be suitably set by the designer. When the equation (10) is expressed in state space representation, the following equation (11) can be obtained. In the equation (11), x.sub.1, x.sub.2, and x.sub.3 are internal state variables, and may be optionally implemented. Consequently, x.sub.1, x.sub.2, and x.sub.3 do not have any physical meaning.

(23) $\begin{array}{cc}\frac{Y}{U}=e^{-\mathrm{Lis}}\approx \frac{b_2{s}^2+b_{1}s+b_0}{s^3+a_2{s}^2+a_{1}s+a_0}+d_0& \left(10\right)\\ \begin{array}{c}\frac{d}{\mathrm{dt}}\left[\begin{array}{c}{x}_1\\ x_2\\ x_3\end{array}\right]=\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ -a_0& -a_1& -a_2\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\\ x_3\end{array}\right]+\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right]u\\ y=\left[b_0{b}_1{b}_2\right]\left[\begin{array}{c}{x}_1\\ x_2\\ x_3\end{array}\right]+d_{0}u\end{array}\}& \left(11\right)\end{array}$

(24) When the equation (8) and the equation (11) are considered together, the state space representations to the sheet temperature variation T.sub.si from the furnace temperature variation ΔT.sub.wi of each heating zone and the temperature variation d.sub.1 of the steel sheet at the inlet side of the heating furnace are expressed by the following equations (12) and (13). In this example, the equation (12) represents the equation of the first heating zone, and the equation (13) represents the equation of the second to fifth heating zones. Moreover, T.sub.si represents the sheet temperature variable indicating the i-th term in the equation (8).

(25) $\begin{array}{cc}\begin{array}{c}\frac{d}{\mathrm{dt}}\left[\begin{array}{c}{x}_{10}\\ x_{11}\\ x_{12}\end{array}\right]=\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ -a_{10}& -a_{11}& -a_{12}\end{array}\right]\left[\begin{array}{c}{x}_{10}\\ x_{11}\\ x_{12}\end{array}\right]+\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right]\\ \left(\frac{\partial T_s}{\partial T_{w_1}}\Delta T_{w_1}+\frac{\partial T_s}{\partial d_1}{d}_1\right)\\ T_{s_1}=\left[b_{10}{b}_{11}{b}_{12}\right]\left[\begin{array}{c}{x}_{10}\\ x_{11}\\ x_{12}\end{array}\right]+d_{10}\left(\frac{\partial T_s}{\partial T_{w_1}}\Delta T_{w_1}+\frac{\partial T_s}{\partial d_1}{d}_1\right)\end{array}\}& \left(12\right)\\ \begin{array}{c}\frac{d}{\mathrm{dt}}\left[\begin{array}{c}{x}_{i0}\\ x_{i1}\\ x_{i2}\end{array}\right]=\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ -a_{i0}& -a_{i1}& -a_{i2}\end{array}\right]\left[\begin{array}{c}{x}_{i0}\\ x_{i1}\\ x_{i2}\end{array}\right]+\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right]\\ \left(\frac{\partial T_s}{\partial T_{w_i}}\Delta T_{w_i}\right)\\ T_{s_1}=\left[b_{i0}{b}_{i1}{b}_{i2}\right]\left[\begin{array}{c}{x}_{i0}\\ x_{i1}\\ x_{i2}\end{array}\right]+d_{i0}\left(\frac{\partial T_s}{\partial T_{w_i}}\Delta T_{w_i}\right)\end{array}\}& \left(13\right)\end{array}$

(26) Moreover, the state space representation of the dynamic characteristic equation of the furnace temperature control system represented by the equation (9) is expressed as the following equation (14).

(27) $\begin{array}{cc}\frac{d\Delta T_{w_i}}{\mathrm{dt}}=-\frac{1}{T_i}\Delta T_{w_i}+\frac{1}{T_i}\Delta T_{w_i}^{\mathrm{ref}},i=1,2,3,4,5& \left(14\right)\end{array}$

(28) The observable output of the furnace temperature control system is the furnace temperature variable ΔT.sub.wi of each heating zone and the temperature T.sub.s of the steel sheet at the outlet side of the heating furnace. When an unknown variable d.sub.2 indicating a disturbance applied to the temperature of the steel sheet at the outlet side of the heating furnace is introduced to the temperature T.sub.s of the steel sheet, the temperature T.sub.s of the steel sheet is expressed by the following equation (15). When it is assumed that the time differentiation of the temperature variable d.sub.1 of the steel sheet at the inlet side of the steel sheet is 0, as expressed by the equation (16), the state space representation expressed by the following equation (17) is obtained from the equations (12) to (16).

(29) $\begin{array}{cc}{T}_s=T_{s_1}+T_{s_2}+T_{s_3}+T_{s_4}+T_{s_5}+d_2& \left(15\right)\\ \frac{d}{\mathrm{dt}}{d}_1=0& \left(16\right)\\ \begin{array}{c}\frac{\mathrm{dx}}{\mathrm{dt}}=\mathrm{Ax}+\mathrm{Bu}+{\mathrm{Ed}}_2\\ y=\mathrm{Cx}+{\mathrm{Fd}}_2\end{array}\}\mathrm{where},x=\left[\begin{array}{c}\Delta T_{w_1}\\ \mathrm{.Math.}\\ \Delta T_{w_5}\\ x_{010}\\ x_{011}\\ x_{012}\\ \mathrm{.Math.}\\ x_{052}\\ d_1\end{array}\right]y=\left[\begin{array}{c}\Delta T_{w_1}\\ \mathrm{.Math.}\\ \Delta T_{w_5}\\ T_s\end{array}\right]u=\left[\begin{array}{c}\Delta T_{w_1}^{\mathrm{ref}}\\ \mathrm{.Math.}\\ \Delta T_{w_5}^{\mathrm{ref}}\end{array}\right]A\text{:}21\times 21\mathrm{matrix}B\text{:}21\times 5\mathrm{matrix}E\text{:}21\times 1\mathrm{matrix}C\text{:}6\times 20\mathrm{matrix}F\text{:}6\times 1\mathrm{matrix}& \left(17\right)\end{array}$

(30) The control model setting unit 14 then outputs the result obtained by discretizing the matrices A to F in the equation (17) (hereinafter, the continuous time representation and the discrete time representation are represented by the same symbol) by the control period, to the state variable/disturbance estimation unit 15 and the furnace temperature change amount calculation unit 16, as a parameter of the control model equation.

(31) The state variable/disturbance estimation unit 15 estimates the state variable and the disturbance variable of the control model equation calculated by the control model setting unit 14 at each control period, using an estimation method such as observer and Kalman filter, and outputs electric signals representing the estimated values to the furnace temperature change amount calculation unit 16. When the observer is used for estimation, the state variable/disturbance estimation unit 15 modifies the equation (17) to the following equation (18). The state variable/disturbance estimation unit 15 then designs an observer for the system. The following equation (19) is the observer, and is obtained by multiplying the observer gain L by a deviation between the observed value y and a model prediction value, while setting the state estimated value to x′ and the disturbance estimated value to d2′. The following equation (19) updates the estimated values of the state amount and the disturbance. In the equation (19), u(k) represents the furnace temperature target value of each heating zone input by the furnace temperature control unit 17. To design the observer gain, a designing method to stabilize the system has been known (for example, System Control Theory Introduction (Jikkyo Shuppan, 1979)).

(32) $\begin{array}{cc}\begin{array}{c}\left[\begin{array}{c}x\left(k+1\right)\\ d_2\left(k+1\right)\end{array}\right]=\left[\begin{array}{cc}A& E\\ 0_{1\times 21}& 1\end{array}\right]\left[\begin{array}{c}x\left(k\right)\\ d_2\left(k\right)\end{array}\right]x+\left[\begin{array}{c}B\\ 0_{1\times 5}\end{array}\right]u\left(k\right)\\ y\left(k\right)=\left[CF\right]\left[\begin{array}{c}x\left(k\right)\\ d_2\left(k\right)\end{array}\right]\end{array}\}& \left(18\right)\\ \left[\begin{array}{c}{x}^{\prime }\left(k+1\right)\\ d_2^{\prime }\left(k+1\right)\end{array}\right]=\left[\begin{array}{cc}A& E\\ 0_{1\times 21}& 1\end{array}\right]\left[\begin{array}{c}{x}^{\prime }\left(k\right)\\ d_2^{\prime }\left(k\right)\end{array}\right]+\left[\begin{array}{c}B\\ 0_{1\times 5}\end{array}\right]u\left(k\right)+L\left(y\left(k\right)-\left[CF\right]\left[\begin{array}{c}{x}^{\prime }\left(k\right)\\ d_2^{\prime }\left(k\right)\end{array}\right]\right)& \left(19\right)\end{array}$

(33) The furnace temperature change amount calculation unit 16 calculates the furnace temperature change amount such that the square sum of the deviation between the target value and the actual value of the temperature of the steel sheet at the outlet side of the heating furnace becomes minimum, in other words, the variation from the target value of the temperature of the steel sheet at the outlet side of the heating furnace becomes minimum, by using the estimated values of the state variable and the disturbance variable output from the state variable/disturbance estimation unit 15. This leads to a problem of minimizing the target function under the constraint conditions. More specifically, even though the equation (18) is already obtained as the control model equation, the input is modified as the following equation (20) to handle the variation constraint of the furnace temperature target value. The furnace temperature change amount calculation unit 16 then calculates the furnace temperature change amount Δu(k) with which the sheet temperature variation T.sub.s.sup.2 becomes minimum by using the control model equation. This is an optimization problem for calculating the time series data of the furnace temperature change amount Δu(k) for minimizing the evaluation function expressed by the following equation (21).

(34) 0$\begin{array}{cc}\begin{array}{c}\left[\begin{array}{c}x\left(k+1\right)\\ d\left(k+1\right)\\ u\left(k+1\right)\end{array}\right]=\left[\begin{array}{ccc}A& E& B\\ O_{1\times 21}& I_{1\times 1}& O_{1\times 5}\\ O_{5\times 21}& O_{5\times 1}& I_{5\times 5}\end{array}\right]\left[\begin{array}{c}x\left(k\right)\\ d\left(k\right)\\ u\left(k\right)\end{array}\right]+\left[\begin{array}{c}{O}_{n\times 5}\\ O_{1\times 5}\\ I_{5\times 5}\end{array}\right]\Delta u\left(k\right)\\ y\left(k\right)=\left[CF{O}_{6\times 5}\right]\left[\begin{array}{c}x\left(k\right)\\ d\left(k\right)\\ u\left(k\right)\end{array}\right]\end{array}\}& \left(20\right)\\ \underset{\Delta u\left(0\right),\Delta u\left(1\right)\mathrm{.Math.},\Delta u\left(N\right)}{\min }J=\underset{k=0}{\overset{N-1}{.Math.}}\left({x\left(k\right)}^T\mathrm{Qx}\left(k\right)+\Delta {u\left(k\right)}^{T}R\Delta u\left(k\right)\right)& \left(21\right)\end{array}$

(35) In this example, values output from the state variable/disturbance estimation unit 15 are used as the initial values of the state variable and the disturbance variable. In the equation (21), x(k).sup.T represents transposition of a vector. N in the equation (21) is the prediction period and means that the future N control period is evaluated from the current time. By setting Q=c.sup.Tc (c represents the last line corresponding to the steel sheet temperature of the [C F O.sub.6×5] matrix), the evaluation function can minimize the temperature variation of the steel sheet including the disturbance at the inlet side and the outlet side of the heating furnace.

(36) Moreover, the constraint conditions include constraint condition relating to the upper and lower limit values of the furnace temperature, constraint condition relating to the furnace temperature change amount per unit time, constraint condition relating to the upper and lower limit values of the fuel flow rate, and condition relating to the fuel flow rate change amount per unit time. Furthermore, it is possible to obtain a relation between the fuel flow rate and the furnace temperature target value u(k) and integrating the relation in the constraints, or constrain the furnace temperature target value u(k). In this manner, it is possible to integrate the constraint conditions of the operation. Among the time series data of the furnace temperature change amount Δu(k) calculated in this process, the furnace temperature change amount calculation unit 16 outputs the furnace temperature change amount Δu(0) of the first time to the furnace temperature control unit 17.

(37) The furnace temperature control unit 17 adds the furnace temperature change amount Δu(0) to the furnace temperature target at the current time, and sets the usage amount of the fuel amount flow rate in each heating zone to achieve the target. It is preferable that the influence coefficient calculation unit 13, the control model setting unit 14, the state variable/disturbance estimation unit 15, and the furnace temperature change amount calculation unit 16 each execute a process for each set value of a plurality of sheet passing speeds that can be assumed during the actual operation. It is also preferable that the furnace temperature control unit 17 controls the fuel flow rate used in each heating zone to achieve the furnace temperature change amount calculated from the set value of the sheet passing speed close to the actual sheet passing speed.

(38) As is evident from the above description, in the steel sheet temperature control device 1 according to the embodiment of the present invention, the state variable/disturbance estimation unit 15 estimates the values of the state variable and the temperature disturbance variable of the control model at the same time. Moreover, the furnace temperature change amount calculation unit 16 calculates the furnace temperature change amount of each heating zone under the constraint conditions such that the square sum of the deviation between the target value and the actual value of the temperature of the steel sheet at the outlet side of the heating furnace becomes minimum, using the values of the state variable and the temperature disturbance variable of the control model. Furthermore, the furnace temperature control unit 17 controls the fuel flow rate used in each heating zone to achieve the calculated furnace temperature change amount. Consequently, it is possible to control the temperature of the steel sheet in the heating furnace with a good responsiveness and a good follow-up capability.

EXAMPLES

(39) The effectiveness of aspects of the present invention method was validated by simulation. The set values of the heating zones are described in the following table 1 and the set values of the steel sheets are described in the following table 2. As the constraint condition according to aspects of the present invention method, the furnace temperature target change amount [° C./s] in all the heating zones is set to equal to or less than ±1.0° C./sec. The prediction period N of the evaluation function is set to 30. Meanwhile, an exemplary configuration of a conventional method is illustrated in FIG. 2 for comparison. As illustrated in FIG. 2, in the exemplary configuration of the conventional method, the sheet temperature variation due to the temperature disturbance at the inlet side of the heating furnace is suppressed by feedforward (FF) control (FF correction), and the actual control deviation of the temperature of the steel sheet at the outlet side of the heating furnace is suppressed by proportional-integral-derivative (PID) control (feedback (FB) correction). The two controls are independently designed, and the conventional method differs from aspects of the present invention method in that information on the furnace temperature correction values are not exchanged with each other. The feedforward control calculates the furnace temperature change amount to remove the influence of the disturbance, which is applied to the temperature of the steel sheet at the inlet side of the heating furnace, applied to the temperature of the steel sheet at the outlet side of the heating furnace, using the influence coefficients. To compare the responses between aspects of the present invention method and the conventional method when a disturbance is applied, the disturbance illustrated in FIG. 3 is applied to the temperature of the steel sheet at the inlet side and the outlet side of the heating furnace.

(40) TABLE-US-00001 TABLE 1 Furnace Furnace temperature temperature Installation (Initial set control time length value) [° C.] constant Zone 1 20.4 746 30 Zone 2 5.1 1061 30 Zone 3 5.1 1056 30 Zone 4 5.1 1061 30 Zone 5 5.1 1054 30

(41) TABLE-US-00002 TABLE 2 Unit Value Sheet thickness mm 2.0 Sheet passing speed m/sec 1.0 Total heat transfer coefficient — 1.00 Control period sec 5.0

(42) The furnace temperatures of the heating zones (1 to 5Z) and the temperature response of the steel sheet at the outlet side of the heating furnace in accordance with aspects of the present invention method are illustrated in FIGS. 4(a) and (b). The furnace temperatures of the heating zones (1 to 5Z) and the temperature response of the steel sheet at the outlet side of the heating furnace of the convention method are illustrated in FIGS. 5(a) and (b). As illustrated in FIGS. 4(a) and (b), in accordance with aspects of the present invention method, the temperature of the steel sheet at the outlet side of the heating furnace is converged to the target value (0° C.) at least about 60 seconds have passed. Alternatively, as illustrated in FIGS. 5(a) and (b), in the conventional method, the control deviation is still present in the temperature of the steel sheet at the outlet side of the heating furnace even 100 seconds or more have passed. In this manner, it was confirmed that the time required for the temperature of the steel sheet at the outlet side of the heating furnace to converge to the target value is short, and the control deviation is eliminated in accordance with aspects of the present invention method.

(43) One difference between aspects of the present invention method and the conventional method is the directivity of the change amount of the furnace temperature when a disturbance is applied to the temperature of the steel sheet at the inlet side of the heating furnace. In other words, in the conventional method, even when the temperature of the steel sheet at the outlet side of the heating furnace is lower than the target value, the furnace temperature is lowered when a positive disturbance is applied to the temperature of the steel sheet at the inlet side of the heating furnace. However, this is a reverse operation when viewed from the temperature of the steel sheet at the outlet side of the heating furnace. Thus, the furnace temperature varies, and it takes time to converge. Alternatively, in accordance with aspects of the present invention method, even when a positive disturbance is applied to the temperature of the steel sheet at the inlet side of the heating furnace, when the current temperature of the steel sheet at the outlet side of the heating furnace is lower than the target value, the furnace temperature will not be lowered, and the furnace temperature is controlled to the condition that can eventually eliminate the steady-state deviation. This is because the disturbance applied to the temperature of the steel sheet at the outlet side of the heating furnace is estimated for each control period as illustrated in FIG. 6, and a suitable operation amount is optimally calculated.

(44) Although the embodiment has been described according to aspects of the invention made by the present inventors, the present invention is not limited to the description and the drawings forming a part of the disclosure of the present invention according to the present embodiment. That is, all other embodiments made by those skilled in the art on the basis of the present embodiment, examples, operation techniques, and the like are all included in the scope of the present invention.

INDUSTRIAL APPLICABILITY

(45) With the present invention, it is possible to provide the steel sheet temperature control device and the steel sheet temperature control method that can control the temperature of a steel sheet in a heating furnace with a good responsiveness and a good follow-up capability.

REFERENCE SIGNS LIST

(46) 1 steel sheet temperature control device 11 sheet temperature measurement unit 12 furnace temperature measurement unit 13 influence coefficient calculation unit 14 control model setting unit 15 state variable/disturbance estimation unit 16 furnace temperature change amount calculation unit 17 furnace temperature control unit