JPH0532446B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Industrial Application Field] The present invention relates to a method of controlling a continuous heating furnace having a plurality of control zones.

[Conventional technology]

Conventionally, as a method for determining the temperature rise curve online for temperature control of this type of heating furnace, for example, as shown in Japanese Patent Application Laid-Open No. 56-75533,
Using both nonlinear models, one that calculates the material temperature from the furnace temperature and the other that calculates the fuel flow rate from the furnace and material temperatures, the furnace temperature is varied in steps in order to perform nonlinear fuel minimization. A perturbation simulation method (a method in which linearization coefficients are determined by performing simulations in a reference state and a perturbation state) is used.

[Problem that the invention seeks to solve]

In the conventional continuous heating furnace control method as described above, the number of calculation zones for the furnace temperature is generally greater than the number of zones that can control the fuel flow rate. There was a problem in that the temperature and temperature rise curves were not always in achievable patterns.

In addition, when determining the linearization coefficient and temperature increase pattern, the simulation is performed by ignoring heat loss to the furnace wall, furnace wall temperature distribution, etc., and changing the furnace temperature in steps without considering the response delay of the furnace. As a result, there was a problem in that a temperature rise curve was determined that was far from the actual temperature rise trend of the material and furnace conditions.

In addition, even if some kind of temperature rise curve is determined, the materials charged into the furnace are grouped into combinations of size, physical properties, and type of heated steel (upper and lower limits of extraction temperature of billets, and limits on soaking degree). Due to high-mix, low-volume production, there are sometimes dozens of material groups in the furnace, and it is difficult to bake each material according to the temperature rise curve.

This invention was made in order to solve these problems, and it is possible to obtain a temperature increase curve that is both achievable and realistic, and to improve the accuracy of the extraction temperature of each material and reduce fuel consumption. The purpose of this study is to obtain a control method for a continuous heating furnace.

[Means for solving problems]

The control method for a continuous heating furnace according to the present invention takes into consideration various factors such as the furnace internal temperature, furnace wall temperature, and material temperature based on the fuel flow rate, and optimizes the heating rate to minimize the fuel flow rate for each material. In order to determine the temperature curve and bake various materials in the furnace on average or preferentially bake a certain material along this temperature rise curve, the set furnace temperature of each material is multiplied by the weighting coefficient for furnace temperature setting and the weighted average is calculated. This value is used as the furnace temperature setting value for each control zone.

[Effect]

In this invention, the temperature rise curve that minimizes the fuel flow rate for each material is determined based on the fuel flow rate, taking into account the elements of the furnace temperature, furnace wall temperature, and material temperature. A possible optimal heating curve is obtained. In addition, since the furnace temperature setting value for each control zone is the weighted average value obtained by multiplying the furnace temperature setting for each material by the weighting coefficient for furnace temperature setting, the various materials in the furnace can be fired on average or with priority. The extraction temperature of each material can be controlled with precision.

〔Example〕

The principle of this invention will be explained below.

The furnace temperature calculation model is constructed as follows.

As shown in FIG. 1, the heating furnace is divided into n pieces in the furnace length direction, and the following heat balance equation is established for each divided mesh.

C ₁・dT _gi ／dt … Temperature change in furnace temperature = Q _i … Sensible heat of fuel and air +H _g・W _i … Fuel calorific value +G _i+1・C _pg・T _gi+1 … Exhaust gas calorific value from upstream −G _i・C _pg・T _gi … Calorific value of exhaust gas downstream + _o 〓 ^j=1 K _1ij {(T _gj +273) ⁴ −(T _gi +273) ⁴ } …Radiation from other mesh furnace temperatures + _o 〓 ^{k =1} K _2ik {(T _wk +273) ⁴ −(T _gi +273) ⁴ } ...Radiation from furnace wall + _n 〓 ^l=1 K _3i {(T _s +273) ⁴ −(T _gi +273) ⁴ } ...Material Radiation to +C ₂ (T _wi −T _gi ) +C ₃ (T _si −T _gi )
… Convection to the furnace wall and materials −Q _wi … Skid cooling water loss… (1) Here, H _g is the calorific value per unit flow rate of fuel, C _pg
is the exhaust gas specific heat, G _i is the exhaust gas flow rate of each mesh, K _1ij , K _2ik , and K _3i are radiation exchange coefficients, and C ₁ , C ₂ , and C ₃ are constants. Further, n is the number of furnace length divisions, and m is the number of slabs.

The above equation (1) can be transformed as follows if the fuel flow rate w is given and the furnace wall temperature and slab temperature are known.

be done.

dT _gi /dt= _o 〓 ^j=1 A _ij (T _gj +273) ⁴ + _o 〓 ^k B _ik・T _gk +C _i (i=1...n) ...(2) This is an n-element simultaneous nonlinear differential equation However, by using the furnace temperature distribution one step before as a starting value, discretizing it with respect to time, and converging it using Newton's method, etc., it is possible to easily calculate a new furnace temperature distribution.

In addition, the material temperature model is the well-known 2
From the dimensional heat conduction equation, it can be expressed as follows.

dT _s /dt=λ _s /C _s・γ _s (d ² T _s /dx ² +d ² T _s /dy
² )…(3) The boundary conditions at the surface are: Here, x represents the material thickness direction, y represents the material width direction, and d ₁ and d ₂ represent the material thickness and material width, respectively. Also, C _s , λ _s , and γ _s are the specific heat, thermal conductivity, and specific gravity of the material, respectively. q _s is the surface heat flux of the material and can be expressed by the following equation.

q _s = _o 〓 〓 ⁱ⁼¹ K _3i {(T _gi +273) ⁴ −(T _s +273) ⁴ }+C ₃ (T _s
−T _g )...(5) Equation (3) can be solved by a normal difference method using the boundary condition of Equation (4).

As shown in FIG. 1, the furnace wall temperature model can be expressed as follows using a one-dimensional heat conduction equation in the thickness direction only within the mesh for each division in the furnace length direction.

dT _w ／dt＝λ _w ／C _w・γ _w・d ² T _w ／dx ² …(6) The boundary condition at the inner surface of the furnace is dT _w ／dx｜ _x=0 =1/λ _w・_o 〓 〓 ⁱ⁼¹ K _2ij {(T _gi +273) ⁴ −(T _w +273) ⁴ }+C ₂ (T _gi −T
_w )…(7) The boundary condition on the outer surface of the furnace is dT _w /dx | _x=d3 = 1/λ _w・H _OUT・(T _w −T _air )…(8) Here, x is the furnace wall thickness direction, d ₃ is the thickness of the furnace wall,
C _w , γ _w , and λ _w represent the specific heat, thermal conductivity, and specific gravity of the furnace wall, H _OUT represents the external heat transfer coefficient, and T _air represents the external temperature. Equation (6) can also be solved by a normal difference equation by using the boundary conditions of Equations (7) and (8).

By using the above three models in combination, if the fuel flow rate is given, the current values of the furnace temperature, material temperature, and furnace wall temperature are used as initial values, and the furnace temperature, material temperature,
Furnace wall temperature and future temperatures of the three parties can be calculated.

Next, a method for determining a temperature increase curve for a material that requires the least amount of fuel will be explained with reference to the flowchart shown in FIG. In addition, in the figure, 1 is the first step of temperature rise curve determination, 2 is the same second step, 3 is the same third step, and 4 is the same step.
4 steps, 5 is furnace temperature calculation model, 6 is furnace wall temperature calculation model, 7 is material temperature calculation model, 8 is calculation of material passing position furnace temperature, 9 is average temperature, 10 is linearization coefficient calculation, 11 is linear This is a planning method (LP) calculation.

First, as step 1, by repeatedly using three models 5, 6, and 7 for the time until all materials are extracted at the current flow rate W _K ^o , the average temperature _S ^o at the time of each material extraction, Soaking degree (maximum temperature -
The minimum temperature) ΔT _s ^o and the furnace temperature T _gi ^o at each position when the material passes through can be calculated.

Next, as a second step 2, by changing the fuel flow rate stepwise by Δw _K ^* for each fuel flow rate control, the average temperature _s at the time of each material extraction at each flow rate change is calculated as in the first step 1. ^k , the soaking degree ΔT _s ^k , and the furnace temperature T _gi ^k when the material passes through.

Next, as a third step 3, the following linearization coefficient calculation 10 is executed. By the treatment of 2nd step 2,
The average temperature of each material at the time of extraction, which is the solution of the nonlinear equation,
The degree of soaking and the furnace temperature in each calculation zone when each material passes can be linearized as follows.

_s = _s ^o + _KMAX 〓 ^K=1 P _1K・Δw _K …(9) ΔT _s = ΔT _s +P _KMAX 〓 ^K=1 _2K・Δw _K …(10) T _gi ＝T _gi ^o ＋ _KMAX 〓 ^K=1 P _3iK・Δw _K …(11) Here, KMAX is the number of fuel flow control bands,
P _1K , P _2K , and P _3iK are linearization coefficients when the flow rate is changed, and are given as follows.

P _1K = (T _s ^K −T _s ^O )/Δw _K ^* …(12) P _2K = (ΔT _s ^K −ΔT _s ^O )/Δw _K ^* …(13) P _3iK = (T _gi ^K −T _gi ^O )/Δw _K ^* (14) Furthermore, each fuel flow rate can be expressed as w _K = w _K ^O + Δw _K , where Δw _K is the amount of change in each control band.

The constraints in determining the temperature rise curve are as follows due to metallurgical constraints of the material and constraints on furnace operation.

T _s MIN≦T _s ≦T _{s MAX} ∆T _s MIN≦∆T _s ≦∆T _{s MAX} T _giMIN ≦T _gi ≦T _giMAX w _{K MIN} ≦w _K ≦w _{K MAX} …(15) Here, the subscripts MIN, MAX are Each lower limit value and upper limit value are shown.

Furthermore, since the evaluation relationship for optimization is fuel minimization, it is as follows.

Φ= _KMAX 〓 ^K=1 w _K (16) Minimization of Equation (16) under the constraint condition of Equation (15) can be obtained by ordinary linear programming (LP) calculation 11.

The flow rate of the above solution is the optimal flow rate w _Kppt of each material,
As the fourth step 4, it becomes possible to calculate the optimal temperature rise curve for each material until extraction using the three models 5, 6, and 7 based on this flow rate.

Once the target temperature is determined based on the temperature increase pattern determined in this way, the set furnace temperature at the furnace temperature setting position for each material can be determined from the above-mentioned current material temperature, target temperature, etc.

Generally, in a heating furnace, there are more zones for calculating the furnace temperature than zones that can be controlled, and in order to reach the temperature at the set position, it is necessary to convert it back to the control temperature.
The setting value at that position can be secured. Therefore, T _gA ′=T _gA + (T _g (j)−T _g (k)) …(17) The values in parentheses correspond to the correction term for the set furnace temperature, since the furnace temperature distribution is known above. However, this ensures that the necessary furnace temperature for a given material is obtained.

However, T _gA ′: Furnace temperature setting T _g (j): Furnace temperature of the furnace temperature setting zone T _g (k): Zone where the control thermometer exists in the zone including the furnace temperature setting zone Thus, material 1 The set furnace temperature for each control zone has been determined, and based on this set value, the furnace temperature set value for each control zone is calculated using the following formula.

T _gK = Σc(i)T′ _gA (i)/Σc(i) …(18) Here, c(i) is the setting weighting coefficient for each material, and if all c(i) are the same, each It will be baked on average according to the temperature increase pattern, and if you want to preferentially bake a certain material during operation, you can achieve this by increasing the weight of c(i) related to that material. FIG. 3 shows this state.

Next, heating furnace control based on an embodiment of the present invention will be explained with reference to FIG. 4.

In FIG. 4, a combustion burner 105 and a furnace temperature detector 104 are arranged in a heating furnace 101 divided into a plurality of control zones, and each control zone is set by a furnace temperature setting function 106. The flow rate is controlled by a fuel flow rate controller 103 so that the set temperature is achieved. A material information function 102 instructs the furnace temperature setting function 106 to provide material information such as the dimensions, weight, extraction temperature, and conveyance information of the material in the furnace.

The furnace temperature setting function 106 is the current temperature calculation function 20.
, temperature rise curve determination function 21 and set furnace temperature calculation function 22
It consists of , and is activated periodically. The current temperature calculation function 20 calculates the current material temperature using a furnace temperature calculation model 5, a furnace wall temperature calculation model 6, and a material temperature calculation model 7 based on the material information. The temperature increase curve determination function 21 determines the temperature increase curve for each material while minimizing fuel according to the flowchart shown in FIG. 2, as described in the explanation of the present invention.

The set furnace temperature calculation function 22 compares the target temperature increase curve for each material with the current temperature, calculates the furnace temperature of each control zone, and instructs the fuel flow rate controller 103 to set the furnace temperature.

Therefore, based on the fuel flow rate, we also take into consideration the elements of furnace temperature, furnace wall temperature, and material temperature, and determine a feasible temperature rise curve that minimizes the fuel flow rate for each material. Not only can the extraction temperature of each material be controlled with high precision, but the effect of reducing the fuel flow rate can be greatly increased.

〔Effect of the invention〕

As explained above, this invention determines the optimal temperature rise curve that minimizes the fuel flow rate for each material based on the fuel flow rate and also takes into account the elements of the furnace temperature, furnace wall temperature, and material temperature. As a result, the optimum temperature rise curve that can be achieved can be obtained.

In addition, in order to bake the various materials in the furnace on average or preferentially bake a certain material along each of the temperature rise curves mentioned above, the set furnace temperature of each material is multiplied by the weighting coefficient for furnace temperature setting, and the weighted average value is calculated. Since the furnace temperature is set as the furnace temperature setting value for each control zone, the extraction temperature of each material can be controlled with high precision, and there are effects such as being able to reduce fuel consumption.

[Brief explanation of drawings]

Figure 1 is a schematic diagram showing the zone division of the furnace temperature calculation, Figure 2 is a flowchart for determining the optimal heating curve, and Figure 3
The figure is a conceptual diagram for determining the correction value for the furnace temperature setting value, and FIG. 4 is an overall configuration diagram showing one embodiment of the present invention. 5...Furnace temperature calculation model, 6...Furnace wall temperature calculation model, 7...Material temperature calculation model, 20...Current temperature calculation function, 21...Temperature rise curve calculation function, 22
... Setting furnace temperature calculation function, 101 ... Heating furnace, 10
3...Fuel flow rate controller, 104...Furnace temperature detector,
105... Combustion burner, 106... Furnace temperature setting function.

Claims (1)

[Claims] 1. In the heating control of a continuous heating furnace with multiple control zones, the first function is to calculate the time change in the furnace temperature using an unsteady heat balance formula based on the fuel flow rate.The first function is to calculate the time change in the furnace wall internal temperature from the furnace temperature. A second function to calculate the temporal change in material internal temperature from the furnace temperature, a third function to calculate the average temperature at the time of material extraction at the current fuel flow rate in each control zone using each of the first, second, and third functions. A fourth function that calculates the soaking degree and each furnace temperature when the material passes through, and when the fuel flow rate in each control zone is changed by a certain value from the current flow rate using the first, second, and third functions described above. The fifth function calculates the average temperature during material extraction, the degree of soaking, and each furnace temperature when the material passes through, and calculates the linearization coefficient around the current fuel flow rate based on the results of the fourth and fifth functions above. A sixth function uses this to calculate the optimal fuel flow rate that minimizes fuel under constraint conditions, and a temperature rise curve from the current position of the material to extraction using the first, second, and third functions above. The optimal fuel flow rate obtained in the sixth function is input to the seventh function to determine the optimal temperature rise curve, and the material in the furnace is averaged along each temperature rise curve. In order to preferentially bake a target or a predetermined material,
A method for controlling a continuous heating furnace, characterized in that a weighted average value of the set furnace temperature of each material multiplied by a weighting coefficient for setting the furnace temperature is set as the furnace temperature set value for each control zone.