Strip Cooling Control for Flexible Production of Galvanized Flat Steel

The work is devoted to the problem of flexible small-scale production of galvanized steel of various sizes on a continuous hot-dip galvanizing unit with varying productivity. The main focus is on the heat treatment of steel strip, the requirements for which limit productivity. In conditions of disturbances, it is necessary to proactively control the heat treatment using models, or to reduce the speed of the strip to ensure that the requirements are met. Unlike most of the works that focus on heat control, this work focuses on strip cooling. Based on the analysis of production data of the Magnitogorsk Iron and Steel Works, it is shown that violation of the cooling requirements leads to the appearance of defects in the zinc coating. Dependence of the probability of defect occurrence on the strip temperature is given. Problems of cooling predictive control are formulated using models in the absence of temperature control of the cooling section cavity. For each of the tasks, the model structure and the method of its tuning are determined according to the data accumulated over a significant period of the unit operation under conditions of uncontrolled systematic disturbances. The structure of the cooling control system is proposed by estimation of the cooling section cavity temperature as a controlled variable. The temperature estimate is determined from the model. The lack of measurement of the cooling section cavity temperature is not a problem when varying productivity. The results of the model tuning are presented according to the data of the Magnitogorsk Iron and Steel Works continuous hot-dip galvanizing unit. The proposed structures of the models and methods for their adjustment can be applied in the development of models for metal heating in furnaces.


INTRODUCTION
At present, the products of continuous hot-dip galvanizing units (CHDGUs) are on high demand [1]. In recent decades, demand on galvanized steel strip by building and car industry significantly increased. In 2018, Magnitogorsk Iron and Steel Works (MISW) achieved a record-high volume of galvanized rolled stock, 1.269 million tons. However, such growth occurred under uncertainty and rapidly changing market requirements [2].
CHDGUs consume high quantity of energy, a significant part of which is lost as heat [3]. Optimization of a strip's heat treatment could reduce energy consumption. Control at various stages of the flow process on CHDGUs is usually optimized for the processing of standard size range, which is commonly used at the moment of unit commissioning. At the same time, variable demand on metallurgical products results in a small-scale production of strip of different sizes. This fact can reduce productivity and increase heat losses, which makes the production of galvanized flat product less flexible and restricts its adaptation for current market requirements.
The problem of flexible production of galvanized rolled stock is emphasized in Refs. [4][5][6], which focus on optimization of heating control of steel strip in multizone reheating furnaces. It has been shown that production flexibility could be based on the analysis of accumulated technological information and development of the complex of models to control annealing. It has been demonstrated that complications regarding the adaptation of the accumulated data to the tuning of models represent a principal problem of control at flexible production of galvanized rolled stock. This fact prevents practical application of the solutions similar to [7][8][9], where the problems of optimization of steel heat treatment conditions are considered separately from the problem of model adjustment. In addition, it is necessary not only to fulfill requirements on heating, but also to fulfill those on cooling of steel strip in order to obtain a high-quality product. However, there are few literature data devoted to this prob-lem. The aim of this work is to study and solve the problems associated with the synthesis of the models for the control of strip cooling at flexible production on CHDGUs. The process data accumulated in MISW represent the basis.

PROCESS LINE STRUCTURE OF CHDGU
The first CHDGU in MISW developed by the Danieli Company (Italy) was put into operation in 2002. This unit is designed for the production of 500 thousand tons a year of galvanized flat product with the thickness of 0.4 to 2.0 mm and width of 1000-1650 mm for the automotive and building industry. The diagram of heat treatment of strip is given in Fig. 1.
The heating process is realized in the turret-type drawing furnace with the areas of radiation heating and temperature maintenance. Then, the strip appears at the closed-cycle cooling compartment, which is designed for strip cooling to the temperature, at which oxidation of steel surface is not significant after exit of the strip from the compartment. To control the temperature state of the strip, four optical pyrometers are set at the exit from the sections of heating, thermal maintenance, as well as closed-circuit and deep cooling.

CLOSED-CIRCUIT COOLING COMPARTMENT AS A CONTROL OBJECT
To cool the strip in a compartment, protective nitrogen-hydrogen gas is employed, which is cooled using condensers. Fans are used for gas circulation, which evacuate the protective gas from the compartment. Control of the compartment operation considers exposure on the power developed by the fans.
The absence of workspace temperature control in a closed-circuit compartment is a feature of control. Thus, the effect of power tuning can be evaluated only by the temperature drop of the strip at the entrance and exit from the compartment. Such approach to the control management is aimed at the conditions of the ensured strip cooling. Under such conditions, process disturbances (by the speed of strip, size range, or temperature of metal at the entrance to the compartment) should not result in the exceedance of the maximum allowable temperature of metal at the exit from the compartment.

PROBLEMS OF STRIP COOLING CONTROL
During treatment of strip, the temperature of metal at the exit from heating compartment varies from 720 to 840°C depending on the steel type and could achieve 450-480°C after closed-circuit cooling before zinc pot. Violation of the requirements leads to strip defects. Quality control of the products showed that zinc overlap, insufficient galvanizing, and delamination of zinc coating are most common types of defects. The fraction of the products with such defects amount to 90%.
In order to evaluate the effect of strip temperature at the exit from the closed-circuit cooling compartment on the probability of defect formation in zinc coating, the strip temperatures for a number of coils  Heating compartment Heat soak Closed-circuit cooling with and without defects were compared. The coil database involved information on the dynamic of temperature change of strip for 679 coils with defects and 8595 coils without defects. The maximum strip temperature at the exit from the closed-circuit cooling compartment was measured over the total coil processing period. Then, using the approach suggested in [4], the dependence of the probability of defective production on the strip temperature at the exit from the compartment was determined (Fig. 2), which derives a nonlinear effect of the strip temperature on the probability of defective production. It can be seen that even minimum exceedance of the threshold of 480°C is undesirable, because it leads to a significant increase in the probability of subsequent defect formation.
Investigation of the effect of the strip temperature drop below 450°C on the fraction of defective production showed the absence of such relationship. However, it should be noted that the strip enters the zinc pot after closed-circuit cooling, maintenance of the temperature of which requires energy. A decrease in the strip temperature below 450°C leads to an inconsistent increase in energy losses on cooling and rated temperature maintenance in zinc pot.
To maintain the strip temperature within specified technological limits, the deviation control system is employed. However, there is a weld joint of the strip with different sizes along the unit sections with a change of the metal size range. In this case, a drastic stepwise change of the temperature of metal could occur at the exit from the heating, maintenance, and cooling compartment. To avoid defect formation and excessive cooling of the strip, which results in additional energy consumption, a proactive control of the cooling condition based on a priori knowledge is necessary. Two different approaches to the solution of this problem can be suggested.
The first approach considers the choice of the speed of strip individual for each size range, at which both heating and cooling compartments ensure necessary temperature of metal.
The temperature conditions, which ensure heating of the steel strip, usually consider that the workspace temperature in furnace only marginally (by 10-20°C) exceeds the necessary temperature of metal at the exit from furnace. Thus, the speed of strip is chosen. Such mode would ensure that the metal achieves the required temperature much earlier than its exit from the furnace for heating. In this situation, disturbances by the workspace temperature in individual furnace sections or by steel characteristics would not significantly affect the metal temperature at the exit from furnace. Thus, the reheating furnace not only performs a heating function, but also partially performs a maintenance function even though a separate compartment is designed for this purpose. To implement ensured heating conditions, complex control algorithms based on the strip temperature prediction models are not necessary. It is sufficient to choose once the workspace temperature in furnace for a particular size range and the speed of strip corresponding to it. The stability of metal temperature at the exit from heating and maintenance compartments could once determine the power of the fans, which provide the condition of ensured cooling for a size range. Such approach is widely used in practice; however, it possesses particular drawbacks. Firstly, ensured heating of the strip with large thickness (more than 0.001 m) requires a significant decrease in the strip speed even if the power of burners allows for a high speed; i.e., the productivity of the unit is significantly reduced for a number of size ranges. One example is that the strip speed in CHDGU no. 1 of MISW varies in the range of 20 to 180 m/min. Secondly, variation of productivity is restricted, because the conditions of ensured heating are chosen assuming a particular strip speed.
The second approach to the choice of conditions is alternative to the choice of preliminarily chosen ensured heating and cooling conditions. This approach is based on the models upon control of heat treatment of strip, which could reject ensured conditions.

PROBLEMS IN CLOSED-CIRCUIT COOLING CONTROL USING MODELS
Let us highlight a number of fundamentally different problems in closed-circuit cooling control, which can be solved using models.
Let us relate stabilization of the strip temperature at the exit from the closed-circuit cooling compartment at a constant size range to the first problem. Employ- 600 Probability of defect formation ment of the model could increase the effectiveness of control by deviation through feedforward compensation of disturbances. A main disturbance is represented by the strip temperature at the entrance to the compartment. Assuming that the strip exists in the cooling compartment over 40 s at the speed of 180 m/min, the feedforward control could decrease temperature oscillations, which could maintain temperature near the upper technological limit of 480°C. Existing works on the strip temperature control by deviation are usually aimed at heating control. One example is that a complex model of heating state of furnace and metal supplemented by the observer of strip emissivity based on the Kalman filter is suggested to control the strip temperature in [10][11][12]. A similar solution was suggested in [13]. Results of mentioned works can also be used in the problem of strip cooling control.
The second problem, which requires models, is the feedforward cooling control at the change of size range or the speed of strip during realization of the conditions that are different from ensured heating and cooling. The solutions suggested in [11][12][13] are based on the hypotheses of slow change of emissivity. However, there is a drastic stepwise temperature drop of steel at the change of size range with the transfer of the weld joint through the reference points. The reason is that multiple various characteristics of the strip are simultaneously changed, such as heat capacity, contamination, heat losses on recrystallization, thickness, width, and others. Change of the strip speed also results in a sufficiently rapid change of the metal temperature at the exit from the compartments, which may lead to coating defects. The adjustment system by deviation is ineffective at these periods, which requires feedforward control using models. In spite of a large number of works in the management of thermal processes upon strip galvanization, the problem of synthesis of such models using accumulated technological information is still unsolved. According to [6], the reason is difficulties in the adjustment of models by accumulated data on the operation of units at ensured heating and cooling, which requires more detailed study.
The third problem follows from the aim of the variation possibility of productivity with the choice of a higher strip speed as compared to ensured heating and cooling conditions. An increase in the strip speed at the specified size range is restricted by the maximum limiting power of heating and cooling means of strip. In [4], the problem of tuning of heating models of state of furnace and heated metal was solved. A large variability of the degree of heat losses at different period of unit operation was demonstrated. At the same time, many existing models [14][15][16][17][18][19] do not consider these features and it is unclear how to adjust them under such conditions. Thus, the third problem considers the models for the determination of the maximum possible current productivity.
In [20], the effect of productivity on the quality of temperature control of workspace in furnace was demonstrated, which can be the reason of additional restriction of the limiting productivity. This fact considers the fourth problem, more specifically, employment of the models for evaluation of the control system efficiency or during the synthesis of the workspace's temperature control systems.
The second and third problems are most important among mentioned problems for the flexible control of productivity. Their solution could choose a higher strip speed as compared to ensured heating and cooling conditions.

FEATURES OF TUNING OF FEEDFORWARD COOLING CONTROL MODEL
Dedication of the model for feedforward control of cooling involves the choice of the fan power for maintenance of the necessary strip temperature at the exit from the cooling compartment at known process parameters of the size range (thickness, width, and steel grade), strip speed, and strip temperature values at the entrance to the compartment.
At the same time, investigation of the effect of mentioned model variables on the strip temperature at the exit from the closed-circuit cooling compartment according to the data collected over more than one year of unit operation showed the absence of such multifactorial dependence. Possible reasons include uncertainty of the temperature state of the workspace of the closed-circuit cooling compartment and variability of heat withdrawal from compartment not associated with the fan power.
However, prediction upon management is the dedication of the model. The data on the current strip temperature at the entrance and exit from compartment before process disturbance can be used during prediction. This information indirectly characterizes the current temperature state of the workspace of the cooling compartment; however, its employment upon synthesis of empirical models is complicated by a large number of factors and nonuniform sampling from process data.
To solve the problem of model synthesis, let us introduce uncontrolled variable T s , which represents the estimate of the current temperature of workspace of the cooling compartment. To adjust the model at nonuniform adjusting retrieval, let us determine the relationship between the strip temperature T m and the STEEL where T m is the steel strip temperature, T s is the workspace temperature, h is the strip thickness, and α is adjustable parameter. Assume that the workspace temperature T s is constant upon passing of the strip through the cooling compartment. Then, solution of Eq. (1) relative to T s is the following: (2) where T m (0) and T m (τ cool ) is the strip temperature at the entrance and exit from the compartment, L is the strip length in the closed-circuit cooling compartment, and v 1 and h 1 correspond to the strip speed and strip thickness before technological disturbance.
Еquation (2) can be used for the evaluation of the workspace temperature before process disturbance. Then, assuming T s as known value, we derive the solu- where v 2 and h 2 correspond to the strip speed and strip thickness after process disturbance.
The model was adjusted during study according to the data on the strip temperature at varying thickness (Δh > 0.0002 m, where Δh = |h 2 -h 1 |). The mean absolute error of the prediction of temperature change of the strip at the exit from the cooling compartment during disturbance was used as a criterion. At α from 1.4 to 2.5 (×10 -4 m/s), similar values of criterion were obtained (Fig. 3).
To solve the problem, the normalized dependences of the mean absolute error predicting the variation of T m on α were derived for various subsets of initial data, which were divided into groups according to thickness and speed ( Table 1). The boundary speed was determined assuming the strip thickness for data group derived from heating warranty (Fig. 4a).
Rational value of α = 1.6 × 10 -4 m/s was derived according to the following criterion: (4) In this case, the forecast precision is compromised for the bands possessing various thickness values at different speed. The mean forecast error corresponded to 5.28°C. Figure 5 shows the example results of model testing according to the fraction of test set.
The tuned model can be used in the control with the aim to implement the conditions different from ensured heating and cooling.

APPLICATION OF THE MODEL FOR FEEDFORWARD COOLING CONTROL
Structure of the strip temperature control system is given in Fig. 6. The system includes a controller for strip temperature stabilization at the specified level, as well as the temperature controller of the workspace of closed-circuit cooling compartment.  α, rel. The workspace temperature controller operates at two modes. During the constant size range and speed of strip, the specified strip temperature value is considered in accordance with the task for the current size range (T sp = T sp1 ).
Before changing the size range or speed, the controller calculates the workspace temperature value T s,sp necessary for a new condition in the closed-circuit cooling compartment according to Eq. (2) at T m (0) = T ms and T m (τ cool ) = T sp1 . The current workspace temperature value T s is also determined according to Eq. (2) though according to the data on the measured strip temperature at the entrance and exit from the compartment for the current size range. The error signal ε = T s,sp -T s is used for correction of task on the strip temperature for the current size range. Thus, the necessary cooling mode is provided proactively in the closed-circuit cooling compartment before changing the size range or speed.

FEATURES OF MODEL TUNING FOR DETERMINATION OF MAXIMUM PRODUCTIVITY AND SIMULATION OF CONTROL
According to the structure of control system (Fig. 6), new strip speed v 2 is the specified parameter. However, the power of the cooling system can be where z = hvb, b is the strip width, c m is the specific heat capacity of steel; t m0 and t m correspond to the strip temperature at the entrance and exit from the compartment, and x 1 , x 2 , and x 3 are tuning parameters.
According to Eq. (5), the sum of heat ΔτPx 1 withdrawn by the cooling system and heat losses x 1 ΔτT s of the compartment (assumed proportional to the workspace temperature) corresponds to the sum of heat withdrawn from metal upon cooling and the heat associated with the change of the temperature state of the compartment x 3 ΔT s .
Using the tuned strip cooling model given in Eq. (3), let us represent Eq. (5) as follows: (6) or (7) where C = , After dividing both parts of Eq. (7) by Δτ and passing to the limit, the following can be written: (8) Еquation (8) can be used as a model for the determination of the maximum productivity and simulation of control. However, the choice of the tuning parameters by the accumulated process data is restricted due to the real nonlinearity and systematic bias of the dependences of heat losses on temperature in compartment and withdrawn heat on the fan power. Attempts to choose tuning parameters in Eq. (8) showed that optimal values of all tuning parameters are different for each individual period of unit operation.
Let us consider the features of application of Eq. (8) to the conditions of individual period of unit operation. Assume that the workspace temperature in the compartment was equilibrated at the initial moment of the period. Then, Eq. (8) can be written for τ = 0 as follows: (9) After subtracting Eq. (9) from Eq. (8), we have (10) where ΔP(τ) = P(τ) -P(0), ΔT s (τ) = T s (τ) -T s (0), and Δt m0 (τ) = t m0 (τ) -t m0 (0). Derived from Eq. (10), we write for the rate of the change of the workspace temperature that (11) where is tuned to consider the assumed error of equilibrated temperature in the compartment at τ = 0.
In order to tune the model in the form of Eq. (11) from accumulated data, the periods were chosen, during which significant changes of power P or strip temperature at the entrance to the compartment t m0 were observed. The model (11) was used to determine the dynamics of the change of workspace temperature of the compartment T s according to the data on the dynamics of the change ΔP and Δt m0 . The model (11) does not require information on the strip temperature at the exit from compartment as initial data. The dynamics of the change of T s obtained from the model (11) was compared to the dynamics of change of T s determined using the model from Eq. (2) according to the data on the strip temperature at the entrance and exit from compartment. Initial value of T s during calculation using Eq. (11) was considered equal to the T s according to the model (2) at τ = 0.
The model was adjusted through exhaustive search of the values of . A unique solution { = -35.2; = 40.45; and = 3988.1} was found, which could provide the highest accuracy of modeling upon the choice of individual value of for each specified period of unit operation. The power value was set as the percent value of the maximum during calculations, whereas the values of other variables were set in the SI units. Figure 7 demonstrates the results of modeling for two various periods. During the first period (Figs. 7a-7d), there was a gradual decrease in the strip temperature at the entrance of the closed-circuit cooling compartment. The control system adjusted the fan power to stabilize the strip temperature at the exit from the compartment. During the second period (Figs. 7e-7i), the strip speed was increased. Additional burner groups were switched on simultaneously and fuel consump- * * * * , , , and tion was increased, which resulted in the increase in the strip temperature at the entrance to the closed-circuit cooling compartment. Figure 7 shows the agreement of the modeling results of the workspace temperature in the closed-circuit cooling compartment using models (2) and (11). The model (11), which does not require information on the strip temperature at the exit from the compartment, can be used for the evaluation of the maximum current productivity, as well as at simulation modeling of control and investigation of dynamic characteristics of control object.

VARIATION OF DYNAMIC CHARACTERISTICS OF CONTROL OBJECT
The following can be written at the stable strip temperature at the entrance to the compartment and established temperature of a workspace at the initial time moment of period: (12) According to Eq. (12), dynamics of an object is represented by the aperiodic link with the time constant T ob = . Figure 8 shows the example dynamics of the temperature change T p in the compartment for the period with a gradual change of power at a stable temperature at the entrance. The form of transient response confirms the presentation allowability of the dynamics of an object by the aperiodic link.   The model could estimate the productivity effect on the object transfer coefficient k ob = and the time constant of aperiodic link T ob . Derived from productivity limitations [5], which are due to the power of burners in the heating compartment, the time constant T ob and transfer coefficient can vary by the factor of 2-3.

CONCLUSIONS
Models of heat exchange, which consider adjustment by the data accumulated at various operation periods at systematic disturbances, have been suggested. The models can be employed for the choice of strip cooling conditions at varying productivity without workspace temperature control. The derived solutions allows the producers to abandon the practice of conditions of the steel strip's ensured heat treatment, which reduces productivity. They could also be used in heating products in furnaces of various designs.