Electronic control system for an annealing furnace and associated control method

Abstract

Electronic control system (10) for determining a heating power setpoint (PWR) for a heating section of an annealing furnace, based at least on: a target temperature (T*) for a steel strip at an output of the heating section; and on an error signal (err_model) which is a difference between: a temperature (Tout) of the steel strip at the output of the heating section, and a synchronized predicted output temperature (Tmodel,out) obtained by time-laging a predicted output temperature (Tmodel) determined by a trained model (M) for steel strip heating in the heating section, whose inputs comprises the heating power setpoint and product and process parameters (PP) that include at least: a speed of the steel strip, an input temperature of the steel strip, a width of the steel strip, a thickness of the steel strip.

Description

Electronic control system for an annealing furnace and associated control method

[0001] The technical field is that of steel strip annealing, in particular that of controlling a heating process in an annealing furnace.

[0002] An accurate and responsive temperature control and regulation, in annealing surfaces for steel strips, is difficult to obtain. Indeed, there are intrinsic lag times in the heating process (due to the time required for the strip to traverse the successive heating sections). Besides, the heating inertia varies significantly from one strip to another (due to dimension variations, and possibly chemical composition and metallurgical characteristics variations from strip, that is from one coil to another), while the strips, welded one after each other, follow one another continuously, without interruption, in the annealing furnace. And this heating response may also vary, depending on the condition of heating sections themselves, in a way difficult to anticipate completely.

[0003] In this context, the instant technology provides an electronic control system, for controlling a heating section of an annealing furnace, according to claim 1.

[0004] This electronic control system may comprise one or several additional features, defined in claims 2 to 8, considered alone or in combination.

[0005] The instant technology also concerns an installation according to claim 9, and a control method according to claim 10. It concerns also a computer program comprising instructions whose execution on a computer (possibly connected to relevant sensors and / or actuators) make the computer to execute this control method.

[0006] The instant technology will now be described in more detail and illustrated by examples without introducing limitations, with reference to the appended figures.

[0007] Figure 1 is a schematic representation of an installation comprising an annealing furnace for steel strips, seen from the side.

[0008] Figure 2 is a schematic representation of a control loop employed for controlling a steel strip temperature at an output of a heating section of the annealing furnace of figure 1.

[0009] Figure 3 is a schematic representation of a trained neural network modelling the heating process in the heating section and that is employed in the control loop of figure 2.

[0010] Figure 4 is a histogram fora prediction error of the trained neural network of figure 3.

[0011] Figure 5 represents schematically the evolution of the steel strip temperature, at the output of the heating section, as predicted by a process model module and a time-lag module of the control loop of figure 2.

[0012] Figure 1 schematically represents an installation 1 for the thermal treatment of steel coils 3. This installation comprises an annealing furnace 20 and a cooling system 30 for cooling steel strips when they exit the annealing furnace 20. The installation also comprises a subsequent coating system 31 , here by hot-dip galvanization. The installation 1 is configured for continuously processing successive coils, with no interruption or stops between two successive coils, welded one to each other. In this installation, after a decoiler, the steel strip 5 coming from a coil 3 (also denoted as the strip, in the following) traverses successively:a strip accumulator 7,- then, in the annealing furnace, a preheating section 21 , a first (optional) heating section 22, a second heating section 23, and a soaking section 24 (where most of the annealing occurs),a cooling section 30, where the strip is cooled, by gas jets,and then the coating system 31 , starting here by traversing a zinc bath.

[0013] In this exemplary embodiment, the pre-heating section 21 and the first heating section 22 are both gas heating sections. The pre-heating section 21 is of the direct-flame type (meaning that the gas flames and the steel strip are in the same atmosphere, the steel strip being in contact with an oxidizing atmosphere, due to the presence of gas burners. Conversely, in the first heating section 22, the gas combustion occurs within radiant tubes. The second heating section 23 is an electric heating section, where the steel strip is heated by heating devices 8, here radiant devices electrically heated, namely electric resistors. The heating devices 8 are electrically fed by an electric power supply, depending on a power setpoint received by the electric power supply. The annealing furnace comprises these different, distinct sections, as different kinds of atmospheres are desirable, along the heating route (the soaking atmosphere being for instance a reducing one, here, while the preheating atmosphere is oxidising). A pre-heating section is also distinct from the second (and first) heating sections as different heating rates are employed in these sections. In a variant of this embodiment, the first heating section 22 is omitted.

[0014] The annealing furnace 20 is equipped with different sensors, in particular temperature sensors:a first temperature sensor 25 is arranged to measure a preheating output temperature Tout, 21 of the steel strip 5, at an output of the preheating section 21 , a second temperature sensor 26 is arranged to measure an input temperature Tinof the steel strip 5, at an input of the second section 23,a third temperature sensor 27 is arranged to measure an output temperature Tout of the steel strip 5, at an output of the second heating section 23.

[0015] The input and output of a given section of the annealing furnace 20 may designate, like here, a position outside the section considered, upstream or respectively downstream of it, forinstance immediately upstream or downstream of it (at a junction between two successive sections). It may also designate an input side or respectively output side of the section consider (that is a zone of the section located near an input or output port thereof).

[0016] Each of the first, second and third temperature sensor is a contact-less temperature sensor such as pyrometer, a spectrometer, a thermal camera or a hyperspectral camera. The first temperature sensor 25 may, like here, be implemented in the form of a spectrometer or a hyperspectral camera. This allows, when combined with an appropriate data processing (such as described in JPH0933464 or W02022079680), to determine both the preheating output temperature Tout, 21 and an emissivity sOut,2i of the steel strip at an output of the preheating section 21 (or another quantity representative of the strip emissivity, that is from which the emissivity can be derived directly). Here, the second temperature sensor 26 is also implemented in the form of a spectrometer or a hyperspectral camera, and an input emissivity sin of the steel strip, at the input of the second heating section 23, is determined from the signal acquired by this sensor. Still, in alternative embodiments, the first and second temperature sensors could be implemented differently, additional sensors being then employed to determine the emissivities sOut,2i and Einof the steel strip.

[0017] In this embodiment, the preheating section 21 is further equipped with four additional temperature sensors, arranged to measure temperatures of the still strip in four successive zones of the preheating section 21 respectively, these measured temperatures being notes respectively Ti, T2, T3and T4.

[0018] The installation 1 also comprises an absorptivity measurement device 6, arranged for measuring an absorptivity of the steel strip upstream of the annealing furnace 20. The absorptivity measurement device 6 comprises for instance a radiation source, a radiation sensor and an integrating sphere for measuring a total reflectance of the strip, from which the absorptivity is be derived.

[0019] The installation 1 also comprises a speed sensor measuring the speed v at which the strip moves in the annealing furnace 20, more particularly in the second heating section.

[0020] The installation 1 also comprises an electronic control system 10 configured for controlling the heating process in the second heating section 23 (and possibly for controlling other aspects of the operation of the annealing furnace 20). The electronic control system 10 is configured, for instance programmed, to implement the control method presented further below, with reference to figure 2.

[0021] The electronic control system 10 comprises at least a processor and a non-transitory memory. It comprises also one or more interfaces (like network or communication cards or chips, or like analog-to-digital converters) for receiving and emitting data and / or signals. Here, the electronic monitoring unit 10 is an industrial computer like a Programmable Logic Controller or like a module of a Distributed Control System. Its interface or interfaces are connected tothe above-mentioned sensors, to electric power supply for the heating devices 8, and to a sensor or a driver outputting data representative of a heating power employed for heating the still strip in the preheating section 21 , here a total air flow rate feeding the burners of the preheating section. These connections may be of the wire or wireless type and may be achieved through a local network or bus, for instance of the CAN (Controller Area Network), CAN+ or fieldbus type. One or more of these signals may also be transmitted through a public network, like the internet

[0022] The electronic control system 10 is also connected to a Human-Machine interface which comprises for instance a display screen and one or more input devices (such as a keyboard, buttons or switches or a screen-pointing device). The Human-Machine interface enables an operator to continuously monitoring the output temperature Tout of the steel strip, for instance, and may also be used by the operator for selecting a value for a target temperature T* for the steel strip, at the output of the second heating section 23.

[0023] The electronic control system 10 may also receive the value of the target temperature T*, via its interface(s), from another electronic system such as an upper-level process controller or such as a server storing characteristics of the process routes planned for the coils to be annealed in the annealing furnace.

[0024] As represented in figure 2, the control loop implemented by the electronic control system 10 comprises several modules 11 to 15. The modules may each take the form of a dedicated group of instructions (a distinct program or sub-program), these groups of instructions (possibly completed by additional components) forming together a computer program executed by the electronic control system 10, or employed for configuring it (should it take the form of a programmable circuit like a Field-Programmable Gate Array). Some or all of these modules may also take the form of different electronic units, distinct one from each other (yet possibly mounted on a same electronic card).

[0025] The control method implemented by the electronic control system 10 comprises determining a heating power setpoint PWR, to be transmitted to the electric power supply for the heating devices 8 of the second heating section, based at least on:- the target temperature T*, and onan error signal err_model which is a difference between:o the measured output temperature Tout of the steel strip 5, at the output of the heating section 23, ando a synchronized predicted output temperature TmOdei,out, obtained by applying a heating process time-lag to a predicted output temperature TmOdei which is determined by a trained model M for steel strip heating in the second heating section 23.

[0026] The trained model inputs comprise the heating power setpoint PWR and product and process parameters PP that include at least the speed v of the steel strip, its input temperature Tn, and a width w and thickness tk of the steel strip.

[0027] This control method is more specifically implemented using the control loop represented in figure 2. This control loop comprises:a subtractor 11 , outputting a corrected target temperature T*or, equal to the target temperature T* minus the error signal err_model,a setpoint determining module 12, which receives the corrected target temperature T*or, determines the heating power setpoint PWR as a function of the corrected target temperature Tc*orand outputs the heating power setpoint PWR,a process model module 13, which receives the heating power setpoint PWR and outputs the predicted output temperature Tmodei, determined by the trained model M, a time-lag module 14, outputting the synchronized predicted output temperature Tmodei, out which is obtained by applying the heating process time-lag to the predicted output temperature Tmodei,a comparator 15, outputting the error signal err_model, obtained by subtracting the synchronized predicted output temperature Tmodei, out from the measured output temperature Tout.

[0028] The physical, heating process is represented schematically by the block PRCS, in figure 2.

[0029] The structure of this control loop is partially similar to a control loop including a Smith predictor (the modules 13 and 14 playing the role of the Smith predictor, introduced in the control loop). Such a structure is well suited for controlling a heating process in an annealing furnace. Indeed, lag-times, inertia and inevitable transitory regimes (due to coils transitions) are present, in such a process, while a homogeneous heating all along the strip (to obtain homogeneous mechanical properties) is desirable. Besides, the characteristics of this heating process vary significantly from one coil to another (as the thermal inertia and possibly other features ofcoil influence this process) and depend possibly also on the condition of the furnace itself, these dependencies being difficult to anticipate completely and to model explicitly. Using then a model for the heating process, in the Smith-predictor-like modules, that is a trained model, trained to reproduce observed input-output relationships for the heating process and to reproduce the observed dependencies upon the product and process parameters PP, thus enable an accurate regulation, with an optimized response-time. Key inputs for this trained model are the speed v of the steel strip and its width w and thickness tk, as they directly influence the thermal inertia of the strip and the duration of its exposure to the heating.

[0030] The modules 12, 13 and 14 are now described in more details.

[0031] Setpoint determining module

[0032] The setpoint determining module 12 may, like here, determine the heating power setpoint PWR, as a function of the corrected target temperature T*or, such that, according to the self-same trained model M, the heating power setpoint PWR is expected to lead to the corrected target temperature Tc*or. In other words, the heating power setpoint may be determined by reversing the trained model M prediction.

[0033] To this end, the setpoint determining module 12 is configured, here, for:- for a candidate heating power setpoint, determining a corresponding, expected output temperature for the steel strip, by inputting the candidate heating power setpoint and the product and process parameters PP into the trained model M, - depending on the value of the output temperature thus temperature, compared to the corrected target temperature Tc*or, adjusting the value of the candidate heating power setpoint, and executing again the previous step.

[0034] This iterative determination may be stopped once a given precision is reached (for the difference between T*orand the predicted output temperature corresponding to the candidate heating power setpoint) and / or when a fixed number of iterations is reached. The adjustment of the value of the candidate heating power setpoint may, like here, be achieved, by bisection. The starting value for the candidate heating power, for these iterations, may be the last value of the heating power setpoint PWR, output immediately before by the module 12. The value of the heating power setpoint finally output may correspond to the last iteration (which is the value of the candidate heating power setpoint for which the expected output temperature is the closest to the Tc*or).

[0035] In alternative embodiments, the way to determine the heating power setpoint PWR so that it leads to T*oraccording to the trained model M, may be different. For instance, the trained model M could be reversed, a resulting inverse model of M being then used directly in the control loop. Else, the setpoint determining module may include a sub-loop with the trained model M inserted in its feed-back branch.

[0036] Process model module

[0037] In this embodiment, the product and process parameters PP input in the trained model M further comprise (in addition to Tin, w, tk and v) the input emissivity einof the steel strip 5 has at the input of the second heating section 23. This improves the accuracy of the trained model M, as the emissivity of the strip directly influences radiative exchanges at the strip surface, and thus heating efficiency in the second heating section 23.

[0038] In this embodiment, remarkably, the product and process parameters PP also include process parameters relative to the preheating process that occurred in the pre-heating section, in particular:- the above-mentioned quantity representative of the heating power employed for heating the still strip 5 in the preheating section 21 , here the total air flow rate feeding the burners of the pre-heating section,a preheating setpoint temperature, to be reached at the output of the preheating section 21 , employed for controlling the pre-heating section 21 ,- the preheating output temperature Tout,2i of the strip, measured at the output of the preheating section.

[0039] Taking into account these quantities improves the accuracy of the trained model M. This seems surprising, at first glance, as these quantities are relative to a prior heating process, for the steel strip 5, with a priori no influence on the heating process in the second heating section 23 except for the initial, input temperature and emissivity Tinand ein(as the emissivity may be modified by strip oxidation occurring during the preheating). A possible explanation, for the improvement obtained by taking preheating process parameters into account, is that they non-directly provide information regarding the steel strip and its ability to be heated (which depends on its chemical composition and metallurgical characteristics in a complex manner).

[0040] To further take advantage of this, the process parameters relative to the preheating process may, like here, comprise also:- the absorptivity Abs of the steel strip before entering the annealing furnace 20, - temperatures of the still strip Ti, T2, T3 and T4 in four successive zones of the preheating section 21 (which provides information regarding the preheating dynamic),and possibly also the emissivity sOut,2i of the steel strip at the output of the preheating section 21 .

[0041] In this embodiment, the trained model has thus 15 inputs, namely: PWR, Tin, sin, v, w, tk, Tout, 21 , Abs, total airflow rate for the preheating section, T1, T2, T3, T4and sOut,2i -

[0042] It is noted that some of the quantities measured or otherwise acquired upstream of the second heating section 23, namelyTout, 21 , Abs, the total air flow rate for the preheating section, T1, T2, T3, T4and sOut,2i, are synchronised with the quantities measured at the input of the second heating section 23, namely Tin, sinand v, so that these two groups of data be relative to a same portion of steel strip. To this end, Tout, 21 and sOut,2i, for instance, are time-shifted by the duration taken by the strip (more precisely, by the strip portion in question) for moving from the output of the preheating section 21 to the input of the second heating section 23. In other words, Tin, for instance, is the temperature of a given strip portion, at the input of the second heating section 23, while Tout, 21 is the temperature of the same strip portion, at the output of the preheating section 21 , and the same for the other quantities above mentioned.

[0043] Here, the possible values for the target temperature T* are classified into different target temperatures categories, corresponding to different temperature ranges. More precisely, there are four such categories, in this embodiment: the first one is centred on 790°C, the second is centred on 800°C, the third one is centred is on 810°C, and the fourth one is centred on 830°C. And each target temperatures category has a dedicated trained model, having the above-mentioned inputs. The model employed for determining TmOdei is selected as the one associated to the target temperatures category to which belongs the target temperature T*. Each of these trained models is trained, by supervised learning, using past production data gathering the 15 inputs above mentioned, plus the corresponding, measured output temperature of the strip at the output of the second heating section 23, these past production data gathering data corresponding to heating with final, output temperatures belonging to the category associated to this trained model. In alternative embodiments, operation categories, based not only on the target temperature but also on the dimension(s) and / orgrade of strip, could be employed, each operation category being associated to a dedicated trained model.

[0044] It is even possible that the target temperature T* only takes a few discrete values, for instance 790, 800, 810 and 830 °C, the trained model to be employed for determining TmOdei being selected, among four trained models, depending on the value of T*.

[0045] Using different trained models enables to take into account differences in the heating process, from one temperature range to another (due for instance to different thermal behaviours of the heating devices, or due to changes in the material thermal properties), that would be complex to model directly.

[0046] In this embodiment, each of the trained models above mentioned is a trained neural network with (figure 3):an input layer comprising 15 neurons (one for each of the above-mentioned inputs), an output layer outputting the predicted output temperature TmOdei (or a value from which the predicted output temperature is derived, by rescaling it for instance), and hidden layers, for instance from 1 to 15 hidden layers, connected between the input layer and the output layer.

[0047] More specifically, in this embodiment, for each of the trained models, the neural network is a two-layer feedforward network that comprises 10 hidden layers, each of which comprising 15 neurons (one for each of the above-mentioned inputs), fully connected to the next layer. For the hidden layers, the activation function is the sigmoid function. The output layer comprises a single neuron whose “activation function” is linear. Each of the above-mentioned inputs is normalized prior to being input into the input layer. Here, the data employed for the training comprise 58000 samples, for each trained model (for each temperature class), which corresponds to production data recorded for about 600 coils. These training samples are distributed into a training set (70% of the samples), a validating set (15%of the samples) and a testing set (15% of the samples). The type of training method employed is Levenberg-Marquardt backpropagation.

[0048] Figure 4 is a histogram representing the prediction error err (in °C) of the trained model, for the temperatures category centred on 830°C, for the training set (in black), the validation set (in light grey) and the test set (in dark grey). Figure 4 represents the number n of instances (of samples) in different temperature bins. The prediction error err is the difference between the actual measured output temperature Tout (for the sample considered) and temperature Tmodei predicted by the trained model. As visible in figure 4, the prediction error err is small. Its standard deviation, for the test set, is 3.8°C, here.

[0049] In alternative embodiments, a trained model (a machine learning, regression model) different from a neural network, or a neural network having a structure different from the one above presented, could be used for predicting the output temperature Tout.

[0050] Time-lag module

[0051] In this embodiment, the time-lag module determines the heating process time-lag based on one or more of the product and process parameters PP. More particularly, heating process time-lag is determined here as being equal to L / v, where L is the length travelled by the strip in the second heating section 23, v being the speed at which the strip moves in the annealing furnace 20 (i.e.: the line speed).

[0052] It is noted that the electric power supply for the heating devices 8 may itself comprise one or more control loops (such as PID loops), close to the actuators (from an automation point of view), and typically with a fast response time. In other words, the electronic control system 10 may play the role of a high or medium level automation, transmitting the heating power setpoint PWR to a low-level automation system. Besides, an optional corrector (such as a PID corrector, for instance) may be inserted between setpoint determining module 12 and the electric power supply for the heating devices 8, for filtering the heating power setpoint PWR.

[0053] Some of the product and process parameters PP, measured directly in the embodiment described above, that is measured using a dedicated sensor located at the targeted position (for instance at the output of the second heating section), may be measured non-directly in alternative embodiments, that is may derived from a measurement of another type of quantity, or derived from a measurement carried on upstream ordownstream of the position in question, this derivation being achieved using a model. For instance, the temperatures Ti, T2, T3and T4could be derived from the operation data relative to the preheating section, rather than measured directly using dedicated temperatures sensors.

[0054] Figure 5 represents the evolution of the output temperature of the strip (at the output of the heating section 23) in a case for which the heating section 23 is controlled using a PID control loop (Proportional-lntegrate-Derivate) instead of the control loop of figure 2. This output temperature is noted TOut_Pid (in °C) and is represented as a function of a position x along acontinuous succession of strips (in meters), for an exemplary heating in the annealing furnace 20. Transitions between two successive coils are each represented by a couple of two vertical dashed lines. The horizontal dashed lines represent maximum and minimum temperature limits, not to exceed (resp. not to go under). Figure 5 also represents the temperature Tmodei.out (in °C), output by model M and the time-lag module at each instant t, for the current values of the process and product parameters PP (and heating power setpoint PWR). As can be seen, the temperature Tmodei.out is well centred onto the target temperature T* (better than than Tout_Pid) illustrating that model M, together with the time-lag module, predicts well the output and the process (thus leading to an accurate control of the heating section). Besides, T model, out remains between the minimum and maximum temperature limits, and shows no unwanted transitory regime at the coils transitions.

Claims

1 . Electronic control system (10) arranged for determining and outputting a heating power setpoint (PWR) to be transmitted to a heating device (8) of a heating section (23) of an annealing furnace (20), the heating power setpoint (PWR) being determined based at least on:a target temperature (T*) to be reached by a steel strip (5) at an output of the heating section (23), and onan error signal (err_model) which is a difference between:o a measured output temperature (Tout), measured on the steel strip (5) at the output of the heating section (23), ando a synchronized predicted output temperature (TmOdei,out) obtained by applying a heating process time-lag ( ) to a predicted output temperature (TmOdei) which is determined by a trained model (M) for steel strip heating in the heating section, the trained model inputs comprising the heating power setpoint (PWR) and product and process parameters (PP) that include at least: a speed (v) of the steel strip, an input temperature (Tin) the steel strip (5) has at an input of the heating section, a width of the steel strip, a thickness of the steel strip.

2. Electronic control system (10) according to claim 1 , comprising a setpoint determining module (12) arranged for determining the heating power setpoint (PWR) as a function of a corrected target temperature (Tc*or) which is a difference between the target temperature (T*) and the error signal (err_model), the heating power setpoint (PWR) being determined so that, according to the said trained model (M), said heating power setpoint (PWR) results in said corrected target temperature (T*or).

3. Electronic control system (10) according to claim 2, wherein the setpoint determining module (12) is arranged for:executing iteratively the following step: for a candidate heating power setpoint, determining a corresponding, expected output temperature for the steel strip by inputting the candidate heating power setpoint and the product and process parameters (PP) into said trained model (M), and for- determining the heating power setpoint (PWR) based on one of said candidate heating power setpoint for which the corresponding, expected output temperature equals said corrected target temperature (Tc*or) within a given precision range.

4. Electronic control system (10) according to anyone of the preceding claims, wherein said product and process parameters (PP) include also a quantity representative of an input emissivity the steel strip has at an input of said heating section (23).

5. Electronic control system (10) according to anyone of the preceding claims, wherein the trained model is a neural network withan input layer receiving the heating power setpoint (PWR) and the product and process parameters (PP),an output layer outputting the predicted output temperature (TmOdei) or a value from which the predicted output temperature (TmOdei) is derived, andhidden layers, connected between the input layer and the output layer.

6. Electronic control system (10) according to anyone of the preceding claims, comprising a time-lag module (14) arranged for: determining the heating process time-lag ( ) based on one or more of said product and process parameters (PP), and for applying the heating process time-lag ( ) to the predicted output temperature (TmOdei).

7. Electronic control system (10) according to anyone of the preceding claims, wherein said trained model (M) is used to determine the predicted output temperature (TmOdei) if the target temperature (T*) belongs to a first target temperatures category, while a distinct additional trained model is used to determine the predicted output temperature (TmOdei) if the target temperature (T*) belongs to another, second target temperatures category.

8. Electronic control system (10) according to anyone of the preceding claims, wherein said product and process parameters (PP) include also one or more of:one or more prior temperatures of the still strip (5) measured respectively in one or more successive zones of a preheating section (21) of the annealing furnace (20), which is located upstream of said heating section (23),a quantity representative of a heating power that was employed for heating the still strip in the preheating section (21),a quantity representative of an emissivity of the steel strip at an output of the preheating section (21),a temperature setpoint for the steel strip at an output of the preheating section (21), a quantity representative of an absorptivity of the steel strip before entering the annealing furnace (20).

9. Installation (1) comprising:an annealing furnace (20) for heating and annealing a steel strip (5), the annealing furnace (20) comprising a heating section (23) with a heating device (8), a temperature measurement system (27) arranged for measuring a measured output temperature (Tout) of the steel strip at an output of the heating section, an electronic control system (10) according to anyone of the preceding claims, connected to the heating device (8) and to the temperature measurement system (27).

10. A method for a heating section (23) of an annealing furnace (20), the method comprising:- determining a heating power setpoint (PWR) based at least on:o a target temperature (T*) to be reached by a steel strip (5) at an output of the heating section (23), and ono an error signal (err_model) which is a difference between:- a measured output temperature (Tout), measured on the steel strip (5) at the output of the heating section (23), and- a synchronized predicted output temperature (TmOdei,out) obtained by applying a heating process time-lag ( ) to a predicted output temperature (Tmodei) which is determined by a trained model (M) for steel strip heating in the heating section, the trained model inputs comprising the heating power setpoint (PWR) and product and process parameters (PP) that include at least: a speed (v) of the steel strip, an input temperature (Tin) the steel strip (5) has at an input of the heating section, a width of the steel strip, a thickness of the steel strip,outputting the heating power setpoint (PWR), for its transmission to a heating device (8) of the heating section (23).

11. A computer program comprising instructions which, when executed on the computer, make the computer to execute the method of claim 10.

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