EP3530374B1 - Method for controlling a continuous-casting plant - Google Patents

Description

The invention relates to a method for controlling a continuous casting plant, a computer program product and a control unit for controlling a continuous casting plant.

Continuous casting plants are used to manufacture slabs from various materials such as steel, copper alloys or aluminum. A corresponding melt is transported to the continuous caster and poured from a converter into a ladle. Can via a bottom drain thereupon the melt flow from the ladle into a distributor, from which the melt can flow into so-called molds. Each mold defines the shape of the strand that is cast. In order to prevent the material from sticking to the walls of the mold, the mold is moved in an oscillating manner. Due to the cooling of the walls of the mold, the material solidifies at the edge areas, so that a solidified strand shell results, which is further cooled after leaving the mold. The strand shell or also the strand in general is still supported by rollers after it has left the mold in order to prevent the strand from breaking.

When the strand has solidified in its cross-section, the strand can be distributed to the desired length by a suitable cutting system, for example by cutting torches or scissors.

As a result, the continuous casting process results in individual slabs, which can then be further processed in a rolling mill, for example. One possibility is, for example, hot rolling, for which purpose the slabs are heated to a corresponding temperature above the recrystallization temperature and are reduced to the specified thickness in the roll gap of a hot rolling mill by applying pressure. Since the volume of the slab remains the same, there are changes in length and width. As a result of the rolling process, a slab finally results in a strip which is wound onto a reel to form what is known as a coil.

Continuous casting plants are used in different configurations. So-called multi-strand systems, in which several strands can be cast in parallel and at the same time, are common, for example. Here, the distributor has the function of distributing the liquid material, such as the liquid steel, to the individual molds and thus the individual strands.

The EP 1021261 B1 describes, for example, a method and an apparatus for producing slabs of various formats. The EP 1658533 B1 discloses a method and a device for controlling a plant for the production of steel.

The JP 2000 317 583 A discloses a method for determining a length division of molten steel strands in a multi-strand continuous caster, a standard length being counted on the next foremost strand in a range between a current starting position determined by a foremost strand and an end position determined by the strand end of a shortest strand, and the length division being continued by counting further standard lengths on the strands protruding beyond the end position.

The scientific article " Slab scheduling at parallel continuous casters "by MG Wichmann and TS Spengler, published in December 2015 in the International Journal of Production Economics, Volume 170, Part B, pages 551-562 , discloses a method for dividing and temporally arranging several continuous casting orders over several cast strands. For this purpose, the parameters of the orders are entered into a MIP computer model (GRASP algorithm), which determines the distribution of the slabs to be cast among the cast strands and their chronological order in each cast strand in such a way that a cost function with 19 boundary conditions is minimized. The width of the individual slabs is modeled with a value that varies between an initial width and a final width, the initial and final widths being within a tolerance interval specified by the order.

The scientific article " Decision support system for the batching problems of steelmaking and continuous-casting production "by L. Tang and G. Wang, published in December 2008 in the journal" Omega ", Volume 36, Issue 6, pages 976-991 , discloses two heuristic MIP models for determining solutions to the charging problem in continuous casting: one based on dynamic programming and one based on a greedy algorithm with a neighborhood structure and a taboo list. The number of orderless Additional slabs can be reduced by optimizing slab weights and dimensions.

The invention is based on the object of creating a method for controlling a continuous casting plant for producing slabs, a computer program product and a control unit for controlling a continuous casting plant for producing slabs. The objects on which the invention is based are achieved by the features of the independent patent claims. Preferred embodiments of the invention are indicated by the dependent claims.

• Empfangen mehrerer Gießaufträge, wobei jeder Gießauftrag eine Bedarfsmenge an dem Material, eine zugehörige Brammenbreite und Toleranzangaben bezüglich der Gießaufträge umfasst,
• Bestimmung für jeden der Gießaufträge aus den jeweiligen Bedarfsmengen und den jeweiligen Brammenbreiten eines Satzes von zu gießenden Brammen mit zugehörigen Brammengewichten und Brammenbreiten,
• Sortierung aller zu gießenden Brammen aller Gießaufträge gemäß einem Sortierkriterium zum Erhalt einer sortierten Basisfolge von zu gießenden Brammen, wobei das Sortierkriterium die Brammenbreiten umfasst,
• gleichmäßige Partitionierung der sortierten Basisfolge in eine Anzahl von Teilfolgen, wobei die Anzahl der Teilfolgen der Anzahl der Kokillen entspricht,
• für jede der Teilfolgen, Anpassung der Brammenbreite der zu gießenden Brammen der Teilfolge unter Berücksichtigung der Toleranzangaben, wobei aufgrund der Anpassung die Breitensprünge zwischen zwei in der Teilfolge unmittelbar aufeinanderfolgenden zu gießenden Brammen einen vorbestimmten Sprungwert nicht überschreiten, wobei aufgrund der angepassten Brammenbreiten angepasste Teilfolgen resultieren,
• Übermittlung von Steuerdaten an die Stranggussanlage zur Herstellung der in den angepassten Teilfolgen bestimmten zu gießenden Brammen, wobei in den Steuerdaten für jede der Teilfolgen die Reihenfolge der Herstellung der Brammen der Reihenfolge entspricht, in welcher die zu gießenden Brammen in der jeweiligen angepassten Teilfolge bestimmt sind,

wobei das Sortierkriterium die Brammenbreiten in abnehmender Reihenfolge umfasst.A method for controlling a continuous casting plant for producing slabs from a predetermined material is specified, the continuous casting plant having a number of molds for producing corresponding cast strands, the method comprising:

• Receiving several casting orders, each casting order comprising a required quantity of the material, an associated slab width and tolerance information with regard to the casting orders,
• Determination for each of the casting orders from the respective required quantities and the respective slab widths of a set of slabs to be cast with the associated slab weights and slab widths,
• Sorting of all slabs to be cast of all casting orders according to a sorting criterion to obtain a sorted basic sequence of slabs to be cast, the sorting criterion including the slab widths,
• uniform partitioning of the sorted basic sequence into a number of subsequences, the number of subsequences corresponding to the number of molds,
• for each of the sub-sequences, adaptation of the slab width of the slabs to be cast of the sub-sequence taking into account the tolerance specifications, whereby due to the adaptation the width jumps between two slabs to be cast immediately following one another in the sub-sequence one Do not exceed the predetermined grade rule, resulting in adapted partial consequences due to the adapted slab widths,
• Transmission of control data to the continuous casting plant for the production of the slabs to be cast determined in the adapted partial sequences, whereby in the control data for each of the partial sequences the order of the production of the slabs corresponds to the order in which the slabs to be cast are determined in the respective adapted partial sequence,

wherein the sorting criterion comprises the slab widths in decreasing order.

Embodiments of the invention could have the advantage that the amount of waste (i.e. the production of storage slabs not currently included in the orders) can be reduced through the optimized production of the slabs and thus the casting performance of the continuous casting plant can be maximized. Due to the sorting criteria, the batch purity (one converter filling) of the individual casting orders and thus the assigned customer orders is improved, which means that the sampling effort for these orders is reduced, since one sampling is required for each order. The latter is relevant because the coils must meet certain quality criteria with regard to the materials used. For this reason, sampling must take place per batch (i.e. per melt) in order to check the material quality.

The term “control” of the continuous casting plant is generally understood to mean that the continuous casting plant is provided with the continuous casting data from which the actual continuous casting program can then be created. The control data contain all information relating to the slabs to be produced with regard to the production sequence, as well as their materials and size information. The continuous casting data therefore specify the casting sequence, for example the slab widths and lengths to be produced, from which a control program or continuous casting program for the corresponding control of the molds, the transport speed of the strand, etc. can be created in the continuous casting plant. According to one embodiment of the invention, the continuous casting plant is a multi-strand plant with several parallel strands, each strand being assigned one of the molds, the control being carried out for the parallel simultaneous production of the slabs to be cast determined in the partial sequences. The control data can, for example, specify in which order which slabs with which width are to be produced in parallel and simultaneously.

In this case, the method includes an unambiguous assignment of each of the partial sequences to one of the strands, the assignment being made in such a way that the average slab width of the slabs to be cast determined in the respective partial strands decreases steadily from the inner strands to the outer strands. This could lead to an increase in the quality of the slabs produced, since the quantities of material flowing out of the manifold are regularly distributed through the corresponding pouring pipes into the corresponding molds: In the middle, the greatest material outflows take place through the pouring pipes, whereas the material outflows relating to the outer pouring pipes and Molds are reduced. Overall, this could prevent corresponding turbulence of the liquid material in the distributor.

According to one embodiment of the invention, due to the uniform partitioning, the number of slabs to be cast determined in the respective partial sequences is identical for all partial sequences. All of the casting orders on which the partial sequence is based are fully taken into account. By suitably adapting the slab lengths, the strand lengths of the individual partial strands can be adapted to one another without changing the total weight of all partial strands. As a result of the associated shortening of the maximum partial strand length, the total casting time with regard to the casting orders could also be minimized, whereby overall the utilization of the system and thus the casting performance can be further optimized.

It should be noted at this point that uniform partitioning in the context of the present description is understood to mean that segments of the sorted basic sequence are used unchanged as partial sequences, the sorting contained within the segments being retained with regard to the slabs. For example, if the basic sequence describes 20 slabs to be cast, an even partitioning could look like slabs 1 to 5 are contained in a first partial sequence, slabs 6 to 10 in a second partial sequence, slabs 11 to 15 in a third partial sequence and slabs 16 to 20 are contained in a fourth partial sequence. The slabs to be cast, which are described in the sorted basic sequence, are virtually simply cut out photographically.

• Bestimmung des Gesamtgewichts aller zu gießenden Brammen aller angepassten Teilfolgen,
• Vergleichen des Gesamtgewichts mit einem Zielgewicht zum Erhalt eines Vergleichswertes,
• für alle in den angepassten Teilfolgen bestimmten zu gießenden Brammen, gleichartige Veränderung des Brammengewichts oder der Brammenlänge anhand des Vergleichswertes zum Erhalt aktualisierter angepasster Teilfolgen, wobei im Falle dessen, dass hierdurch veränderte Brammengewichte oder die hierdurch veränderte Brammenlänge die Toleranzangaben des zugehörigen Gießauftrages verletzen, keine Veränderung des Brammengewichts oder der Brammenlänge erfolgt,
• Wiederholung der Schritte der Bestimmung des Gesamtgewichts, des Vergleichens und der Veränderung des Brammengewichts oder der Brammenlänge bis der Vergleichswert in einem vorbestimmten Schwellbereich liegt.

According to one embodiment of the invention, the method further comprises after adjusting the slab widths:

• Determination of the total weight of all slabs to be cast of all adapted partial sequences,
• Comparing the total weight with a target weight to obtain a comparison value,
• for all slabs to be cast determined in the adjusted partial sequences, similar change in the slab weight or the slab length based on the comparative value to obtain updated adjusted partial sequences, whereby in the event that the resulting changed slab weights or the resulting changed slab length violate the tolerance specifications of the associated casting order, no change the slab weight or length,
• Repeating the steps of determining the total weight, comparing and changing the slab weight or the slab length until the comparison value is in a predetermined threshold range.

This could contribute to the fact that when the casting orders are primarily specified, the entire target quantity is planned for the specific order and additional slabs without additional orders to achieve the target weights are avoided.

This could also help to maximize the casting performance of the system while adhering to and utilizing the tolerance specifications with regard to the casting orders, since the swelling range and the target weight can be selected in such a way that the available amount of material from which the slabs are cast, optimally exploits. For example, the target weight corresponds to at least an integral multiple of the weight that can be achieved with the provision of the material from a converter. If, for example, the total weight of the slabs to be cast of the adapted partial sequences is initially 275 tonnes, whereas with a converter, for example, only 270 tonnes can be achieved, this would mean that with regard to the difference of five tonnes, another casting process would have to be carried out with another converter , in which case 265 tons of melt could initially not be used in this regard. If one now uses the tolerance information regarding the casting orders and "exhausts them", the dimensioning of the slabs to be produced could be optimized by the described method so that their total weight is the desired 270 tons and thus the melt using only one converter Casting orders can be fulfilled.

The comparison value comprises, for example, the quotient of the total weight and the target weight, the change in the slab weight or the slab length comprising a multiplication of the slab weight or the slab length by the quotient. This could make it possible in a simple manner to achieve an optimization of the total weight quickly and in a targeted manner in one or more iterations. The swelling range can be, for example, a deviation of the total weight from the target weight of <3%.

According to one embodiment of the invention, after adjustment of the slab widths for all slabs to be cast of all adapted partial sequences, the slab width is changed in each case in the same way while simultaneously shortening the slab length while maintaining the slab weight Casting order violated, no change in slab width or length has taken place.

This could have the advantage that it enables a reduction in the casting times by achieving shorter strand lengths at higher widths. If one assumes that the throughput speed of the strands through the plant is constant or the length of the slab produced per unit of time is constant, then this reduction in the slab length while maintaining the slab weight and correspondingly increasing the slab width leads to the time required for production of the casting program is reduced.

• Bestimmung eines ersten Quotienten von maximal zulässiger Brammenbreite und Breite der aktuellen Bramme,
• Bestimmung eines zweiten Quotienten der Breite der Teilfolge der aktuellen Bramme unmittelbar vorhergehenden Bramme und der Breite der aktuellen Bramme, wobei der zweite Quotient nur bestimmt wird, wenn die aktuelle Bramme nicht die erste Bramme der Teilfolge ist,
• Bestimmung eines dritten Quotienten der Breite der in der Teilfolge der aktuellen Bramme unmittelbar nachfolgenden Bramme plus dem Sprungwert und der Breite der aktuellen Bramme, wobei der dritte Quotient nur bestimmt wird, wenn die aktuelle Bramme nicht die letzte Bramme der Teilfolge ist.

For example, the sorting criterion includes the slab widths in descending order, with the same type of change in the slab width while simultaneously shortening the slab length for all slabs of an adapted partial sequence:

• Determination of a first quotient of the maximum permissible slab width and the width of the current slab,
• Determination of a second quotient of the width of the sub-sequence of the current slab immediately preceding slab and the width of the current slab, the second quotient being only determined if the current slab is not the first slab of the sub-sequence,
• Determination of a third quotient of the width of the slab immediately following in the partial sequence of the current slab plus the grade rule and the width of the current slab, the third quotient only being determined if the current slab is not the last slab of the partial sequence.

While the first quotient initially takes into account the possible tolerances with regard to the slabs, the second quotient ensures that the strand is avoided. Positioning means that in the sequence the successor of the current slab suddenly becomes wider than the predecessor, that is, a width adjustment to larger widths suddenly takes place, which is not desired, however. Based on the initial sorting of the slabs to be cast according to the sorting criterion of decreasing slab widths, it is desired to optimize the casting performance of the system that the width is always adjusted towards smaller widths. The third quotient is ultimately used to avoid a leap in breadth to the successor that cannot be afforded by the system.

• Multiplikation der Breite der aktuellen Bramme und Division der Länge der aktuellen Bramme mit dem kleinsten Wert des ersten, zweiten und dritten Quotienten,
• Wiederholung der Schritte der Bestimmung des ersten, zweiten und dritten Quotienten sowie der Multiplikation, bis entweder keine Änderung der Breite der Bramme mehr erfolgt oder bis eine vorbestimmte Anzahl von Iterationen erreicht oder überschritten wurde.

According to one embodiment of the invention, the similar change in the slab width with a simultaneous shortening of the slab length for all slabs of an adapted partial sequence further comprises:

• Multiplication of the width of the current slab and division of the length of the current slab by the smallest value of the first, second and third quotient,
• Repetition of the steps of determining the first, second and third quotients and of the multiplication until either the width of the slab is no longer changed or until a predetermined number of iterations has been reached or exceeded.

By multiplying by the smallest value of the quotient, it could be ensured that the strand widths can actually be varied in an optimized manner in such a way that the casting sides can actually be optimized with short slabs with a large width, since this allows the process to be carried out in small steps could approximate the optimal strand widths and strand lengths without overshooting the target here.

• Multiplikation der Breiten des Paars der aktuellen Brammen und Division der Längen des Paars der aktuellen Brammen mit dem insgesamt kleinsten der Werte der ersten, zweiten und dritten Quotienten, welche bezüglich dieses Paares der aktuellen Brammen bestimmt wurde,
• Wiederholung der Schritte der Bestimmung des ersten, zweiten und dritten Quotienten sowie der Multiplikation, bis entweder keine Änderung der Breite der Brammen mehr erfolgt oder bis eine vorbestimmte Zahl von Iterationen erreicht oder überschritten wurde.

According to one embodiment of the invention, the continuous casting system has a common cutting system for the two strands for each pair of the strands Cutting parallel cast slabs, for a pair of the adapted partial sequences which are assigned to one of the pairs of strands, each forming a pair of parallel cast slabs at the same position of the respective partial sequences of the specific slabs, the determination of the first, second and third quotient is carried out for a pair of current slabs of the slabs to be cast in parallel, the similar change in the slab width with simultaneous shortening of the slab length for all slabs of all pairs of the adapted partial sequences in each case comprises:

• Multiplication of the widths of the pair of current slabs and division of the lengths of the pair of current slabs by the total smallest of the values of the first, second and third quotients, which was determined for this pair of current slabs,
• Repetition of the steps of determining the first, second and third quotients and of the multiplication until either the width of the slabs is no longer changed or until a predetermined number of iterations has been reached or exceeded.

This could have the advantage that it takes into account the technical characteristics of the system, with the corresponding cutting system for cutting a strand always only being available for a given pair of strands. However, this means that in practice the two parallel strands can only ever be cut simultaneously to obtain slabs of identical length. By using the overall smallest of the values of the quotients, which was determined with respect to the total of the pair of current slabs, this technical restriction is now taken into account in an optimized step sequence and it is ensured that an optimization of casting times is possible and here strand pairs with the Take into account the restriction of identical slab lengths.

According to one embodiment of the invention, each casting order comprises a KIM weight, the sorting criterion being the slab widths as the main criterion decreasing order and includes the KIM weight as a second criterion, the tolerance information each comprising a lower limit and an upper limit with regard to the slab widths and the KIM weights.

It should be noted that the use of KIM weights in relation to coils is a standard specification in the processing and manufacture of strip materials such as strip steel. KIM means a weight specification in kilograms per millimeter of coil width. For example, if the coil width is 570 mm and the coil weight is 10500 kg, this results in a KIM of 18.4 kg / mm. Since the specific weight of the material is constant, the dimensions, weight and KIM can be converted with one another. If, for example, in the case of steel strip, a strip thickness of 3.5 mm and a specific weight of 7.8 kg / dm ^{3 are} assumed, a corresponding length of strip steel can be calculated from this, namely in the above example the KIM weight of 18, 4 kg / mm of a length of 674764 mm. The KIM weight can therefore be used as a width-independent indicator for the slab length, since it can be assumed with regard to the slabs that their thicknesses are to be regarded as predetermined and constant.

• Bestimmung eines minimalen Brammengewichts aus der Untergrenze der Brammenbreiten und der Untergrenze des KIM-Gewichts,
• Bestimmung eines maximalen Brammengewichts aus der Obergrenze der Brammenbreite und der Obergrenze des KIM-Gewichts,
• Bestimmung eines Mittelwertes von minimalem und maximalem Brammengewicht,
• Bestimmung der benötigen Anzahl von zu gießenden Brammen, um bei dem Mittelwert des Brammengewichts die Bedarfsmenge an Material gerade zu überschreiten, wobei durch die Anzahl der zu gießenden Brammen der Satz von zu gießenden Brammen gebildet wird.

According to one embodiment of the invention, determining the set of slabs to be cast comprises for each casting order:

• Determination of a minimum slab weight from the lower limit of the slab widths and the lower limit of the KIM weight,
• Determination of a maximum slab weight from the upper limit of the slab width and the upper limit of the KIM weight,
• Determination of an average value of the minimum and maximum slab weight,
• Determination of the required number of slabs to be cast in order to just exceed the required amount of material at the mean value of the slab weight, the number of slabs to be cast forming the set of slabs to be cast.

This could have the advantage that, with regard to each casting order, the number of slabs corresponding to this casting order can be determined so that there is still enough leeway within the given tolerances to vary the strand widths or strand lengths for the subsequent optimization steps. Overall, this would ensure the greatest possible flexibility with regard to the implementation of the method of scattering the continuous casting plant.

• Ausgehend von der ersten oder der letzten zu gießenden Brammen der Teilfolge, Bestimmung der Breitendifferenz zwischen der aktuellen Bramme und der der aktuellen Bramme in der Teilfolge unmittelbar folgenden Bramme,
• im Falle dessen die Differenz größer ist als der Sprungwert, Reduktion der Breite der aktuellen Bramme so weit, dass die daraus resultierende Breitendifferenz zu der unmittelbar nachfolgenden Bramme dem Sprungwert entspricht, andernfalls Beibehaltung der Breite der aktuellen Bramme.

According to one embodiment of the invention, the adaptation of the slab widths of the slab to be cast comprises the partial sequence:

• Starting from the first or the last slab to be cast in the partial sequence, determining the difference in width between the current slab and the slab immediately following the current slab in the partial sequence,
• In the event that the difference is greater than the grade rule, the width of the current slab is reduced to such an extent that the resulting difference in width to the immediately following slab corresponds to the grade rule, otherwise the width of the current slab is retained.

It is also possible that, in the event that the reduced width of the current slab violates the associated tolerance specifications, the current slab is set to the minimum permissible width in the tolerance range and, after the slab widths have been adjusted for all slabs of the partial sequence, the procedure is reversed starting from the last or the first slab to be cast is repeated.

This could have the advantage that the strand widths are varied in such a way that the most compatible width transitions from slab to slab in the partial sequence are guaranteed. In particular, it could be avoided that there are jumps in width which technically cannot be implemented at all during the transition from one slab to the next through the system, so that what are known as the first step in this regard for implementation Intermediate slabs or storage slabs would have to be inserted into the partial sequence in order to realize such width transitions in several steps. A storage slab, however, in turn means an ineffective utilization of the continuous casting plant, since it is uncertain at what point in time the storage slab can actually be used. In addition, a storage slab would have to be assigned to another casting order at a later point in time, so that there is no uniform, identical quality within the casting order and the resulting slabs.

• Bestimmung für jede zu gießenden Brammen aller Teilfolgen aus den angepassten Brammenbreiten und der zugehörigen Untergrenze und Obergrenze des KIM-Gewichts eine dementsprechende minimale und maximale Länge der Bramme,
• für jedes Paar von parallel zu gießenden Brammen Bestimmen eines Durchschnittswerts bezüglich der beiden minimalen und maximalen Längen der Brammen und Festlegung der Länge der beiden Brammen auf dem Durchschnittswert.

According to one embodiment of the invention, each casting order comprises a KIM weight, the tolerance specifications each including a lower limit and an upper limit with respect to the KIM weights, the continuous casting system having a common cutting system for each pair of the strands for cutting parallel cast slabs for a pair of adapted partial sequences which are assigned to one of the pairs of the strands, the slabs determined in each case at the same position of the respective partial sequences forming a pair of slabs to be cast in parallel, the method further comprising after adaptation of the slab lengths:

• Determination for each slab to be cast of all partial sequences from the adapted slab widths and the associated lower limit and upper limit of the KIM weight, a corresponding minimum and maximum length of the slab,
• for each pair of slabs to be cast in parallel, determining an average value with respect to the two minimum and maximum lengths of the slabs and determining the length of the two slabs on the average value.

On the one hand, this could ensure that an identical length of the slabs produced can be guaranteed with respect to the parallel sub-strands associated with one another. On the other hand, for this special case, a continuous casting plant with pairs of strands, which one each have common cutting system, it can be ensured that here also compatible slab lengths are produced in the most effective way possible. Even though the continuous casting system has a common cutting system for a pair of strands and the two parallel strands must have the same length as a result, it could still be guaranteed that the casting performance of the system is maximized, i.e. in the above example the number of necessary storage slabs is minimized .

In a further aspect, the invention relates to a computer program product with instructions that can be executed by a processor for carrying out the method described above.

In a further aspect, the invention relates to a control unit for controlling a continuous casting plant for producing slabs from a predetermined material, the continuous casting plant having a number of molds for producing corresponding cast strands, the control unit having a processor and a memory, the memory being provided by the Processor contains executable instructions, the execution of the instructions by the processor controlling the control unit to: receive a plurality of casting orders, each casting order comprising a required quantity of the material, an associated slab width and tolerance specifications relating to the casting orders; Determination for each of the casting orders from the respective required quantities and the respective slab widths of a set of slabs to be cast with associated slab weights and slab widths; Sorting of all slabs to be cast of all sets of all casting orders according to a sorting criterion in order to obtain a sorted basic sequence of slabs to be cast, the sorting criterion comprising the slab widths; Uniform partitioning of the sorted basic sequence into a number of subsequences, the number of subsequences corresponding to the number of molds; For each of the sub-sequences, adaptation of the slab widths of the slabs to be cast of the sub-sequence taking into account the tolerance specifications, with the width jumps between two slabs to be cast immediately following one another in the sub-sequence being a predetermined one Do not exceed the grade rule, with modified partial consequences resulting from the adjusted slab widths; Transmission of control data to the continuous casting plant for the production of the slabs to be cast determined in the adapted partial sequences, whereby in the control data for each of the partial sequences the order of the production of the slabs corresponds to the order in which the slabs to be cast are determined in the respective adapted partial sequence, wherein the sorting criterion comprises the slab widths in decreasing order.

It should be noted that the examples and embodiments described above can be combined with one another in any way, as long as their combination falls under the subject matter of the claims.

Figur 1

ein System von Steuereinheit und Stranggussanlage,

Figur 2

ein Flussdiagramm eines Verfahrens zur Steuerung einer Stranggussanlage,

Figuren 3 - 9

die Umwandlung verschiedener Gießaufträge in entsprechende Steuerdaten für eine Stranggussanlage in tabellarischer Form.

In the following, preferred embodiments of the invention are explained in more detail with reference to the drawings. Show it:

Figure 1

a system of control unit and continuous casting plant,

Figure 2

a flow chart of a method for controlling a continuous casting plant,

Figures 3 - 9

the conversion of various casting orders into corresponding control data for a continuous casting plant in tabular form.

In the following, elements that are similar to one another are identified by the same reference symbols.

The Figure 1 shows a system comprising a control unit 100 and a continuous casting plant 101. Here, the continuous casting plant 101 will first be explained in more detail. A converter 122 is used to provide liquid material. in the In the following, it is assumed, without loss of generality, that the material is steel, so that the converter can take up liquid steel. The liquid steel can be fed into a distributor 124 via a pan (not shown in more detail), the distributor then having the function of distributing the liquid steel to the individual strands in the case of the multi-strand system shown. Specifically, the liquid steel is introduced from the distributor 124 into the molds 126 via pouring pipes, which are likewise not shown in detail. The molds are cooled on their insides, so that the liquid steel solidifies on the insides. During casting, the mold is moved in an oscillating manner in order to prevent the steel from sticking to the cooled walls and to support the transport process. When leaving the mold, the strand now has that solidified shell a few centimeters thick, while the majority of the cross-section is still liquid. The strand is then cooled again and, supported by rollers 130, moved on.

The result in the example is Figure 1 a set of four strands in total. Also in the example of the continuous casting plant from Figure 1 The two left strands form a pair and the two right strands also form a pair 128. The pair formation is given because a cutting device 134 is provided for each pair 128 of strands, which is provided for dividing the strand to obtain individual slabs 132 . This leads to the technical restriction that the slabs 132 of a strand pair 128 inevitably always have to have identical lengths.

The control parameters that are important for the products are controlled, ie the width of the molds 126 and the slab lengths to be produced by the cutting devices 134, as well as the continuous casting process, ie the movement of the strand, the pouring of the molten steel into the ladle into the distributor, the movement of the mold 126 etc. by a continuous casting program which is transmitted to the external system by means of the interface and is contained in the memory 120 of a control computer 114. The control computer 114 also has a processor 118 that is capable of what is contained in the memory 120 Execute a continuous casting program in order to control the continuous casting plant. The control computer 114 also has an interface 116 via which the control computer can receive control data 112 from a control unit 100.

The control data 112 determine the slabs that are to be produced by the continuous casting plant. The control data determine the sequence and distribution of the slabs on the individual strands, as well as the geometric dimensions of the slabs in detail.

The control unit 100 has a processor 102, an interface 104 and a memory 106. The interface 104 is used for communication with the interface 116. The memory 106 comprises various casting orders 108 and instructions 110 the control unit 100 is able to perform the following in Figure 2 to carry out the described method with respect to the casting orders 108.

The implementation of each in Figure 2 The process steps discussed here are exemplified using various casting orders in the Figures 3 - 9 reproduced in tabular form.

The method for controlling the continuous casting plant 101 begins in step 200 of FIG Figure 2 with the receipt of the casting orders 108, which are then contained in the memory 106 of the control unit 100. In Figure 3 various casting orders with the designation order 1, order 2, ... order 7 are specified, for example, order 1 specifies a required quantity of 50 t with a rolling width of 520 mm, with tolerances relating to the rolling width of a minimum of 490 mm and Maximum 550 mm are specified. Since the casting orders are all given for the goal of producing steel coils, an associated minimum and maximum KIM weight is also specified for each of the casting orders.

The fact that coils are to be produced from the slabs is only to be seen as an exemplary application - other processing options for slabs are well known to the person skilled in the art.

For order 1, the minimum KIM weight is 15 kg / mm and the maximum KIM weight is 20 kg / mm. From this, an associated semi-finished product weight of at least 7959 kg and a maximum semi-finished product weight of a maximum of 10192 kg can be calculated with regard to the roll width of 520 mm, whereby an output of 98% is taken into account here (for example 520 x 15 / 0.98). In other words, a slab from which a coil with the aforementioned details of the rolling width and the KIM weights will have a total weight of between at least 7959 kg and a maximum of 10192 kg.

Each order therefore specifies a required quantity of material (in the example of the Figure 3 , Order 1 with 50,000 kg) and an associated slab width, in the example of Figure 3 with order 1 520 mm and tolerance specifications with regard to the widths, again in the example of Figure 3 for order 1, the minimum and maximum KIM weight and the resulting slab weights.

First of all, a set of slabs to be cast with associated slab weights and slab widths is determined for each of the orders from the respective required quantities and the respective slab widths. From the in Figure 3 Minimum and maximum weight of semi-finished products (slab weight) determined for each order, an average value can now be determined, which in Figure 3 with regard to order 1 corresponds to an amount of 9076 kg. In order to achieve the required quantity of 50 t required for order 1, this corresponds to a number of six slabs, since the required quantity of 50 t is only achieved with a number of six slabs of 9076 kg each. In the example of order 1, the amount that has to be produced with regard to order 1 is even clearly exceeded, namely 54456 kg are achieved by these six slabs at the assumed average slab weight.

The slabs are then sorted in step 204 to obtain a basic sequence. The sorting takes place according to a sorting criterion, the sorting criterion including the width of the slab. Starting from Figure 4 the rolling widths carried out there are now listed and sorted individually for each order, starting from the largest rolling width to the smallest rolling width, with the corresponding associated result in Figure 5 can be seen. Order 2 with the largest rolling width of 650 appears with the number of specified slabs of three initially in the top three lines of the basic sequence of Figure 5 , followed by the four slabs relating to order 6 with a rolling width of 600 mm, then followed by the five slabs from order 5 with a rolling width of 550 mm, etc. The in Figure 5 The sequence of the sorted slabs to be cast shown here is referred to below as the “sorted basic sequence of slabs to be cast”.

Now, in step 206, the sorted basic sequence becomes the Figure 5 partitioned into a number of subsequences corresponding to the number of molds 126 of the Figure 1 corresponds to. There in Figure 1 If the continuous casting plant has four molds, the table is now partitioned Figure 5 in four partial sequences. Each partial sequence comprises an identical number of slabs to be cast. For this purpose, starting from the first slab to be cast, the table of Figure 5 a directly connected set of slabs to be cast is selected and defined as partial sequence 1. Partial sequence 1 and all other partial sequences include exactly eight slabs to be cast. These are marked with T1 in the following. This is followed by the next eight slabs to be cast on the table of Figure 5 which are marked as T2. This is followed by T3 and then T4, each comprising eight slabs to be cast. The resulting partial sequences T1, T2, T3 and T4 are in the Figure 6 shown.

After step 206 of partitioning into partial sequences, in step 208 each of the partial sequences is uniquely assigned to one of the strands, i.e. to one of the molds 126, the allocation being made in such a way that the average slab width going from the inner strands to the outer strands the slabs to be cast determined in the respective partial sequence steadily decreases. This leads to the fact that with regard to the continuous casting plant Figure 1 the two inner strands have the partial sequence 1 and partial sequence 2 with the large slab widths and the two outer strands have the partial sequences 3 and 4 with the smaller slab widths.

The result of the assignment of the individual partial sequences to the strands or the strand allocation scheme is in the Figure 7 shown.

Subsequently, in step 210, the slab widths of the slabs of the partial sequences to be cast are adapted for each of the partial sequences, taking into account the tolerance information. The aim is to keep the jumps in width between consecutive slabs to be cast in a partial sequence in a range that corresponds to the permissible specifications for the continuous casting plant. In the following, the maximum permissible difference in width between two consecutive slabs is referred to as the "grade rule", with the Figure 1 this grade rule is assumed to be a maximum of 25 mm. For the sake of simplicity, only the main strand 1 including the sub-strings 1 and 2 with the sub-strings 3 and 2 will be discussed in the following, with calculations relating to the second main branch including sub-strings 3 and 4 with the sub-strings 1 and 4 being able to be set in a similar manner.

If one now considers the sub-run 1 with partial sequence T3, there is a jump in width between order 1 and order 4 in lines 1 and 2 with regard to the slabs in the rolling width from 520 to 470 mm. This clearly exceeds the said 25 mm as a grade rule. The same applies to the jump from job 4 with a roll width of 470 mm to line 7 and job 7 with a roll width of 430 mm. In order to carry out the adjustment of the slab widths in step 210, the difference in width to the width of the following position is checked starting with the first position of the respective sorted partial sequences. If the difference is greater than the grade rule, the width of the current slab or the current position is reduced to such an extent that the resulting The difference in width corresponds to the grade rule. This is repeated cyclically. As a result, a maximum of 25 mm jumps result from the first position to the last position with regard to sub-line 1. It should be noted that the exact way in which this adjustment of the slab widths takes place in order to take into account the maximum grade rules of the width increments is possible in a variety of ways. Ultimately, the result is decisive here, namely that the grade rule is not exceeded in a partial sequence from one slab to be cast to the next.

As a special feature of the continuous casting plant of Figure 1 is that this is a so-called twin casting system, in which only one common cutting system 134 is available for a pair of the strands 128, it must be ensured that the slabs of the parallel sub-strands 128, i.e. the slabs in the Sub-strands 1 and 2 have identical lengths. However, this has not yet been taken into account in the previous adjustments. For this reason, the slab lengths are adapted, which is outlined in general in step 212 and specifically in steps 214-216. After the slab widths have now been adjusted in step 210, a corresponding associated minimum and maximum length of the slab can be calculated for a given strand width from the respective lower and upper limit of the slab weight. In the Figure 1 With regard to the first line and order 1, the adjusted strand width 500 mm results in a minimum slab length of 7849 mm and a maximum slab length of 10051 mm. These calculations can now be carried out for all slabs specified in the partial sequences. This corresponds to step 214 of FIG Figure 2 . Now, for each pair of slabs to be cast in parallel, an average value is determined with regard to the two minimum and maximum lengths of the slabs, and from this an average length is calculated for both slabs. With regard to sub-strand 1 and partial sequence T3, this results in an average slab length of 8757 mm, which is identical to sub-strand 2 (T2) and the first slab, order 5. Due to the different strand widths of 500 mm and 550 mm with regard to this first line there are correspondingly different associated slab weights of 8880 kg and 9768 kg.

It should also be noted here that it is irrelevant in which way this mean slab length is calculated exactly. It is possible, for example, that the target length (slab length) for the two slabs is selected as the middle of the tolerance range of the lengths of the two slabs as follows: Target length = length_min of lower strand 1 + (length_max of lower strand 2 - length_min of lower strand 1) / 2.

It should be noted that the minimum and maximum slab lengths can again be calculated using the density of steel, the constant thickness of the slab (e.g. 260 mm) and a certain tolerance deduction of e.g. 2% according to the known formula length = weight / (thickness x width x density).

The determination of the average value with regard to the two minimum and maximum lengths of the slabs and the determination of the length of the two slabs to the average value takes place in the Figure 2 in step 216.

The method continues in step 218 with the adaptation of the slab weights to the actual amount of liquid steel available in a converter. If one adds up in the Figure 8 the slab weights resulting from the slab lengths determined in step 216, then taking into account all sub-strands (including sub-strands 3 and 4, not shown), a total weight may result that does not optimally take into account the amount of liquid steel that is supplied with one or more converters To be available. For example, if the total weight is 275 t, but if only 270 t can be made available with a liquid steel converter, then the slab weight or length is changed evenly across all slabs of all sub-strands until the total weight obtained from this corresponds to the desired target weight . Here too, of course, the corresponding tolerances with regard to minimum and maximum slab width or minimum and maximum slab length must be taken into account.

By way of example, this can be implemented in step 218, the adjustment of the slab weights, in such a way that a quotient of the resulting total weight and target weight is determined across all slabs of all sub-strands, with the change in the slab weight or slab length of each individual slab being a multiplication of the slab weight or the slab length with this coefficient. The result in this regard is in the Figure 9 shown as an example. As a result, the total weights of the lower strands have increased here in order to optimally achieve the target weight.

After step 218, the casting times are optimized in step 220, the details of step 220 being outlined in steps 222-232. The aim is to increase the strand width while at the same time shortening the strand length in such a way that the weight is retained and no tolerance violation occurs. The steps of optimizing the casting times are detailed in Figure 2 with steps 222 to 232. For this purpose, the value Q1_i is first determined in step 222, with i indicating the respective pair of parallel slabs with respect to a pair of billets.

In the Figure 9 For example, i would specify the first line for the pair of slabs Order 1 and Order 5 with regard to substrings 1 and 2. Thus, with regard to order 1, the quotient of the maximum width (550 mm) and the width of the current slab (500 mm) is calculated and saved. Likewise, the quotient with regard to the first line or the first slab for lower strand 1, order 5 is calculated as 580 mm by 550 mm.

After this calculation in step 222, a further quotient is calculated in step 224 for the slabs of this pair of slabs, although there is no "pre-slab" here, since those specified in the first line Slabs are the first slabs. In this respect, Q2 does not play a role here. Then, in step 226, the quotient Q3 is calculated as the quotient of the width of the subsequent slab plus the grade rule and the width of the current slab. With regard to sub-strand 1, this would be 475 mm + 25/500 mm = 1. After the quotients Q1, Q2 (not available because there is no pre-slab) and Q3 have been calculated for the first line, sub-strand 1 and sub-strand 2 are now common (since parallel slab) uses the smallest value of the thus calculated quotient for the first row (step 230). This smallest quotient is then used to multiply the width of the current slab in row 1 for sub-strand 1 and sub-strand 2, and the length of the current slab is divided in each case (step 232).

The same is now carried out for the next row of sub-strand 1 and 2, that is, the next pair of slabs. Here Q2 can be calculated this time, because e.g. with regard to row 2 of lower strand 1, the pre-slab has a width of 500 mm and the current slab a width of 475 mm, so that Q2 = 500/475.

Ultimately, the steps of determining the various quotients and multiplying the widths and dividing the lengths, i.e. steps 222 to 232, can initially be carried out iteratively for all slabs of a pair of bars and for all bars, this process being repeated several times after these steps have been completed it can be repeated until either the width of the slabs is no longer changed or a certain number of iterations has been reached or exceeded. The result is slabs that are to be cast in this way, which are optimized with regard to the casting time in that the strand width is increased within the tolerances without any tolerance violations occurring.

The method finally ends in step 234 with the transmission of the control data 112 to the continuous casting plant using the interfaces 104 and 116. The control data contain information relating to the order in which the slabs are produced with the corresponding calculated width and length should. The control computer 114 can then control the control system in such a way that the corresponding production of the slabs takes place.

List of reference symbols

100

Control unit

101

Continuous casting plant

102

processor

104

interface

106

Storage

108

Casting orders

110

instructions

112

Tax data

114

Control computer

116

interface

118

processor

120

Storage

122

converter

124

Distributor

126

Mold

128

Strand pair

130

Leadership roles

132

Slab

134

Cutting device

Claims (18)

1. A method for controlling a continuous casting system (101) for producing slabs (132) from a predetermined material, the continuous casting system (101) comprising a plurality of molds (126) for creating corresponding cast strands, the method comprising:

   - receiving a plurality of casting orders (108), each casting order including a required quantity of the material, an associated slab width, and tolerance specifications with respect to the casting orders (108);

   - determining for each of the casting orders (108), from the respective required quantities and the respective slab widths, a set of slabs (132) to be cast with associated slab weights and slab widths;

   - sorting all slabs (132) to be cast of all sets of all casting orders (108) according to a sorting criterion to obtain a sorted base sequence of slabs to be cast, the sorting criterion including the slab widths;

   - uniformly partitioning the sorted base sequence into a number of subsequences, the number of subsequences corresponding to the number of molds (126);

   - adjusting, for each of the subsequences, the slab widths of the slabs (132) to be cast of the subsequence, taking the tolerance specifications into consideration, the jumps in widths between two slabs (132) to be cast immediately following one another in the subsequence not exceeding a predetermined jump value as a result of the adjustment, adjusted subsequences resulting from the adjusted slab widths; and

   - transmitting control data to the continuous casting system (101) for producing the slabs to be cast determined in the adjusted subsequences, the order of production of the slabs (132) in the control data for each of the subsequences corresponding to the order in which the slabs (132) to be cast are determined in the respective adjusted subsequence,

   wherein the sorting criterion includes the slab widths in descending order.
2. The method according to claim 1, wherein the continuous casting system (101) is a multi-strand system with a plurality of strands arranged in parallel, each strand being assigned one of the molds (126), and the control being carried out for the parallel simultaneous production of the slabs (132) to be cast determined in the subsequences.
3. The method according to claim 2, furthermore comprising an unambiguous assignment of each of the subsequences to one of the strands, the assignment being carried out in such a way that the average slab width of the slabs (132) to be cast determined in the respective subsequences continuously decreases from the inner strands to the outer strands.
4. The method according to any one of the preceding claims, wherein, as a result of the uniform partitioning, the number of slabs (132) to be cast determined in the respective subsequences is identical for all subsequences.
5. The method according to any one of the preceding claims, after the adjustment of the slab widths furthermore comprising:

   - determining the total weight of all slabs (132) to be cast of all adjusted subsequences;

   - comparing the total weight to a target weight for obtaining a comparison value;

   - for all slabs (132) to be cast determined in the adjusted subsequences, changing the slab weight or the slab length in the same manner based on the comparison value so as to obtain updated adjusted subsequences, no change being made in the slab weight or the slab length in the event that the slab weight thus changed, or the slab length thus changed, violates the tolerance specifications of the associated casting order; and

   - repeating the steps of determining the total weight, comparing, and changing the slab weight or the slab length until the comparison value is within a predetermined threshold range.
6. The method according to claim 5, wherein the target weight corresponds to at least one integer multiple of the weight achievable by providing the material from a converter.
7. The method according to claim 5 or 6, wherein the comparison value comprises the quotient of total weight and target weight, the change in the slab weight or the slab length including multiplying the slab weight or the slab length by the quotient.
8. The method according to any one of the preceding claims 5 to 7, wherein the threshold range is a deviation of the total weight from the target weight of less than 3%.
9. The method according to any one of the preceding claims, wherein, after the adjusting of the slab widths for all slabs (132) to be cast of all of the adjusted subsequences, the slab width is changed in each case in the same manner, while shorting the slab length and maintaining the slab weight, no change being made in the slab weight or the slab length in the event that the slab weight thus changed, or the slab length thus changed, violates the tolerance specifications of the associated casting order.
10. The method according to claim 9, wherein the sorting criterion includes the slab widths in descending order, the change of the slab width in the same manner, while shortening the slab length for all slabs (132) of an adjusted subsequence in each case comprising:

    - determining a first quotient of maximum allowable slab width and width of the current slab (132);

    - determining a second quotient of the width of the slab immediately preceding the current slab in the subsequence and the width of the current slab (132), the second quotient only being determined when the current slab is not the first slab in the subsequence; and

    - determining a third quotient of the width of the slab immediately following the current slab in the subsequence, plus the jump value, and the width of the current slab (132), the third quotient only being determined when the current slab is not the last slab in the subsequence.
11. The method according to claim 10, wherein the change of the slab width in the same manner, while shortening the slab length for all slabs (132) of an adjusted subsequence in each case furthermore comprises:

    - multiplying the width of the current slab and dividing the length of the current slab by the smallest value of the first, second and third quotients; and

    - repeating the steps of determining the first, second, and third quotients and multiplying, until either the width of the slabs (132) no longer changes or a predetermined number of iterations has been reached or exceeded.
12. The method according to claim 10, wherein the continuous casting system (101), for each pair of strands (128), comprises a shared cutting system (134) for the two strands for cutting slabs (132) cast in parallel, wherein, for a pair of the adjusted subsequences, which are assigned to one of the pairs of strands, the slabs (132) determined in the same position of the respective subsequences form a pair of slabs (132) to be cast in parallel, the determination of the first, second and third quotients being carried out for each pair of current slabs (132) of the slabs (132) to be cast in parallel, the change of the slab width in the same manner, while shortening the slab length for all slabs (132) of all pairs of the adjusted subsequences in each case comprising:

    - multiplying the widths of the pair of current slabs (132) and dividing the lengths of the pair of current slabs (132) by the overall smallest of the values of the first, second and third quotients which was determined with respect to the pair of current slabs (132); and

    - repeating the steps of determining the first, second, and third quotients and multiplying, until either the width of the slabs (132) no longer changes or a predetermined number of iterations has been reached or exceeded.
13. The method according to any one of the preceding claims, wherein each casting order includes a KIM weight, the sorting criterion including the slab widths in descending order as a primary criterion and the KIM weight as a secondary criterion, and the tolerance specifications in each case including a lower limit and an upper limit with respect to the slab widths and the KIM weights
14. The method according to claim 13, wherein the determination of the set of slabs (132) to be cast for each casting order comprises:

    - determining a minimum slab weight from the lower limit of the slab width and the lower limit of the KIM weight;

    - determining a maximum slab weight from the upper limit of the slab width and the upper limit of the KIM weight;

    - determining of a mean value of the minimum and the maximum slab weights, and

    - determining the required number of slabs (132) to be cast in order to just exceed the required amount of material at the mean value of the slab weight, the set of slabs (132) to be cast being formed by the number of slabs (132) to be cast.
15. The method according to any one of the preceding claims, wherein the adjustment of the slab widths of the slabs (132) to be cast of the subsequence comprises:

    - proceeding from the first or the last slab to be cast of the subsequence, determining the difference in width between the current slab and the slab (132) immediately following the current slab in the subsequence; and

    - if the difference is greater than the jump value, reducing the width of the current slab to such an extent that the resulting width difference with respect to the immediately following slab corresponds to the jump value, otherwise maintaining the width of the current slab.
16. The method according to any one of the preceding claims 2 to 15, wherein each casting order includes a KIM weight, the tolerance specifications in each case including a lower limit and an upper limit with respect to the KIM weights, the continuous casting system (101), for each pair of strands (128) comprising a shared cutting system (134) for the two strands for cutting slabs (132) cast in parallel, wherein, for a pair of adjusted subsequences, which are assigned to one of the pairs of strands, the slabs (132) determined in the same position of the respective subsequences form a pair of slabs (132) to be cast in parallel, after the adjustment of the slab widths the method furthermore comprising:

    - determining, for each slab to be cast of all subsequences, corresponding minimum and maximum lengths of the slab (132) from the adapted slab widths and the associated lower limit and upper limit of the KIM weight; and

    - for each pair of slabs to be cast in parallel, determining an average value with respect to the two minimum and maximum lengths of the slabs (132), and setting the length of the two slabs (132) to the average value.
17. A computer program product, comprising instructions executable by a processor for carrying out the method according to any one of the preceding claims.
18. A control unit (100) for controlling a continuous casting system (101) for producing slabs (132) from a predetermined material, wherein the continuous casting system (101) comprises a plurality of molds (126) for creating corresponding cast strands, the control unit comprising a processor and a memory, the memory including instructions executable by said processor, the execution of the instructions by the processor controlling the control device for:

    - receiving a plurality of casting orders (108), each casting order including a required quantity of the material, an associated slab width, and tolerance specifications with respect to the casting orders (108);

    - determining for each of the casting orders (108), from the respective required quantities and the respective slab widths, a set of slabs (132) to be cast with associated slab weights and slab widths;

    - sorting all slabs (132) to be cast of all sets of all casting orders (108) according to a sorting criterion to obtain a sorted base sequence of slabs to be cast, the sorting criterion including the slab widths;

    - uniformly partitioning the sorted base sequence into a number of subsequences, the number of subsequences corresponding to the number of molds (126);

    - adjusting, for each of the subsequences, the slab widths of the slabs (132) to be cast of the subsequence, taking the tolerance specifications into consideration, the jumps in widths between two slabs (132) to be cast immediately following one another in the subsequence not exceeding a predetermined jump value as a result of the adjustment, adjusted subsequences resulting from the adjusted slab widths; and

    - transmitting control data (112) to the continuous casting system (101) for producing the slabs to be cast determined in the adjusted subsequences, the order of production of the slabs (132) in the control data (112) for each of the subsequences corresponding to the order in which the slabs (132) to be cast are determined in the respective adjusted subsequence,

    wherein the sorting criterion includes the slab widths in descending order.

Images