Abstract:
Before the rolling of a metal strip on a finishing train, the actual width and actual temperature of portions of the metal strip are respectively detected. The portions of the metal strip are tracked while they run through the finishing train. The rolling stands are respectively assigned width controlling devices which determine the setpoint width and the actual width after the rolling in the assigned rolling stand, and a downstream additional setpoint value, by which the desired tension downstream of the assigned rolling stand is corrected in order to bring the actual width closer to the setpoint width. The downstream additional setpoint value is both taken into account in the determination of the actual width and fed to a tension controller, which sets an actual tension, in the metal strip downstream of the assigned rolling stand, in accordance with the corrected setpoint tension. Determining the downstream additional setpoint value by the difference between the setpoint width and the actual width of a portion of the metal strip.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    The present application is a 35 U.S.C. §§371 national phase conversion of PCT/EP2015/069501, filed Aug. 26, 2015, which claims priority of European Patent Application No. 14185055.2, filed Sep. 17, 2014, the contents of which are incorporated by reference herein. The PCT International Application was published in the German language. 
     
    
     TECHNICAL FIELD 
       [0002]    The present invention is directed to a method for rolling a metal strip in a finishing train, wherein the finishing train has multiple rolling stands, through which the metal strip passes in succession, and wherein the actual width and the actual temperature thereof is detected for each of the sections of the metal strip before they enter the finishing train. 
         [0003]    The present invention is furthermore directed to a computer program, which comprises machine code, which is executable by a control unit for a finishing train, wherein the execution of the machine code by the control unit causes the machine unit to operate the finishing train according to such a method. 
         [0004]    The present invention is furthermore directed to a control unit for a finishing train, wherein the control unit is programmed using such a computer program, so that the control unit operates the finishing train according to such a method. 
         [0005]    The present invention is furthermore directed to a finishing train for rolling a metal strip, wherein the finishing train has multiple rolling stands through which the metal strip passes in succession, and wherein the finishing train has such a control unit, which operates the finishing train according to such a method. 
       TECHNICAL BACKGROUND 
       [0006]    A hot rolling train for rolling metal strip generally consists of a roughing train, a finishing train, and a coiling device. The metal strip firstly passes through the roughing train and then the finishing train and is finally supplied to the coiling device. In many cases generally at least in hot strip trains for rolling steel strip, furthermore a cooling line is provided. If it is provided, the cooling line is arranged downstream of the finishing train and upstream of the coiling device. 
         [0007]    Narrow width tolerances are often specified for the rolling of the metal strip. Maintaining these width tolerances is an important quality feature. Actively influencing the width of the metal strip therefore generates an economic utility. 
         [0008]    The width of the metal strip is influenced both in the roughing train and also in the finishing train and also on the way to the coiling device. In some cases, this influencing is actively performed. 
         [0009]    Thus, for example, a method is known from the technical article “Development of Automatic Width Control System for Hot Strip Finishing Mills” by M. Nakayama et al., Proceedings of the Third International Conference on Technology of Plasticity, Kyoto, Jul. 1/6, 1990, vol. II, pages 791 to 796, in which a width measurement is performed after multiple (but not all) rolling stands of the finishing train. Using all provided width measurements, the missing width measured values are estimated by means of a model. A compensation for width deviations is performed by the calculation and switching on of an additional strip tension for each loop lifter controller. 
         [0010]    Performing a pilot control for the width deviations is known from the technical article “Automatische Breitenregelung in der Warmbandstraβe Borlänge der SSAB Tunnplat [automatic width regulation in the hot strip train Borlänge of SSAB Tunnplat]” by Harald Natusch et al., stahl and eisen 122 (2002), issue 11, pages 93 to 100. The width in the finishing train is ascertained in a manner supported by a model. A measurement of the width is performed before and after the roughing train and after the finishing train. 
         [0011]    Disclosed in “Automatische Breitenregelung in der Warmbandstraβe Borlânge der SSAB Tunnplåt” by Harald Natusch et al., is an integrated width control concept (“ein integriertes Breitenregelungskonzept”, page 95, left col., last paragraph). This concept comprises (see  FIG. 4 ) an edger E 1 , a measurement system, and sensors for monitoring the material position to derive the width of the rolled product along its length in the roughing mill (R 1 , R 2 ), the finishing mill (F 1 -F 6 ) and downstream of the finishing mill and furthermore algorithms and strategies for controlling the width of the rolled stock. 
         [0012]    Essential Measurement of the Width is Done at: 
         [0013]    Entry width at Edger E 1 , width of transfer bar downstream of R 2 , measurement of final strip width downstream of F 6 . Measured width data are considered by a level  2  process control (“PSC”), page 96, paragraph “Messwertverarbeitung”) of the roughing mill. The measured width data are assigned to specific positions of the rolled strip (rolled stock). 
         [0014]    Detecting the width of the metal strip in each case after the second and after the last rolling stand of a finishing train is known from the technical article “Automatic width control system using interstand tension in hot strip finishing mill” by Y. Hoshi et al., La Revue de Metallurgie-CIT, November 1996, pages 1413 to 1420. The tension between the first and the second rolling stands is regulated by means of the former measurement. The tensions between the third and the last rolling stand are regulated by means of the latter measurement. 
         [0015]    Detecting a variable which is characteristic for the mass flow between each two rolling stands and, building on the detected variable, setting the strip tension between the two rolling stands, in order to reduce a width change, is known from DE 103 38 470 B4. 
         [0016]    A method for regulating the width in a rolling train having at least two rolling stands, through which the metal strip passes in succession, is known from DE 198 51 053 A1. In this method, the width is detected after the last rolling stand passes through. The tension between the two rolling stands is regulated to influence the width of the metal strip. 
         [0017]    A method for regulating the strip width during the finish rolling of hot strip in a multi-stand rolling train is known from EP 0 375 095 B1. In this method, the strip width is measured before the next-to-last stand and after the last stand. A width regulation using pilot control is performed. The strip tension before the last rolling stand of the rolling train is used as the control variable. 
         [0018]    A width model for a finishing train is known from the technical article “Strip width variation behavior and its mathematical model in hot strip finishing mills” by Atsushi Ishii et al., Proceedings of The 7th International Conference on Steel Rolling 1998, Chiba, Japan, pages 93 to 98. Width influences in the rolling gap, for example, a relative strip profile change, a roller bend, a compressed length, and the intake-side and outlet-side tension are taken into consideration. Furthermore, width influences in the region between two rolling stands are taken into consideration, for example, the temperature, the tension prevailing in the metal strip, the yield strength, the strip temperature, and the duration. 
         [0019]    A simplified width model is derived building on a width model based on finite elements in the technical article “Direct Width Control Systems Based on Width Prediction Models in Hot Strip Mill” by Cheol Jae Park et al., ISIJ International, vol. (2007), issue 1, pages 105 to 113. The simplified width model is supplemented using a neuronal network. It models the width in the finishing train as a function of the intake-side tension in the metal strip, the present width, the thickness reduction, the compressed length, and the dimensional change resistance. 
         [0020]    The methods of the prior art already cause the actual width of the metal strip to approximate the target width. The methods often only function inadequately, however. In addition, in a hot strip train without coil box, the temperature distribution is often uneven viewed over the length of the metal strip, which in turn results in an uneven widening of the metal strip in the finishing train. 
       SUMMARY OF THE INVENTION 
       [0021]    The object of the present invention is to provide possibilities, by means of which the width of the metal strip can be set exactly in a simple and efficient manner. 
         [0022]    According to the invention, a method is provided for rolling a metal strip in a finishing train which has multiple rolling stands through which the metal strip passes in succession. 
         [0023]    The actual width and the actual temperature thereof are detected for each of the sections of the metal strip before they enter the finishing train. 
         [0024]    An actual width derived from the detected actual width, an initial target width, an actual temperature derived from the detected actual temperature, and a target temperature are associated with each of the sections of the metal strip. 
         [0025]    The sections of the metal strip are path-tracked during the passage through the finishing train. 
         [0026]    A width control unit is associated at least with each of the rolling stands with the exception of the last rolling stand. 
         [0027]    The respective width control unit for the section of the metal strip rolled in the associated rolling stand.
       a) On the basis of all of its target width before the rolling in the associated rolling stand, a target tension desired in the metal strip before the associated rolling stand, a target tension desired in the metal strip after the associated rolling stand, the target temperature associated with the respective section and parameters of the rolling procedure performed in the associated rolling stand, ascertains a target width after the rolling in the associated rolling stand and associates it with the respective section of the metal strip.   b) On the basis of all of its actual width before the rolling in the associated rolling stand, the target tension, which is corrected by an upstream additional target value, desired in the metal strip before the associated rolling stand, the target tension, which is corrected by a downstream additional target value, desired in the metal strip after the associated rolling stand, the actual temperature associated with the respective section, and the parameters of the rolling procedure performed in the associated rolling stand, ascertains an actual width after the rolling in the associated rolling stand and associates it with the respective section of the metal strip. The respective width control unit ascertains the downstream additional target value on the basis of the target tension desired in the metal strip after the associated rolling stand, the target temperature and the actual temperature of the section of the metal strip rolled in the associated rolling stand, the difference of target width and actual width of a section of the metal strip which is located at a predetermined point after the associated rolling stand, and the parameters of the rolling procedure.       
 
         [0030]    The respective width control unit ascertains the downstream additional target value such that the actual width of the section of the metal strip rolled in the associated rolling stand approximates the target width of the rolled section. 
         [0031]    The respective width control unit supplies the downstream additional target value to a respective tension regulator, which sets an actual tension prevailing in the metal strip after the associated rolling stand corresponding to the target tension corrected by the downstream additional target value. 
         [0032]    Only a single width measurement and a single temperature measurement are thus required, specifically between the roughening train and the finishing train. Width deviations can be compensated for highly accurately. If a width regulation is additionally also to be implemented, an additional width measurement after the finishing train is required for this purpose. Such a width measurement is typically provided, however, and therefore does not require additional hardware expenditure. 
         [0033]    In the simplest case, the actual widths and actual temperatures associated with the sections are identical to the detected actual widths and actual temperatures. However, preferably at least the detected actual widths, preferably also the detected actual temperatures are filtered, in particular low-pass filtered. By way of this procedure, the rolling of the metal strip can be performed relatively calmly (i.e., without high-frequency control interventions) in particular. The manipulation of the actual width via the strip tension thus has no negative effects on the rolling process. 
         [0034]    The filtering can be in particular such that no phase offset is induced by the filtering in the filtered variable (actual width or actual temperature) in relation to the unfiltered variable. Thus, filterings are to be performed in zero-phase filters. For this purpose, it is possible to provide a corresponding symmetrical filter, for example. Alternatively, it is possible that the detected actual widths are subjected to a first filtering and thus preliminarily filtered actual widths are ascertained and then the preliminarily filtered actual widths are subjected to a second filtering and the filtered actual widths are thus ascertained. Alternatively, the detected actual widths can be subjected in parallel to both the first filtering and also the second filtering and the mean value of the two filterings can be used as the filtered actual width. In both cases, the two filterings can have phasing. It is only required that the two filterings have inverse phasing in relation to one another, so that the phase offset caused by one filtering can be compensated for or balanced out by the other filtering. Similar procedures are possible if necessary with respect to the actual temperatures. 
         [0035]    It is possible that the initial target width is predefined. Alternatively, the initial target width can be ascertained on the basis of the actual width associated with the sections. 
         [0036]    It is possible that the predetermined point is permanently specified. Alternatively, it is possible that the predetermined point is specified to the width control units (optionally individually for each width control unit). For example, the middle between the associated rolling stand and the rolling stand directly downstream can be specified as the predetermined point for the respective width control unit. It is also optionally possible to provide the location at which a loop lifter engages on the metal strip as the predetermined point. 
         [0037]    A point in time at which the metal strip enters this rolling stand is preferably detected at least for the rolling stand of the finishing train through which the metal strip passes first. In this case, the path tracking can be adapted on the basis of this point in time, i.e., in particular started in a timely manner. 
         [0038]    It is alternatively possible to detect the actual width at the outlet of the roughening train or at the inlet of the finishing train. It is also alternatively possible to detect the actual temperature at the outlet of the roughening train or at the inlet of the finishing train. It is furthermore alternatively possible to firstly detect the respective actual width and the respective actual temperature for the entire metal strip (i.e., for all sections of the metal strip) and only then to perform the low-pass filterings. Alternatively, it is possible to perform the low-pass filterings simultaneously with the detection of the actual width and the actual temperature. Performing the low-pass filterings beforehand is advisable in particular if the actual width and the actual temperature are detected at the outlet of the roughening train. Performing the low-pass filterings together with the detection of the actual width and the actual temperature is advisable in particular if the actual width and actual temperature are detected at the inlet of the finishing train. Depending on how much time passes between the low-pass filterings and the entries of the sections of the metal strip into the first rolling stand of the finishing train, it can be necessary to progress the time development of the temperature of the sections by means of a temperature model. 
         [0039]    The number of rolling stands of the finishing train can be determined as needed. In general, the number of rolling stands is 3 to 8, usually 4 to 7, in particular 5 or 6. 
         [0040]    In particular steel, aluminum, and copper come into consideration as the metal. However, it is also possible that the metal strip consists of another metal. 
         [0041]    In the scope of the present invention, it is necessary at various points to know the velocity of the metal strip. For this purpose, it is possible to perform a corresponding velocity measurement directly. Alternatively, it is possible to ascertain the respective velocity in that, in relation to the point for which the velocity of the metal strip is to be detected, the circumferential velocity of rollers of an upstream rolling stand is detected and the velocity of the metal strip is ascertained therefrom in consideration of the lead. In a similar manner, it is possible, vice versa, to ascertain the respective velocity in that the circumferential velocity of rollers of a downstream rolling stand is detected and the velocity of the metal strip is ascertained therefrom in consideration of the lag. 
         [0042]    In many cases, a final rolling temperature is specified, which the metal strip is to have at the outlet of the finishing train. In this case, the final rolling temperature is preferably used as the target temperature. The actual temperature of the sections of the metal strip, in contrast, is preferably continuously tracked in a model-supported manner during the passage of the sections of the metal strip through the finishing train. 
         [0043]    The parameters of the rolling procedure can be determined as needed. In general, the rolling force, the rolling torque, the strip velocity on the inlet side and/or outlet side of the associated rolling stand, the rolling gap, the pass reduction, the compressed length of the metal strip, and material variables of the metal strip can be used as parameters of the rolling procedure, with respect to the associated rolling stand. 
         [0044]    In the simplest case, in the scope of the method according to the invention, only the widening during rolling in the rolling stands themselves is taken into consideration. However, it is preferably provided that the respective width control unit for the sections of the metal strip already rolled in the associated rolling stand tracks the target width after the rolling as a function of the spacing from the downstream rolling stand, the strip velocity on the outlet side of the associated rolling stand, the target tension desired in the metal strip after the associated rolling stand, the target temperature, and material characteristic variables of the metal strip and also tracks the actual width after the rolling as a function of the spacing from the downstream rolling stand, the strip velocity on the outlet side of the associated rolling stand, the target tension desired in the metal strip after the associated rolling stand, which is corrected by the downstream additional target value, the actual temperature, and the material characteristic variables of the metal strip. 
         [0045]    The creeping of the width between the rolling stands can also be taken into consideration by this procedure. 
         [0046]    The object is furthermore achieved by a computer program such that the execution of the machine code by the control unit causes the control unit to operate the finishing train according to a method according to the invention. 
         [0047]    The object is furthermore achieved by a control unit for a finishing train, wherein the finishing train is programmed using a computer program according to the invention, so that the control unit operates the finishing train according to a method according to the invention. 
         [0048]    The object is furthermore achieved by a finishing train for rolling a metal strip. The control unit of the finishing train is designed to operate the finishing train according to a method according to the invention. 
         [0049]    The above-described properties, features, and advantages of this invention and the manner in which they are achieved will become clearer and more comprehensible in conjunction with the following description of the exemplary embodiments, which are explained in greater detail in conjunction with the drawings. In the schematic figures: 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0050]      FIG. 1  shows a hot strip train, 
           [0051]      FIG. 2  shows sections of a metal strip, 
           [0052]      FIG. 3  shows a flow chart, 
           [0053]      FIGS. 4 to 6  show filterings, and 
           [0054]      FIG. 7A  shows a section of a finishing train; and 
           [0055]      FIG. 7B  shows a width control unit for a metal strip. 
       
    
    
     DESCRIPTION OF EMBODIMENTS 
       [0056]    According to  FIG. 1 , a hot strip train for rolling a metal strip  1  has a roughening train  2 , a finishing train  3 , and a coiling device  4 . The roughening train  2  can be omitted in individual cases—for example, in the case in which the metal strip  1  is already cast relatively thin. The finishing train  3  has, according to  FIG. 1 , multiple rolling stands  5 , through which the metal strip  1  passes in succession. The number of rolling stands  5  is generally between three and eight, in particular between four and seven, for example, five or six. 
         [0057]    The metal strip  1  can be, for example, a steel strip, an aluminum strip, a copper strip, or a strip made of another metal. 
         [0058]    The hot strip train—in particular the finishing train  3 —is controlled by a control unit  6 . The control unit  6  is programmed using a computer program  7 . The computer program  7  comprises machine code  8 , which is executable by the control unit  6 . The execution of the machine code  8  by the control unit  6  causes the control unit  6  to operate the finishing train  3  according to a method which will be explained in greater detail hereafter in conjunction with  FIG. 2  and the further figures. As a result of the programming using the computer program  7 , the control unit  6  thus operates the finishing train  3  accordingly. 
         [0059]    The metal strip  1  is virtually divided into sections  9  inside control unit  6 . The sections  9  can be defined, for example, according to  FIG. 2  by a uniform length  1 , by a uniform mass m, or by a detection at chronologically equidistant steps. 
         [0060]    According to  FIG. 3 , in a step S 1 , the actual width b 0  and the actual temperature T 0  thereof is detected for each of the sections  9  of the metal strip  1 . The detection of the actual width b 0  and the actual temperature T 0  is performed before the entry of the corresponding sections  9  into the finishing train  3 . For example, according to  FIG. 1 , corresponding measurement units can be arranged at the outlet of the roughening train  2 . Alternatively, the measuring units can be arranged at the inlet of the finishing train  3 . It is possible that the detection of the actual widths b 0  and the actual temperatures T 0  is completed for all sections  9  even before the frontmost section  9  of the metal strip  1  enters the finishing train  3 . Alternatively, it is possible that the detection of the actual widths b 0  and actual temperatures T 0  is still carried out for rear sections  9  of the metal strip  1  while front sections  9  of the metal strip  1  have already entered the finishing train  3 . Independently of the specific procedure used, the detection is performed, however, such that the association of an actual width b and an actual temperature T subsequently performed in a step S 2  is completed for each section  9  before the corresponding section  9  enters the finishing train  3 . 
         [0061]    In the simplest case, in step S 2 , the detected actual widths b 0  and actual temperatures T 0  are associated directly with the sections  9 . However, at least the detected actual widths b 0 , and preferably also the detected actual temperatures T 0 , are preferably filtered. In particular, low-pass filtering can be performed according to the illustration in  FIGS. 4 to 6 . In the case of a filtering, in step S 2 , a respective filtered actual width bF and a respective filtered actual temperature TF is ascertained for each section  9 . 
         [0062]    The filtering of step S 2  is preferably performed such that the filtered actual widths bF do not have a phase offset in relation to the original, unfiltered actual widths b 0  (zero-phase filtering). For example, for this purpose, according to  FIG. 4 , a filtering can be performed using a Gaussian bell curve (or another, symmetrical bell curve). Alternatively, one of the two following procedures is used. 
         [0063]    On the one hand, it is possible according to the illustration in  FIG. 5  that the detected actual widths b 0  are firstly subjected to a first filtering in a first filter block  10 . Preliminarily filtered actual widths bV are thus ascertained. The preliminarily filtered actual widths bV are then subjected to a second filtering in a downstream second filter block  11 . The results of the second filtering are the filtered actual widths bF. In this case, both the first filtering in the first filter block  10  and also the second filtering in the second filter block  11  can be subject to phasing. It is decisive in this case that the two filterings in the two filter blocks  10 ,  11  are subject to inverse phasing in relation to one another. The second filtering in the second filter block  11  therefore compensates the phase offset which was caused by the first filtering in the first filter block  10 . 
         [0064]    Alternatively, it is possible according to the illustration in  FIG. 6  to carry out the two filterings in the two filter blocks  10 ,  11  in parallel. In this case, the detected actual widths b 0  are thus subjected to both the first filtering and also the second filtering. The results of the two filterings are supplied in this case to a node point, in which the mean value of the two filterings is calculated. The mean value corresponds in this case to the filtered actual width bF. 
         [0065]    Similar procedures can be used for the ascertainment of the filtered actual temperatures TF. In general, the same type of filtering is used for the ascertainment of the filtered actual temperatures TF as for the ascertainment of the filtered actual widths bF. However, this is not absolutely required. A zero-phase filtering is preferably also to be performed with respect to the actual temperatures T 0 . 
         [0066]    In the case of a filtering, the filtered actual width bF ascertained for the respective section  9  of the metal strip  1  and the filtered actual temperature TF ascertained for the respective section  9  of the metal strip  1  are thus associated with the respective section  9  as the (new) actual width b or (new) actual temperature T, respectively. Furthermore, an initial target width b 0 * is associated with the respective section  9  as the target width b* and an initial target temperature T 0 * is associated as the target temperature T* in a step S 3 . 
         [0067]    It is possible that the initial target width b 0 * is externally specified to the control unit  6 , for example, by a higher-order control unit (not shown) or by an operator  12 . Alternatively, it is possible that the control unit  6  ascertains the initial target width b 0 * on the basis of the actual width b associated with the sections  9 . For example, the control unit  6  can perform a mean value calculation over all sections  9  of the metal strip  1 . In general, a final rolling temperature is specified to the control unit  6 , i.e., the temperature which the metal strip  1  is to have upon exiting from the finishing train  3 . It is possible that this temperature is used as the initial target temperature T 0 * or the initial target temperature T 0 * is ascertained on the basis of the final rolling temperature. 
         [0068]    The control unit  6  implements a path tracking for the sections  9  of the metal strip  1  on the basis of the execution of the computer program  7  in a step S 4 . It is therefore known to the control unit  6  at every point in time which section  9  of the metal strip  1  is located at which point of the finishing train  3 . The implementation of a path tracking is generally known to a person skilled in the art and therefore does not have to be explained in greater detail. 
         [0069]    For the correct path tracking of the sections  9  of the metal strip  1 , it is often necessary to detect a point in time t 1  at which the metal strip  1  more precisely: the frontmost section  9  of the metal strip  1  enters the rolling stand  5  through which the metal strip  1  passes first. The point in time t 1  can be detected, for example, in that the rolling force of this rolling stand  5  suddenly increases. In a similar manner, corresponding points in time t 2 , t 3 , etc. can also be detected for the other rolling stands  5  of the finishing train  3 . The path tracking can be adapted in this manner on the basis of the detected points in time t 1 , t 2 , etc. 
         [0070]    The control unit  6  furthermore implements a width control unit at least for each of the rolling stands  5  with the exception of the last rolling stand  5  of the finishing train  3  on the basis of the execution of the computer program  7  in a step S 5 . The respective width control unit  13  is associated with the respective rolling stand  5 . It is possible that such a width control unit  13  is also provided for the last rolling stand  5  of the finishing train  3 . However, this is not absolutely required. The construction and the functionality of one of the width control units  13  will be explained hereafter in conjunction with  FIG. 7B  as a representative for all width control units  13 . Similar statements apply for the other width control units  13 . 
         [0071]    The width control unit  13  is associated with a specific rolling stand  5 . In the illustration of  FIG. 7A , this is the middle rolling stand  5 , referred to hereafter as the associated rolling stand and provided with reference sign  5   b . The rolling stand  5  upstream from the associated rolling stand  5   b  is provided hereafter with the reference sign  5   a . In a similar manner, the rolling stand  5  downstream from the associated rolling stand  5   b  is provided hereafter with the reference sign  5   c.    
         [0072]    The width control unit  13  of  FIG. 7B  has at least function blocks  14  to  19 . 
         [0073]    The following variables are supplied to the function block  14 :
       The target width b*, which is associated with the section  9  of the metal strip  1  presently being rolled in the associated rolling stand  5   b  before the rolling in the associated rolling stand  5   b . In the case of the width control unit  13  associated with the first rolling stand  5  of the finishing train  3 , the target width b* corresponds to the initial target width b*. In the case of the other width control units  13 , the target width b* is provided by the function block  15  of the width control unit  13  associated with the upstream rolling stand  5   a.      A target tension Z 1 * is to prevail in the metal strip  1  before the associated rolling stand  5   b . The target tension Z 1 * is determined by a corresponding specification from the higher-order control unit. Additional control interventions of the operator  12  can be taken into consideration if necessary.   A target tension Z 2 * is to prevail in the metal strip  1  after the associated rolling stand  5   b . The target tension Z 2 * is determined by a corresponding specification from the higher-order control unit. Additional control interventions of the operator  12  can also be taken into consideration if necessary here.   The target temperature T* is associated with the section  9  of the metal strip  1  presently being rolled in the associated rolling stand  5   a  before the rolling in the associated rolling stand  5   b.      Parameters P of the rolling procedure occur in the associated rolling stand  5   b . For example, always in relation to the associated rolling stand  5   b , the rolling force, the rolling torque, the strip velocity on the inlet side and/or outlet side of the associated rolling stand, the rolling gap, the pass reduction, the compressed length of metal strip  1 , and possibly temperature-related material variables M of the metal strip  1  can be used as the parameters P of the rolling procedure. The material characteristic variables M can comprise, for example, the modulus of elasticity, the yield strength, the forming resistance, and the like.       
 
         [0079]    On the basis of the variables applied to the function block  14 , the function block  14  ascertains a target width after the rolling in the associated rolling stand  5   b . The function block  14  associates the ascertained target width as the new target width b* with the corresponding section  9  of the metal strip  1 . The function block  14  supplies the new target width b* to the function block  15 . The function block  14  thus internally models, with respect to the target values b*, T* of the respective section  9  of the metal strip  1 , the widening behavior thereof in the rolling gap of the associated rolling stand  5   b . The function block  14  therefore internally comprises a model of the associated rolling stand  5   b  which is based on mathematical-physical equations, in particular algebraic and differential equations. Such models are known per se to those skilled in the art. See the two technical articles mentioned at the outset “Strip width variation behaviour and its mathematical model in hot strip finishing mills” by Atsushi Ishii et al. and “Direct Width Control Systems Based on Width Prediction Models in Hot Strip Mill” by Cheol Jae Park et al. 
         [0080]    In the simplest case, the function block  15  is designed as a simple buffer memory in the manner of a shift register or the like, in which solely the transport of the sections  9  of the metal strip  1  (including the target variables b*, T* which are associated with the sections  9 ) to the downstream rolling stand  5   c  is modeled. However, the target tension Z 2 *, which is desired in the metal strip  1  after the associated rolling stand  5   b , and the material characteristic variables M of the metal strip  1  are preferably supplied to the function block  15 . In this case, the function block  15  implements, in addition to the simple transport of the sections  9  of the metal strip  1 , the creeping behavior of the target width b* of the sections  9  of the metal strip  1  buffered in the function block  15 . The function block  15  thus tracks, for the buffered sections  9 , the respective target width b* after the rolling in the associated rolling stand  5   b  as a function of the target tension Z 2 *, which is desired in the metal strip  1  after the associated rolling stand  5   b , the target temperature T*, and the material characteristic variables M of the metal strip  1 . Furthermore, the spacing a in relation to the downstream rolling stand  5   c  (more precisely: the spacing a plus the strip reserve stored between the associated rolling stand  5   b  and the downstream rolling stand  5   c ) and the strip velocity v after the associated rolling stand  5   b  are implicitly incorporated into the ascertainment of the function block  15 . This is because these two variables a, v determine the transport time for which the sections  9  of the metal strip  1  are located in the inter-stand region between the associated rolling stand  5   b  and the downstream rolling stand  5   c . The function block  15  provides, at the point in time of the rolling of a respective section  9  of the metal strip  1  in the downstream rolling stand  5   c , the target width b* before the rolling in the downstream rolling stand  5   c  to the width control unit  13  associated with the downstream rolling stand  5   c.    
         [0081]    The spacing is a fixed variable, which only has to be parameterized once. If the stored strip reserve is also to be taken into consideration, this is easily possible. This is because the stored strip reserve can be ascertained in a simple manner by the position of a loop lifter  20 , which is arranged between the associated rolling stand  5   b  and the downstream rolling stand  5   c . The strip velocity v can vary in operation. It is possible to measure the strip velocity v directly by means of a corresponding measuring unit. Alternatively, the circumferential velocity of rollers of the associated rolling stand  5   b  can be measured and the strip velocity v can be ascertained therefrom in conjunction with the known lead. Again alternatively, the circumferential velocity of rollers of the downstream rolling stand  5  can be measured and the strip velocity v can be ascertained therefrom in conjunction with the known lag. The procedure which is used is the choice of a person skilled in the art. 
         [0082]    The function block  16  is structurally and functionally equivalent to the function block  14  with regard to the approach. However, the following input variables are changed:
       Instead of the target width b*, the actual width b of the section  9  of the metal strip  1  presently being rolled in the associated rolling stand  5   b  is used. In the case of the width control unit  13  associated with the first rolling stand  5  of the finishing train  3 , the actual width b corresponds to the actual width b associated with the sections  9  in step S 2  of  FIG. 3 . In the case of the other width control units  13 , the actual width b is provided by the function block  17  of the width control unit  13  associated with the upstream rolling stand  5   a.      Instead of the target tension Z 1 *, a target tension corrected by an upstream additional target value δZ 1 * is used. In the case of the width control unit  13  associated with the first rolling stand  5  of the finishing train  3 , the upstream additional target value δZ 1 * has the value 0. In the case of the other width control units  13 , the upstream additional target value δZ 1 * is provided by the function block  19  of the width control unit  13  associated with the upstream rolling stand  5 .   Instead of the target tension Z 2 *, a target tension corrected by a downstream additional target value δZ 2 * is used. The downstream additional target value δZ 2 * is provided according to  FIG. 7  by the function block  19  of the respective width control unit  13  of  FIG. 7B .   Instead of the target temperature T*, the actual temperature T is used. In the case of the width control unit  13  associated with the first rolling stand  5  of the finishing train  3 , the actual temperature T corresponds to the actual temperature T associated with the sections  9  in step S 2  of  FIG. 3 . In the case of the other width control units  13 , the actual temperature T is provided by the width control unit  13  associated with the upstream rolling stand  5   a.          
 
         [0087]    The remaining variables are identical to those of the function block  14 . 
         [0088]    On the basis of the variables supplied to the function block  16 , the function block  16  ascertains an actual width after the rolling in the associated rolling stand  5   b . The function block  16  associates the ascertained actual width as the new actual width b with the corresponding section  9  of the metal strip  1 . The function block  16  supplies the new actual width b to the function block  17 . The function block  16  thus internally models, with respect to the actual values b, T of the respective section  9  of the metal strip  1 , the widening behavior thereof in the rolling gap of the associated rolling stand  5   b.    
         [0089]    The function block  17  is structurally and functionally equivalent to the function block  15  with regard to the approach. However, if the function block  17  similarly to the function block  15  implements not only the transport of the sections  9  of the metal strip  1  (including the actual variables b, T associated with the sections  9 ) to the downstream rolling stand  5   c , but rather also the creeping behavior of the actual width b of the sections  9  of the metal strip  1  buffered in the function block  15 , the target tension Z 2 * corrected by the downstream additional target value δZ 2 * and furthermore as also in the function block  15  the material characteristic variables M of the metal strip  1  are supplied to the function block  17 . In this case, the function block  17  thus tracks the respective actual width b for the buffered sections  9  after the rolling in the associated rolling stand  5   b  as a function of the target tension Z 2 *, which is corrected by the downstream additional target value δZ 2 *, the actual temperature T, and the material characteristic variables M of the metal strip  1 . The spacing a in relation to the downstream rolling stand  5   c  and the strip velocity v after the associated rolling stand  5   b  are implicitly also incorporated into the ascertainment of the function block  17 , as previously in the function block  15 . 
         [0090]    Furthermore and a difference exists here from the function block  15  the function block  17  generally tracks the actual temperature T of the sections  9 , which are stored in the function block  17 , continuously in a model-supported manner. The corresponding models are known to a person skilled in the art from the two above-mentioned technical articles and also in other ways. As a result, the actual temperature T of the sections  9  is therefore continuously tracked in a model-supported manner during the passage of the sections  9  of the metal strip  1  through the finishing train  3 . 
         [0091]    The newly ascertained target width b* is supplied by the function block  14  and the newly ascertained actual width b is supplied by the function block  15  to the function block  18 . The function block  15  calculates the difference δb between target width b* and actual width b. Furthermore, the function block  18  buffers the difference δb ascertained thereby. The buffering is determined such that the section  9  of the metal strip  1  to which the ascertained difference δb relates, is located at a predetermined point between the associated rolling stand  5   b  and the downstream rolling stand  5   c  at the point in time at which the difference δb is output by the function block  18 . 
         [0092]    The predetermined point can be established as needed. The predetermined point can be, for example, the location at which the loop lifter  20  downstream from the associated rolling stand  5   b  acts on the metal strip  1 . Alternatively, it can be a location in the region of the middle between the associated rolling stand  5   b  and the downstream rolling stand  5   c , in particular exactly at the middle. The predetermined point can preferably be specified to the respective width control unit  13 , in particular by the operator  12  or by the above-mentioned higher-order control unit. 
         [0093]    The function block  18  supplies the difference δb to the function block  19 . Furthermore, the target tension Z 2 *, the target temperature T*, and the actual temperature T, as well as the parameters P of the rolling procedure occurring in the respective rolling stand  5 , are supplied to the function block  19 . Furthermore, the widths b*, b, which are output from the function blocks  14  and  16 , are often supplied per se to the function block  19 . The function block  19  ascertains the downstream additional target value δZ 2 * on the basis of the variables supplied thereto. The ascertainment is performed such that the actual width b of the section  9  of the metal strip  1  rolled in the associated rolling stand  5   b  approximates the target width b* of the rolled section  9 . In particular, the ascertainment is preferably performed such that the approximation is optimized for the point in time at which the section  9 , for which the downstream additional target value δZ 2 * is ascertained, runs out of the downstream rolling stand  5   c.    
         [0094]    It is possible that the ascertainment is performed such that the actual width b is equal to the target width b*, i.e., complete correction is performed. Alternatively, it is possible that only partial correction is performed. The procedure which is utilized in the individual case is the choice of the person skilled in the art. In particular, it is possible to perform complete or nearly complete correction for the upstream rolling stands  5  of the finishing train  3 , so that no or only residual corrections still have to be performed in the downstream rolling stands  5  of the finishing train  3 . 
         [0095]    The function block  19  furthermore supplies the downstream additional target value δZ 2 * to a tension regulator  21 . Furthermore, the target tension Z 2 * and an actual tension Z 2 , which prevails in the metal strip  1  after the associated rolling stand  5   b , are supplied to the tension regulator  21 . The tension regulator  21  sets the actual tension Z 2 , which prevails in the metal strip  1  after the associated rolling stand  5   b , in accordance with the target tension Z 2 * corrected by the downstream additional target value δZ 2 *. For example, the tension regulator  21  can act for this purpose on the loop lifter  20  in accordance with the illustration in  FIG. 7 . Alternatively or additionally, the tension regulator  21  can act on the roller circumferential velocity of the associated rolling stand  5   b  and/or the downstream rolling stand  5   c . Alternatively or additionally, the tension regulator  21  can act on the setting of the downstream rolling stand  5   c.    
         [0096]    In summary, the present invention therefore relates to the following substantive matter: 
         [0097]    Before the rolling of a metal strip  1  in a finishing train  3 , the actual width b 0  and the actual temperature T 0  thereof is detected in each case for sections  9  of the metal strip  1 . Variables bF, TF, which are derived from the detected variables b 0 , T 0 , and the corresponding target variables b*, T* are associated with the sections  9 . The sections  9  of the metal strip  1  are tracked during the passage through the finishing train  3 . A width control unit  13  is associated with each of the rolling stands  5 . The width control units  13  ascertain, on the basis of various input variables, the target width b* and the actual width b after the rolling in the associated rolling stand  5   b . The width control units  13  furthermore ascertain a downstream additional target value  5 Z 2 *, by which the target tension Z 2 * is to be corrected after the associated rolling stand  5   b , to approximate the actual width b to the target width b*. The downstream additional target value δZ 2 * is both taken into consideration in the ascertainment of the actual width b and also supplied to a tension regulator  21 , which sets an actual tension Z 2 , which prevails in the metal strip  1  after the associated rolling stand  5   b , in accordance with the corrected target tension Z 2 *. For the ascertainment of the downstream additional target value δZ 2 *, inter alia, the difference δb of target width b* and actual width b of a section  9  of the metal strip  1  is used, which is located at a predetermined point after the associated rolling stand  5 . 
         [0098]    The present invention has many advantages. Thus, for example, in the scope of the present invention, no measurement of temperatures T and widths b is required within the finishing train  3 . Such a detection is only required before the finishing train  3 . These detections are typically provided. In addition, the width b can be detected at the outlet of the finishing train  3  for quality control, for adaptation of the process model used, and possibly for optional width regulation. However, this is not absolutely required. If a width regulation is also implemented in addition to the width control according to the invention, the width regulation corrects, as a function of the actual width b after the finishing train  3  and the target width b* at this point, at least the target widths b*, possibly also the actual widths b. 
         [0099]    The correction is performed for the individual rolling stands  5 , with which a width control unit  13  is associated. The correction is performed such that the ascertained auxiliary target values δZ 1 *,  5 Z 2 * compensate for the width deviation at the outlet of the finishing train  3 . The control interventions are allocated onto multiple rolling stands  5  within the finishing train  3 . The compensation in the upstream rolling stands  5  preferably dominates in this case. Preferably, only residual deviations are compensated for in the downstream rolling stands  5 . 
         [0100]    Although the invention was illustrated and described in greater detail by the preferred exemplary embodiment, the invention is not thus restricted by the disclosed examples and other variations can be derived therefrom by a person skilled in the art, without leaving the scope of protection of the invention. 
       LIST OF REFERENCE SIGNS 
       [0000]    
       
           1  metal strip 
           2  roughening train 
           3  finishing train 
           4  coiling device 
           5 ,  5   a  to  5   c  rolling stands 
           6  control unit 
           7  computer program 
           8  machine code 
           9  sections 
           10 ,  11  filter blocks 
           12  operator 
           13  width control units 
           14  to  19  function blocks 
           20  loop lifter 
           21  tension regulator 
         a spacing 
         b, b 0  actual widths 
         b*, b 0 * target widths 
         bF filtered actual widths 
         bV preliminarily filtered actual widths 
         L length 
         m mass 
         M material characteristic variables of the metal strip 
         P parameters of the rolling procedure 
         S 1  to S 5  steps 
         t time span 
         t 1 , points in time 
         T, T 0  actual temperatures 
         T*, T 0 * target temperatures 
         TF filtered actual temperatures 
         TV preliminarily filtered actual temperatures 
         v strip velocity 
         Z 1 , Z 2  actual tensions 
         Z 1 *, Z 2 * target tensions 
         δb difference between target width and actual width 
         δZ 1 *, δZ 2 * auxiliary target values