DETERMINING A SENSITIVITY OF A TARGET VARIABLE OF A ROLLING MATERIAL FROM AN OPERATING VARIABLE OF A HOT ROLLING MILL
20230089119 · 2023-03-23
Assignee
Inventors
Cpc classification
B21B37/76
PERFORMING OPERATIONS; TRANSPORTING
B21B37/00
PERFORMING OPERATIONS; TRANSPORTING
B21B37/58
PERFORMING OPERATIONS; TRANSPORTING
B21B37/16
PERFORMING OPERATIONS; TRANSPORTING
International classification
B21B37/76
PERFORMING OPERATIONS; TRANSPORTING
B21B37/16
PERFORMING OPERATIONS; TRANSPORTING
Abstract
A control device for a section of a hot rolling mill is supplied with respective primary data for a plurality of rolling materials and respective preliminary target values for the target variables of the respective rolling material. The respective primary data describes the respective rolling material before being supplied to the section of the hot rolling mill. The respective preliminary target values of the target variables describe a desired target state of the respective rolling material after passing through the section of the hot rolling mill. At least one of the target variables is a particular target variable, whereby the control device determines a respective final target value in such a way that it changes the respective preliminary target value by a respective offset. The respective offset is determined independently of the primary data and the other particular target variables and the normal target variables for the respective rolling material.
Claims
1-10. (canceled)
11. An operating method for a portion of a hot rolling mill, comprising: supplying a control device for the portion of the hot rolling mill with respective primary data for a plurality of rolling materials and respective provisional setpoints for target variables of the respective rolling material, the respective primary data describing the respective rolling material before being supplied to the portion of the hot rolling mill, and the respective provisional setpoints of the target variables describing a desired nominal state of the respective rolling material after passing through the portion of the hot rolling mill; determining, by the control device, operating values for the portion of the hot rolling mill such that the respective rolling material, after passing through the portion of the hot rolling mill, reaches definitive setpoints of the target variables as well as possible; and operating, by the control device during processing of the respective rolling material, the portion of the hot rolling mill according to the determined operating values; wherein at least one of the target variables is a particular target variable, and the remaining target variables are normal target variables; wherein the control device determines the respective definitive setpoint for the particular target variable in that it changes the respective provisional setpoint by a respective offset which is determined independently of the primary data, the other particular target variables and the normal target variables for the respective rolling material, and also independently of the operating values of the hot rolling mill determined for processing the respective rolling material; wherein the offsets, with respect to the respective particular target variable, have multiple different values when all the rolling materials are viewed as a whole; and wherein the control device, for the normal target variables, uses the respective provisional setpoint unchanged as the respective definitive setpoint.
12. The operating method as claimed in claim 11, wherein the offset is freely selectable completely or within a predefined value range.
13. The operating method as claimed in claim 11, wherein: during passage of the respective rolling material through the portion of the hot rolling mill, an actual value of a state variable of the rolling material is supplied to the control device; the state variable is one of the particular target variables, so a setpoint of the state variable corresponds to the definitive setpoint of this particular target variable, or the state variable correlates with the at least one particular target variable, so that a setpoint of the state variable is determined by the definitive setpoint of the at least one particular target variable; and on a deviation of the actual value of the state variable from the setpoint of the state variable, the control device provides at least one operating value which influences the state variable during passage of the respective rolling material through the portion of the hot rolling mill, in order to compensate for the deviation of the actual value of the state variable from the setpoint of the state variable.
14. The operating method as claimed in claim 13, wherein with respect to a particular definitive setpoint of a particular target variable, the at least one operating value varies with a statistical spread, and with respect to this particular target variable, the offsets are selected such that the mean values of the at least one operating value for the respective definitive setpoint of this target variable deviate by less than the spread from the respective mean value of the least one operating value which results on use of the respective provisional setpoint as the definitive setpoint of this particular target variable.
15. The operating method as claimed in claim 14, wherein the offsets are selected such that the mean values of the at least one operating value for the respective definitive setpoint of this target variable deviate by less than half the spread.
16. The operating method as claimed in claim 11, wherein with respect to a respective particular target variable, the actual value which would result on use of the respective provisional setpoint as a respective definitive setpoint, on condition that the operating values for the respective rolling material are not updated on passage through the portion of the hot rolling mill, would vary with a statistical spread, and the respective offset for this particular target variable is smaller than the spread.
17. The operating method as claimed in claim 16, wherein the respective offset for this particular target variable is smaller than half the spread.
18. The operating method as claimed in claim 11, wherein the portion of the hot rolling mill comprises a cooling line, and one of the particular target variables is the reeling temperature of the rolling material at the outlet from the cooling line or correlates with the reeling temperature of the rolling material at the outlet from the cooling line, and at least one of the operating values influences at least one of the number of actuated valves of the cooling line and an extent of actuation of the valves of the cooling line.
19. The operating method as claimed in claim 11, wherein at least one of the particular target variables is a microscopic or macroscopic material property of the respective rolling material.
20. A computer program for a control device for a portion of a hot rolling mill for processing a plurality of rolling materials, wherein the computer program comprises machine code which can be processed by the control device, wherein the processing of the machine code by the control device causes the control device to execute an operating method as claimed in claim 11.
21. A control device for a portion of a hot rolling mill for processing a plurality of rolling materials, wherein the control device is programmed with a computer program as claimed in claim 20 so that, during operation, the control device executes an operating method.
22. A portion of a hot rolling mill for processing a plurality rolling materials, wherein the portion of the hot rolling mill is controlled by a control device as claimed in claim 21.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
[0055] The above-described properties, features and advantages of this invention, and the manner and fashion in which these are achieved, will become evident and more clearly comprehensible in connection with the following description of exemplary embodiments, which are explained in more detail in conjunction with the drawings. For this, in schematic illustrations:
[0056]
[0057]
[0058]
[0059]
[0060]
[0061]
DETAILED DESCRIPTION
[0062] According to
[0063] The hot rolling mill has at least one roll stand 2. Often, several roll stands 2 are arranged sequentially behind one another. The roll stands 2 may for example form a multistand production line. In many cases, furthermore a cooling line is arranged downstream of the roll stand 2 (or in the case of multiple roll stands 2, the last roll stand 2).
[0064] In many cases, the hot rolling mill furthermore comprises a reeling device with at least one reel 5. The reeling device is in each case arranged downstream of the roll stands 2. If the cooling line is present, the reeling device is also arranged downstream of the cooling line. In this case, the cooling line is thus arranged between the roll stands 2 and the reeling device.
[0065] The hot rolling mill may furthermore also comprise units which are arranged upstream of the roll stands 2. One example of such a unit is a descaling device.
[0066] The hot rolling mill thus comprises at least one portion. It is possible that the roll stands 2, or the production line together with the cooling line and/or at least one upstream device, are regarded as the portion of the hot rolling mill. Alternatively, it is possible to regard only the roll stands 2 or the production line as the portion of the hot rolling mill. It is also possible to regard only the cooling line or only the upstream device as the portion of the hot rolling mill. In the description which follows, the cooling line is considered as the portion of the hot rolling mill. This is however not absolutely necessary.
[0067] The portion of the hot rolling mill is controlled by a control device 6. In the present case, the control device 6 in particular controls the valves 4 of the cooling devices 3. Alternatively or additionally, the control device 6 may also actuate at least one pump (not shown) by means of which the working pressure and/or the coolant flow may be set. In some cases, the control device 6 may also control further parts of the hot rolling mill, such as for example the roll stands 2 and the reel 5 or reels 5. The control device 6 is programmed with a computer program 7. The computer program 7 comprises machine code 8 which can be processed by the control device 6. The processing of the machine code 8 by the control device 6 causes the control device 6 to control the portion of the hot rolling mill according to an operating method which will be described in more detail below.
[0068] The flat rolling materials 1 are processed individually and successively in the portion of the hot rolling mill. Insofar as the portion of the hot rolling mill is controlled directly, this control is executed separately for each individual flat rolling material 1. This control is explained below in connection with
[0069] According to
[0070] In a step S2, the control device 6 receives provisional setpoints Z* for target variables for the rolling material 1. The provisional setpoints Z* of the target variables describe properties of the respective rolling material 1 which the latter should have after passing through the portion of the hot rolling mill. These properties are therefore target properties. The target variables or their provisional setpoints Z* thus indicate the desired properties of the rolling material 1 after passage through the portion of the hot rolling mill, and/or the desired state of the respective rolling material 1 at that time. The target variables may for example be macroscopic or microscopic material properties of the flat rolling material 1. A macroscopic material property may for example be the tensile strength, the yield strength or the ductile yield. A microscopic material property may for example be the grain structure or grain size. Also, a setpoint T2* may be predefined for the reeling temperature T2 which the flat rolling material 1 should have after the cooling line. In this case, the reeling temperature T2 is a target variable.
[0071] At least one of the target variables is a particular target variable. It is conceivable that the control device 6 itself determines which of the target variables are particular target variables. Usually however, it is prespecified for the control device 6 which of the target variables are particular target variables. This may be prespecified for example as part of the computer program 7 or by an operator (not shown).
[0072] For the particular target variables, in a step S3, the control device 6 changes the respective provisional setpoint Z* by an offset δZ, and thus determines a respective definitive setpoint Z′*. The definitive setpoint Z′* for the respective particular target variable is therefore Z′*=Z*+δZ.
[0073] It is possible that the control device 6 itself determines the respective offset δZ. In this case, usually the control device 6 is given a framework—for example as part of the computer program 7 or by an operator—within which the control device 6 itself determines the respective offset δZ. For example, the control device 6 may be given a maximum amount of the offset δZ, below which the control device 6 establishes a value at random. It is also possible that the control device 6 is given several concrete possible values for the offset δZ, and the control device 6 selects one of these values. In this case, the respective offset δZ may be freely selected by the control device 6 within a predefined value range. The value range is predefined either by the framework or by the smallest and largest possible offset δZ. It is also possible that the respective offset δZ of the control device 6 is predefined by the operator. In this case, the respective offset δZ may be freely selected by the operator. In some cases, it may be possible that a corresponding value range or several possible values are stored in the control device, and the operator each time selects a value from this value range or one of the possible values. Irrespective of the method of establishing the offset δZ, the offset δZ is however established independently of the primary data PD and also independently of the other target values. Also, the offsets are determined independently of operating values A of the hot rolling mill.
[0074] For the other target variables, i.e. the target variables which are not particular target variables, in a step S4, the control device 6 directly uses the respective provisional setpoint Z* as the respective definitive setpoint Z′*. For these target variables, referred to below as normal target variables, therefore Z′*=Z*.
[0075] Then, in a step S5, the control device 6 determines the operating values A of the portion of the hot rolling mill. These are determined such that, after passing through the portion of the hot rolling mill, the respective rolling material 1 has reached the definitive setpoints Z′* of the target variables as well as possible. The operating values A thus indicate how the portion of the hot rolling mill must be actuated in order for the rolling material 1, for given primary data PD, to reach the definitive setpoints Z′* of the target variables. At least this is expected. For example, the control device 6 may supply the primary data PD and the definitive setpoints Z* of the target variables to a model 10 of the portion of the hot rolling mill, as shown in the illustration in
[0076] In a step S6, the control device 6 controls the portion of the hot rolling mill. This control takes place during processing of the corresponding flat rolling material 1, i.e. in particular during passage of the respective rolling material 1 through the portion of the hot rolling mill. During step S6, the control device 6 operates the portion of the hot rolling mill according to the determined operating values A. It thus actuates the control elements of the portion of the hot rolling mill—for example, the valves 4 of the cooling devices 3—in accordance with the determined operating values A.
[0077] The states which the rolling material 1 may have after processing in the portion of the hot rolling mill may be either target variables or operating values A. The two situations are however mutually exclusive. A state which the rolling material 1 has after processing in the portion of the hot rolling mill cannot therefore be both a target variable and an operating value A simultaneously. For example, the reeling temperature T2 may be either a target variable or an operating value A. If the reeling temperature T2 is one of the operating values A, usually the target variables are mechanical properties of the rolling material 1 which the rolling material 1 should have after processing in the portion of the hot rolling mill.
[0078] Also, the operating values A may be determined as required. In particular, they may be values which correspond directly to correcting variables for the control elements of the hot rolling mill. For example, one of the control variables may be the number of valves 4 which are opened in order for the corresponding cooling devices 3 to spray coolant onto the flat rolling material 1. Alternatively or additionally (in a similar fashion, but not completely identically), it may be the extent to which the valves 4 are opened.
[0079] After processing of the rolling material 1, the control device 6 returns to step S1. Steps S1 to S6 are thus carried out iteratively for a new rolling material 1 each time. It is important here that, with respect to the respective particular target variable, the offset δZ which is used for the respective performance of step S3 is not always the same. When all rolling materials 1 are considered, the offset δZ for a specific particular target variable therefore has several different values. This applies to each particular target variable.
[0080] In the simplest case, the offset δZ always has one of two values, wherein the two values are equal in amount. If, for example, a target variable is the reeling temperature T2, the provisional setpoint T2* for the reeling temperature T2 may be increased by a specific amount, for example 5 K or 10 K, for some of the flat rolling materials 1, and reduced by the same amount for others of the flat rolling materials 1. In a further simple case, the offset δZ always has one of three values, wherein one of these values is 0 and the other two values are different from 0 and equal in amount. Similarly to the previous example, the provisional setpoint T2* for the reeling temperature T2 may remain unchanged for some of the flat rolling materials 1, be increased by a specific amount, for example 5 K or 10 K, for some others of the flat rolling materials 1, and reduced by the same amount for yet others of the flat rolling materials 1. In a further simple case, the offset δZ always has one of two values, wherein one of the values is 0 and the other value differs from 0. Evidently, other values are also possible for the offset δZ. For example, the offset δZ may be determined by means of a random generator.
[0081] With reference to
[0082] According to
[0083] According to
AM=(ΣA)/n
wherein n is the number of value pairs which was selected in step S13.
[0084] In a step S15, the computing device checks whether it has performed steps S12 to S14 already for all definitive setpoints Z′* of the particular target variable. If this is not the case, the computing device returns to step S12. On further performance of step S12, the computing device selects a new definitive setpoint Z′* of the particular target variable which it has not yet selected during the procedure of
[0085]
[0086] According to
[0087] In a step S22, the computing device selects one of the definitive setpoints Z′* of the particular target variable (where known) or a specific, usually relatively small value range for the actual value Z. Step S22 largely corresponds to step S2 from
[0088] In a step S23, the computing device selects the value pairs of which the definitive setpoint corresponds to the definitive setpoint Z′* selected in step S22, or the actual value of which lies in the selected value range. Step S23 largely corresponds to step S13 of
[0089] In a step S24, the computing device determines the mean value AM of the operating values A of the value pairs selected in step S23. It thus determines the mean value AM as
AM=(ΣA)/n
wherein n is the number of value pairs which was selected in step S13. Step S24 largely corresponds to step S14 in
[0090] In a step S25, in a similar fashion to the procedure in step S24 for the value pairs selected in step S22, the computing device determines the mean value ZM of the actual values Z of the particular target variable. It thus determines the mean value ZM as
ZM=(ΣZ)/n
wherein, as before, n is the number of value pairs which was selected in step S22.
[0091] In a step S26, the computing device checks whether it has already carried out steps S22 to S25 for all definitive setpoints Z′* of the particular target variable or value ranges of the associated actual value Z. If this is not the case, the computing device returns to step S22.
[0092] On repeat performance of step S22, the computing device selects a new definitive setpoint Z′* of the particular target variable which it has not yet selected during the procedure of
[0093] In a step S27, from the determined mean values AM of the updated actuating values A and the respective associated mean values ZM of the actual values Z of the particular target variable, the computing device determines the sensitivity S of the particular target variable to the operating variable. For example, in step S27, similarly to step S16, the computing device may perform a linear regression and determine the gradient of the resulting straight line as sensitivity S.
[0094] The sensitivity S of the particular target variable to the operating variable is thus determined from the setpoints or the mean values of the actual values of the particular target variable and the mean values of the setpoints or actual values of the operating values A.
[0095] The procedure in
[0096] In cases in which the target variables are themselves again determined using superordinate values, the sensitivities S of the superordinate values on the operating values may still be determined. One example: the superordinate value is a mechanical property of the rolling material 1, for example the tensile strength. From the tensile strength, the setpoint T2* for the reeling temperature T2 is determined. The reeling temperature T2 is the target variable, so the offset is added to its setpoint. The correcting variable is the actuation of the valves 4. In this case, alternatively or additionally to determining the sensitivity of the reeling temperature T2 to the actuation of the valves 4, the sensitivity of the mechanical property of the rolling material 1 to the actuation of the valves 4 may also be determined.
[0097] Possible embodiments of the procedure according to the invention (see
[0098]
[0099]
[0100] A further possible embodiment of the procedure according to the invention (see
[0101]
[0102] According to
[0103] In a step S52, the control device 6 receives the detected actual value of the state variable (for example, the detected reeling temperature T2). The state variable—see, purely as an example, the statements relating to
[0104] Irrespective of whether the one or the other situation applies, in a step s53, the control device 6 compares the actual value T2 of the state variable with the associated setpoint T2*. In the case of a deviation, the control device 6 proceeds to a step S54. In step S54, the control device 6 updates at least one operating value A. The state variable T2 is influenced by the updated operating variable A. The updating takes place to compensate for the deviation of the actual value T2 of the state variable from the associated setpoint T2*.
[0105] Then in a step S55, the control device 6 checks whether the processing of the rolling material 1 in the portion of the hot rolling mill is ended. If this is not the case, the control device 6 returns to step S51. On renewed performance of step S51, the control device 6 however uses the now current operating values A, i.e. as they have resulted following any update in step SM. If treatment of the rolling material 1 in the portion of the hot rolling mill has ended, the procedure of
[0106] In the context of the procedure of
[0107] As already stated, the offset δZ is freely selectable as long as its absolute value remains below a particular threshold. In connection with
[0108] In the context of
[0109] In the case of the above assumptions, the operating values A always remain the same from rolling material 1 to rolling material 1. The operating values A are no longer changed after their determination in step S5. In this case however, the actual value Z of the particular target variable—for example the reeling temperature T2—varies from rolling material 1 to rolling material 1. The reason for the spread may be assumed to be an external fault. The cause of the spread may be known but need not be known.
[0110] The spread of the actual value Z of the particular target variable has a standard deviation σ about the mean value ZM of the actual value Z of the particular target variable. The standard deviation σ is often also called the variance. The standard deviation σ is defined in that it covers a symmetrical region around the mean value ZM. With a normal distribution, around ⅔ of all measurement values (more precisely 68.27%) lie in the region with one times the standard deviation σ (i.e. in the region which extends from the mean value ZM of the actual value Z of the particular target variable minus the standard deviation σ to the mean value ZM of the actual value Z of the particular target variable plus the standard deviation σ). With a normal distribution, around 95% of all measurement values (more precisely 95.45%) lie in the range with two times the standard deviation σ. With a normal distribution, almost all measurement values (more precisely 99.73%) lie in the region with three times the standard deviation σ.
[0111] According to the illustration in
[0112]
[0113] In the context of
[0114] In the case of
[0115] In this case, the operating values A have a standard deviation σ′ around their mean value AM. The standard deviation σ′ is defined similarly to
[0116] The offset δZ may be determined for example such that—with respect to the respective offset δZ—the mean value AM of the operating values A deviates by less than the spread from the mean value AM which results on use of the provisional setpoint Z* itself as the definitive setpoint Z′* of the particular target variable. It is naturally even better if the amount of the offset 6Z has an even smaller value, in particular a value which corresponds at most to half the spread of the operating values A.
[0117] The procedure from
[0118] It is assumed that an unknown error, if not compensated by updating of the operating values A, would cause a spread of the reeling temperature T2 by 7 K (i.e. σ=7 K). The provisional setpoint Z* is 600° C. In the context of the procedure according to the invention, 2500 rolling materials 1 are processed for which the definitive setpoint Z′* of the particular target variable is 599° C., i.e. the offset δZ is −1 K. For a further 2500 rolling materials 1, a definitive setpoint Z′* of the particular target variable of 601° C. is used, i.e. the offset δZ is +1 K.
[0119] If, for the embodiment according to
[0120] Initially, this procedure supplies the correct prefix of the sensitivity S. This in itself constitutes a substantial advantage in comparison with the prior art. The determination is still however only accurate to around 15%. This accuracy is nonetheless completely adequate for many applications. It may be improved further by a corresponding increase in the number of rolling materials 1. On the other hand, the slight variation in the setpoint T2* has almost no effects on the quality of the rolling materials 1 actually processed. The resulting spread over all 5000 rolling materials 1 is increased only from 7 K to around 7.07 K, and hence relatively only by around 1%. Alternatively or additionally, naturally it is also possible to increase the offset 6Z.
[0121] The determined sensitivity S may in particular be used to update the model 10. If, at a later time, in the context of the model 10, the operating values A are to be determined for at least one further flat rolling material 1, the determined sensitivity S may be used for determining the operating values A. This may be advantageous in particular if the setpoint Z0* or the target value Z0′ of the particular target variable has changed, and/or if the primary data PD have changed.
[0122] The present invention has many advantages.
[0123] In contrast to the prior art, the aim is not to establish, by a global approach, a direct correlation between the measured material properties of the flat rolling materials 1 on one side, and adjustment values in the portion of the hot rolling mill on the other. Instead, without more extensive assumptions, the sensitivity S is determined, or at least its prefix and approximate value are determined. The advantage is that the operator of the portion of the hot rolling mill usually knows very precisely the primary data PD and the provisional setpoints Z* of the target variables, but does not usually know how he must change the operating values A in order to set the actual values Z of the target variables in deterministic fashion. With the procedure of the present invention however, this becomes possible. In particular, the working point of the portion of the hot rolling mill can be shifted in targeted fashion, so as to give a flat rolling material 1 with improved actual values Z of the target variables. Furthermore, errors in upstream processing procedures, i.e. in processes which influence the primary data PD, can be completely or at least partially compensated.
[0124] The present invention has largely been explained above for the case that the portion of the hot rolling mill corresponds to a cooling line or at least comprises a cooling line. Usually, the reeling temperature T2 of the rolling material 1 at the outlet from the cooling line is taken as a particular target variable. Usually, the number of actuated valves 4 of the cooling line and/or the extent of actuation of the valves 4 of the cooling line is taken as an operating value A. The present invention is not however restricted to this embodiment.
[0125] For example, it is possible that the portion of the hot rolling mill is indeed a cooling line or comprises a cooling line, but the particular target variable is not the reeling temperature T2. In this case, the procedure may be followed similarly to the procedure explained above. It must merely be considered that the setpoint T2* of the reeling temperature T2 (or in general, the setpoint of the state variable to be regulated) correlates with the particular target variable. If, for example, a specific tensile strength is predefined as a particular target variable, the tensile strength varies stochastically independently of the other target variables and the primary data PD. In each case, the respective setpoint T2* of the reeling temperature T2 is determined and regulated to this value. The associated mean values AM of the operating values A are in this case determined and evaluated in relation to the respective mean value ZM of the actual values Z of the tensile strength. Similar procedures apply for other particular target variables.
[0126] It is also possible that the procedure according to the invention is carried out for a portion of a hot rolling mill which does not comprise a cooling line. For example, in the case of a production line, the final rolling temperature T1 may be given as a particular target variable, and the final rolling speed v used as the particular correcting variable. Also, another target variable may be used, and the final rolling temperature T1 used as the state variable.
[0127] It is also possible to provide other particular target variables. One example is the extent to which a phase conversion of the rolling material 1 has taken place at the outlet from the considered portion of the hot rolling mill. The measurement value, on the basis of which the operating values A are updated, may be the final rolling temperature T1 in the case of a production line, or the reeling temperature T2 in the case of a cooling line.
[0128] Other embodiments are also possible. For example, insofar as the portion of the hot rolling mill is configured as a multistand production line, or comprises a multistand production line, the thickness, profile and/or flatness of the rolling material 1 may be used as a particular target variable, and as operating values A, values may be used which influence the roll gap of the last roll stand 2 of the multistand production line, and/or the penultimate roll stand 2 of the multistand production line, and/or further roll stands 2 of the multistand production line.
[0129] The above-mentioned examples should not be regarded as restrictive. Other embodiments are also possible.
[0130] Although the invention has been illustrated and described in detail with reference to the preferred exemplary embodiment, the invention is not restricted by the disclosed examples, and other variants may be derived by the person skilled in the art without leaving the scope of protection of the invention.
LIST OF REFERENCE SIGNS
[0131] 1 Rolling materials [0132] 2 Roll stands [0133] 3 Cooling devices [0134] 4 Valves [0135] 5 Reel [0136] 6 Control device [0137] 7 Computer program [0138] 8 Machine code [0139] 9, 11 Temperature measurement point [0140] 10 Model [0141] A Operating values [0142] AM Mean value of actuation values of particular correcting variable [0143] PD Primary data [0144] S Sensitivity [0145] S1 to S55 Steps [0146] T1 Final rolling temperature [0147] T2* Setpoint of reeling temperature [0148] T2 Reeling temperature [0149] V Final rolling speed [0150] Z* Provisional setpoints of target variables [0151] Z′* Definitive setpoints of target variables [0152] Z Actual value of particular target variable [0153] ZM Mean value of actual values of particular target variable [0154] δT Temperature offset [0155] δZ Offset [0156] σ, σ′ Standard deviations