CN116881613A - Setting method of high-order item plate-shaped target curve based on flatness - Google Patents
Setting method of high-order item plate-shaped target curve based on flatness Download PDFInfo
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Abstract
According to the method for setting the high-order item plate-shaped target curve based on the flatness, disclosed by the invention, the quantization solving method of each coefficient in the plate-shaped target curve is obtained by utilizing the concept of flatness, so that the setting precision of the plate-shaped target curve is improved, and the production requirement of high-precision strip steel is met. The invention firstly provides a setting and processing method of a high-order item plate-shaped target curve, and three kinds of classification are carried out on the high-order item plate-shaped target curve according to the target width of strip steel; secondly, determining an action section of each coefficient in a plate-shaped target curve by using statistical analysis based on the determined target width of the strip steel, and establishing a solving equation of each coefficient by using regression analysis; finally, the function value of each coefficient solving equation is determined by using the concept of flatness, the production index of the downstream process and the action characteristics of each coefficient, and each coefficient value is obtained. The method of the invention realizes the precision setting requirement of the plate-shaped target curve and provides a feasible optimization scheme for obtaining high-precision cold-rolled strip steel products.
Description
Technical Field
The invention belongs to the technical field of metallurgical rolling, and relates to a setting method of a high-order item plate-shaped target curve based on flatness.
Background
The automatic control system of the cold-rolled strip steel generally comprises a basic level control part and a process level control part. The basic level control part calculates the preset value of the rolling process parameter according to the calculation model in the basic level control server, and transmits the preset value to the process level control part to guide the rolling production. The process level control part processes and receives the preset value transmitted by the basic level control part, and also needs to ensure continuous rolling production, monitor the production condition in real time and acquire production feedback data. The plate shape closed loop feedback control is to calculate the deviation of the actual plate shape and the target plate shape by taking the actually measured plate shape signal of the plate shape roller as feedback information under the stable rolling working condition, analyze and calculate the adjustment quantity of the plate shape adjusting means required by eliminating the plate shape deviation through a feedback calculation model, and then continuously send out adjustment instructions to various plate shape adjusting mechanisms of the rolling mill, so that the rolling mill can continuously, dynamically and real-time adjust the plate shape of the strip steel in rolling, and finally the plate shape of the strip steel product is stable and good.
The plate shape target curve is a key factor for the plate shape control system to automatically correct the plate shape deviation. When the first set of cold rolling control system and equipment are introduced from abroad in China, only related using technology is introduced, and no setting method of a plate-shaped target curve is introduced. Along with the development of rolling technology, various production enterprises begin to adopt high-order plate-shaped target curves to meet the production requirements of high-precision cold-rolled strip steel. However, the coefficients of the higher-order plate-shaped target curve are numerous, and the influence degree of each coefficient on the curve is different, so that the difficulty is increased for setting the higher-order plate-shaped target curve, and the problem to be solved in the current production is also solved.
Aiming at the setting problem of the plate-shaped target curve of the cold-rolled strip steel, domestic researchers do some related researches. The Chinese journal article "cold-rolled strip steel plate-shaped target curve setting model research and application" (China metallurgy, 2022, 32 (12): 57-65) is based on basic plate-shaped target curves and compensation curves, a plate-shaped target curve generalized equation in an 8-degree polynomial form is established by using a function modeling method, normalization processing is carried out on the plate-shaped target curve generalized equation by using a linear function normalization algorithm, and a gain coefficient is multiplied to obtain a normalized 8-degree plate-shaped target curve final model; the method comprises the steps of (1) setting and researching and optimizing dynamic cold-rolled plate-shaped target curve in China's Shuoshi paper' (Jin Shuren, yan Shanda science, 2022), defining the basic form of a plate-shaped target curve equation by adopting a mode of combining mechanism analysis and mathematical modeling, establishing a setting flow and a solving method of each coefficient of a plate-shaped target curve in a steady-state rolling stage and an unsteady-state rolling stage by utilizing an intelligent algorithm and a statistical analysis technology, and developing a plate-shaped control expert system according to a knowledge engineering technology; the Chinese Shuoshi paper (Yan Mingze, yan Shanda science, 2021) aims at the defect that convexity after rolling of each pass cannot be quantitatively controlled in the traditional cold-rolled plate shape target curve formulation thought, and sets each pass target convexity by combining a total proportional convexity change distribution model in the hot rolling field and a instability discrimination model in the cold rolling field, thereby providing a plate shape target curve setting method considering target convexity; the Chinese doctor paper 'study and application of cold-rolled strip steel plate shape control technology' (northeast university, 2011) takes strip steel convexity control, flatness control and subsequent processing requirement meeting as principles to set a model of a plate shape target curve, and simultaneously, based on actual production conditions, the dynamic correction and compensation model of the plate shape target curve in the links of coiling shape, equipment installation geometric errors, strip steel transverse temperature difference, strip steel edge thinning, manual adjustment of a plate shape adjusting mechanism and the like is researched and formulated.
The deficiencies of the above research mainly have three aspects:
(1) The general scholars establish an expression equation of a plate-shaped target curve based on the cold-rolled strip steel plastic deformation theory, but the theoretical calculation result is different from the actual production condition, so that the calculated plate-shaped target curve cannot accurately control the quality of the strip steel;
(2) The general practitioner, although giving an expression model of the strip-shaped target curve, does not mention how to set the coefficients to obtain this type of strip-shaped target curve when knowing the general shape of the strip-shaped target curve required for the downstream process.
(3) Although some scholars establish a dynamic setting method of the plate-shaped target curve based on decision type according to the production data, the setting result can cause inaccurate coefficient values obtained by solving due to noise in the production data.
Disclosure of Invention
In order to solve the technical problems, the invention aims to provide a setting method of a higher order item plate-shaped target curve based on flatness.
The invention provides a setting method of a higher order item plate-shaped target curve based on flatness, comprising the following steps:
step 1: establishing a higher order term plate shape target curve basic equation, and carrying out standardized treatment on the higher order term plate shape target curve basic equation to obtain a standardized higher order term plate shape target curve equation;
step 2: according to the target width of the strip steelBDividing a standardized higher-order term plate-shaped target curve equation into three expression forms;
step 3: determining the set coefficient in the basic equation of the higher order term plate-shaped target curvea k And gain coefficientGIn whichk=2,4,6,8；
Step 4: let the higher order term plate shape target curve basic equationa k For a fixed value in its range of values, only the change is madeGObtaining a plurality of standardized higher term plate-shaped target curves, and determiningGIs provided;
step 5: one of the setting coefficients of the basic equation of the higher order term plate-shaped target curve takes a plurality of values at equal intervals in the range of the setting coefficients, and the other setting coefficients are equal toGTaking a fixed value, obtaining a plurality of standardized higher term plate-shaped target curves, and determining alla k Is provided;
step 6: according toGAnda k is determined by the area of action of (a)GAnda k is measured at the position of the set reference sectionA section;
step 7: according to the setting result of the reference section, establishing according to the regression analysis of the dataGSetting coefficients of quadratic termsa 2 Solving the equation and solvingGA value;
step 8: introduce the concept of flatness and define asflaEstablishing a rule for obtaining plate type theoretical values at a set reference section of a set coefficient based on flatness by using parallel line spacing, and solving the set coefficienta 2 ；
Step 9: to solve forGValue suma 2 Setting up the coefficient according to regression analysis of dataa k Regression equation of (2)f(a k ) And solve fora k , wherein k=4,6,8；
Step 10: to be solved forGValue suma k Substituting values into a normalized higher order term sigmoid target curve equation and drawing an image, whereink=2,4,6,8。
The method for setting the higher term plate-shaped target curve based on flatness has the following beneficial effects:
1. according to the method for setting the high-order item plate-shaped target curve based on flatness, the application conditions of the plate-shaped target curves with different product specifications are considered, and the plate-shaped control accuracy is improved;
2. the flatness concept is adopted to indirectly set the higher-order item plate-shaped target curve coefficient, so that the accuracy of the higher-order item coefficient value is ensured;
3. according to the invention, on the basis of the existing influence factor analysis, the statistical regression analysis calculation is applied to the setting of the plate-shaped target curve coefficient, so that the setting difficulty of each coefficient is reduced;
4. the invention is based on rolling theory and on-site production data, can effectively avoid the increase of rejection rate caused by the difference between a theoretical model and actual production, and reduces the enterprise cost.
Drawings
FIG. 1 is a flow chart of a method for setting a high-order item plate-shaped target curve based on flatness;
FIG. 2 is an analysis diagram of the gain factor G action segment;
FIG. 3 shows the setting coefficientsa 2 A coefficient action area analysis chart;
FIG. 4 shows the setting coefficientsa 4 A coefficient action area analysis chart;
FIG. 5 shows the setting coefficientsa 6 A coefficient action area analysis chart;
FIG. 6 is a set coefficienta 8 A coefficient action area analysis chart;
FIG. 7 is a conceptual explanatory diagram of flatness of the present embodiment;
fig. 8 is a schematic diagram of a normalized platelike target curve.
Detailed Description
As shown in FIG. 1, the method for setting the high-order item plate-shaped target curve based on flatness comprises the following steps:
step 1: establishing a higher order term plate shape target curve basic equation, and carrying out standardization processing on the higher order term plate shape target curve basic equation to obtain a standardized higher order term plate shape target curve equation, wherein the step 1 specifically comprises the following steps:
step 1.1: the expression of the higher order term sigmoid objective curve base equation with highest Xiang Ci being 8 is:
；
in the formula ,yrepresent the firstiTheoretical calculations of the plate shape at the measurement section,P i is the first one of the contact type plate-shaped rollersiThe physical position of the segments is measured,i∈[b,e]，b、erespectively corresponding to the initial number and the termination number of the measuring section of the target width B of the strip steel;a k setting coefficients for the higher order term plate-shaped target curve,k=2,4,6,8，a 0 is a constant term coefficient;
step 1.2: according to the following pairiMeasuring physical position of a segmentP i And (3) carrying out standardization treatment:
；
in the above-mentioned method, the step of,x i is normalized to the firstiMeasuring a physical location at the segment;
step 1.3: and (3) carrying out standardization processing on the set coefficient and the constant term coefficient of the plate-shaped target curve according to the following steps:
；
in the formula ,setting coefficients for the normalized plate-shaped target curve,k=2,4,6,8，/>constant term coefficient normalized for a plate-shaped target curve,/->A calculation factor of the constant term coefficient standardization processing process;
step 1.4: respectively by the first standardized treatmentiMeasuring physical position of a segmentx i And normalized coefficients of the sigmoid target curve, replacing the first order item in the sigmoid target curve basic equationiMeasuring physical position of a segmentP i And the set coefficient and the constant term coefficient of the plate-shaped target curve to obtain the following standardized higher term plate-shaped target curve equation:
；
wherein ,Gas the gain factor of the gain factor,represents normalized theoretical calculations of plate shape at the i-th measurement section.
In this example, the target width B of the strip steel is 1200mm,x i the values of (2) are shown in Table 1.
Table 1 showsx i Numerical value table
| i | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| x i | -0.962 | -0.921 | -0.88 | -0.839 | -0.798 | -0.757 | -0.716 |
| i | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
| x i | -0.675 | -0.634 | -0.593 | -0.552 | -0.491 | -0.409 | -0.327 |
| i | 17 | 18 | 19 | 20 | 21 | 22 | 23 |
| x i | -0.245 | -0.163 | -0.081 | 0 | 0.081 | 0.163 | 0.245 |
| i | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
| x i | 0.327 | 0.409 | 0.491 | 0.552 | 0.593 | 0.634 | 0.6751 |
| i | 31 | 32 | 33 | 34 | 35 | 36 | 37 |
| x i | 0.716 | 0.757 | 0.798 | 0.839 | 0.880 | 0.921 | 0.962 |
Step 2: according to the target width of the strip steelBDividing a standardized higher term plate-shaped target curve equation into three expression forms in three different value intervals, wherein the expression forms are as follows:
；
in the formula ,B 1 、B 2 、B 3 andB 4 respectively the target width of the strip steelBThe 1 st, 2 nd, 3 rd and 4 th distinguishing points are obtained by inquiring production planning information;、/>、/>three expression forms of the standard high order term plate shape target curve equation.
In this embodiment:B 1 is the diameter of the glass fiber reinforced plastic film is 750mm,B 2 is of the order of 960mm,B 3 is the size of the particle size of 1120mm,B 4 1280mm.
Step 3: determining the set coefficient in the basic equation of the higher order term plate-shaped target curvea k And gain coefficientGThe value range of (2) is specifically:
found by field debugging experience and plate-shaped closed loop feedback control system, when the coefficient isGAn absolute value of greater than 50 or a set systemNumber of digitsa k When the absolute value of (2) is larger than 20, the plate shape control effect cannot meet the downstream process requirements. Thus, the gain coefficientGThe range of the value of (C) is [ -50,50]Setting coefficientsa k The value range of (2) is set to be [0,20 ]]Whereink=2,4,6,8。
Step 4: let the higher order term plate shape target curve basic equationa k For a fixed value in its range of values, only the change is madeGObtaining a plurality of standardized higher term plate-shaped target curves, and determiningGThe step 4 specifically includes:
will bea k Set to [0,20 ]]Any value within, wherein,k=2, 4,6,8, inGTaking a plurality of values at equal intervals in the value range of (1), drawing a corresponding number of standardized high-order item plate-shaped target curves, and finding a plate-shaped theoretical value in the standardized high-order item plate-shaped target curvesIU i And (3) withGCorresponding measuring sections of equal proportion and setting the measuring sections asGIs arranged in the region of action of (a),i∈[b, e]。
in the present embodiment, it willGAt [ -20, -1]Taking 11 values in the interval with-20 as the starting point, -1 as the end point and 2 as the step lengtha 0 ~a 8 Is 0.5 and a set of 11 curves is plotted according to the normalized higher order term sigmoid objective curve equation in step 1, as shown in fig. 2. As can be seen from fig. 2, whenGAt [ -20, -1]When the interval is changed at equal intervals, the plate shape calculated values at the 4 th measuring section and the 36 th measuring section are also changed at equal intervals by taking 2 as step length, and the determination can be madeGThe action segments of (a) are the 4 th segment and the 36 th segment.
Step 5: one of the setting coefficients of the basic equation of the higher order term plate-shaped target curve takes a plurality of values at equal intervals in the range of the setting coefficients, and the other setting coefficients are equal toGTaking a fixed value, obtaining a plurality of standardized higher term plate-shaped target curves, and determining alla k The step 5 specifically includes:
order thea k One of which is set to a coefficient of [0,20 ]]Taking several values at medium interval, taking fixed values for other setting coefficients and gain coefficients, drawinga k The corresponding normalized higher order term plate-shaped target curves are taken as the measuring sections in the intersection points of the non-end points of the normalized higher order term plate-shaped target curvesa k In whichk=2,4,6,8。
In the present embodiment, the following is performedGTaking-20. Order thea k One of the coefficients takes values at 0.01, 0.1, 1, 2 and 20, and the other coefficients take fixed values of 0.5, and curves are respectively drawn according to the standard high-order term plate-shaped target curve equation in the step 1, as shown in fig. 3 to 6. Taking each segment in the intersection point at the non-end point of each normalized higher term plate-shaped target curve as a coefficienta k Is the active area of (1)a k The region of action is shown in Table 2, in whichk=2,4,6,8。
Table 2 showsa k Is of the area of action
| Setting coefficients | a 2 | a 4 | a 6 | a 8 |
| Region of action | [14,26] | [11,29] | [14,26] | [13,27] |
Step 6: according toGAnda k is determined by the area of action of (a)GAnda k the step 6 specifically includes:
step 6.1: value and ratio in b measurement section and e measurement section according to the normalized higher order term plate shape target curve in step 4GIn one-to-one correspondence, the standard high-order item plate-shaped target curve is a symmetrical curve, so thatGSetting the reference section asDagp 1 And meet the followingDagp 1 =b or e；
Step 6.2: will beiTake the value ofThe corresponding measuring section is set asDagp 2 And willDagp 2 Defined as the set coefficienta k Is set up in the reference section:
；
where, int is a downward rounding function,k=2,4,6,8。
in the present embodiment of the present invention,bis the number of the water-soluble polymer in the water solution of 4,e36, thenGSetting the reference section as the 4 th measurement section or the 36 th measurement section, so thatDagp 1 4. When (when)BIn the case of 1200 the number of the holes,Dagp 2 is 20.
Step 7: according to the setting result of the reference section, establishing according to the regression analysis of the dataGSetting coefficients of quadratic termsa 2 Solving the equation and solvingGThe value, the step 7 specifically is:
step 7.1: establishing a gain systemNumber of digitsGThe solution equation of (2) is:
；
wherein ,IU b the set value of the (B) is checked by the production standard of the downstream process;
step 7.2: using the calculatedGThe value and the number are takena 2 Numerical value, other setting coefficients take any fixed value in the range of the numerical value, and the numerical value is based on the target width of the strip steelBSelecting a standardized higher order term plate-shaped target curve equation of a corresponding range according to the step 2 and drawing a plurality of standardized higher order term plate-shaped target curvesC 1 And record each item of mark curveC 1 Middle inDagp 2 Theoretical value of plate shape atIU C1 ；
In this example, since B is 1200mm, a normalized plate shape target curve equation is selected:. Solving the gain coefficientG、Setting coefficientsa 2 Anda 8 the corresponding standardized plate-shaped target curve equation can be obtained.
Step 7.3: by means ofa 2 AndIU C1 performing nonlinear regression analysis, selecting regression equation with maximum fitting goodness, and establishinga 2 Is a regression equation of (2):
；
in the formula ,f(a 2 ) To be abouta 2 A regression function of the coefficients and,A 3 、A 2 、A 1 andA 0 respectively isf(a 2 ) The third order term coefficient, the second order term coefficient, the first order term coefficient and the constant term coefficient are calculated according to regression analysis.
In the present embodiment of the present invention,b=4 is found from the downstream process production criteria,IU 4 has a value of-18, thenGHas a value of-18.f(a 2 ) The regression equation of (2) is:
。
step 8: introduce the concept of flatness and define asflaEstablishing a rule for obtaining plate type theoretical values at a set reference section of a set coefficient based on flatness by using parallel line spacing, and solving the set coefficienta 2 The step 8 specifically comprises the following steps:
step 8.1: order thea 2 In order to take the maximum value within the range of values,a k drawing a standardized higher-order term plate-shaped target curve F according to the standardized higher-order term plate-shaped target curve equation of the corresponding range selected in the step 7.2 for any value less than 0.5 in the value range 1 The method comprises the steps of carrying out a first treatment on the surface of the Order thea k In order to take the maximum value within the range of values,a 2 drawing a standardized higher order term plate-shaped target curve F for any value less than 0.5 in the value range 2； wherein k=4,6,8；
Step 8.2: let F 1 and F2 At the setting reference sectionDagp 2 At a distance of D 1 Taking F 1 To the left of the symmetry axis of (a) as an analysis zone in which F is set 1 and F2 The intersection points of A and B are respectively connected to form a straight lineL 1 ；
Step 8.3: let the measurement sections of A and B be respectivelySeg A And (3) withSeg B Calculate F 1 and F2 Upper partSeg A And (3) withSeg B Absolute value of difference between theoretical values of plate shape at all same measuring sectionsAnd find +.>Measuring section where maximum value is locatedSeg C Will beSeg C The corresponding plate shape theoretical value is in a normalized higher term plate shape target curve F 2 The position of (a) is defined as a point C, and the passing point C is parallel toL 1 Straight line of (2)L 2 Order-makingL 1 And (3) withL 2 The distance between them isD 2 ；
Step 8.4: will beD 1 And (3) withD 2 Equally dividing into N parts, each part being respectively deltaD 1 And deltaD 2 Obtained by fitting analysisD 1 And (3) withD 2 Fitting coefficient betweenk f The method comprises the steps of carrying out a first treatment on the surface of the Definition of flatness asflaAnd its value is obtained from debugging experience, letD 2 Expressed as:
；
thenD 1 Expressed as:
；
then calculate according to the following equationf(a 2 )：
；
wherein ,IU s andk f is the set value of the downstream production process, and is obtained by solving the equationa 2 Is a numerical value of (2).
In the present embodiment, F 1 and F2 As shown in fig. 7. Straight lineL 1 And (3) withL 2 The equations of (2) are:
；
；
ΔD 2 at the level of 0.0158,k f 29.418, according to the production debugging experience,fla5, then D 1 2.324. According to downstream process indexesIU S With a value of 7, thenf(a 2 ) Is 9.324. Solving forf(a 2 ) The equation is combined with a real solution to obtain coefficientsa 2 The value of (3) was 0.013.
Step 9: to solve forGValue suma 2 Setting up the coefficient according to regression analysis of dataa k Regression equation of (2)f(a k ) And solve fora k The step 9 specifically comprises the following steps:
step 9.1: to be used forGValue and value ofa 2 Based on the value, leta k Taking a plurality of values, and drawing a standardized high-order term plate-shaped target curve according to the standardized high-order term plate-shaped target curve equation of the corresponding range selected in the step 7.2C 2 And record each curveC 2 Middle inDagp 2 Theoretical value of plate shape atIU C2, wherein k=4,6,8；
Step 9.2: by means ofa k Numerical valueIU C2 Performing nonlinear regression analysis and establishinga k The regression equation is:
in the formula ,f(a k ) Is thata k Is a regression function of (2);A k andC k respectively isf(a k ) Is calculated according to regression analysis; using in step 8IU s As a means off(a k ) The function value of the equation is obtained by solving the equationa k Whereink=4,6,8。
Due to the choice of the normalized sigmoid target curve equation:therefore only need to solvea 8 And obtaining a final standardized plate-shaped target curve equation.
In the present embodiment of the present invention,f(a 8 ) The equation of (2) is:
；
let step 8IU s The value of (2) isf(a 8 ) The function value of the equation can be obtained by solvinga 8 Has a value of 0.026.
Step 10: to be solved forGValue suma k Substituting values into a normalized higher order term sigmoid target curve equation and drawing an image, whereink=2,4,6,8。
In this embodiment, the process is performed in step 7GValue, step 8a 2 Value and step 9a 8 The value is obtained by performing a normalization processing methodBThe corresponding normalized plate-shaped target curve at 1200mm is:
；
the corresponding curve image is shown in fig. 8.
The foregoing description of the preferred embodiments of the invention is not intended to limit the scope of the invention, but rather to enable any modification, equivalent replacement, improvement or the like to be made without departing from the spirit and principles of the invention.
Claims (10)
1. The method for setting the higher-order item plate-shaped target curve based on flatness is characterized by comprising the following steps of:
step 1: establishing a higher order term plate shape target curve basic equation, and carrying out standardized treatment on the higher order term plate shape target curve basic equation to obtain a standardized higher order term plate shape target curve equation;
step 2: according to the target width of the strip steelBDividing a standardized higher-order term plate-shaped target curve equation into three expression forms;
step 3: determining the set coefficient in the basic equation of the higher order term plate-shaped target curvea k And gain coefficientGIn whichk=2,4,6,8；
Step 4: let the higher order term plate shape target curve basic equationa k For a fixed value in its range of values, only the change is madeGObtaining a plurality of standardized higher term plate-shaped target curves, and determiningGIs provided;
step 5: one of the setting coefficients of the basic equation of the higher order term plate-shaped target curve takes a plurality of values at equal intervals in the range of the setting coefficients, and the other setting coefficients are equal toGTaking a fixed value, obtaining a plurality of standardized higher term plate-shaped target curves, and determining alla k Is provided;
step 6: according toGAnda k is determined by the area of action of (a)GAnda k a measurement section where the reference section is located;
step 7: according to the setting result of the reference section, establishing according to the regression analysis of the dataGSetting coefficients of quadratic termsa 2 Solving the equation and solvingGA value;
step 8: introduce the concept of flatness and define asflaEstablishing a rule for obtaining plate type theoretical values at a set reference section of a set coefficient based on flatness by using parallel line spacing, and solving the set coefficienta 2 ；
Step 9: to solve forGValue suma 2 Setting up the coefficient according to regression analysis of dataa k Regression equation of (2)f(a k ) And solve fora k , wherein k=4,6,8；
Step 10: to be solved forGValue suma k Substituting values into a normalized higher order term sigmoid target curve equation and drawing an image, whereink=2,4,6,8。
2. The method for setting a higher order term plate-shaped target curve based on flatness according to claim 1, wherein the step 1 specifically comprises:
step 1.1: the expression of the higher order term plate-shaped target curve basic equation is set as follows:
；
in the formula ,yrepresent the firstiTheoretical calculations of the plate shape at the measurement section,P i is the first one of the contact type plate-shaped rollersiThe physical position of the segments is measured,i∈[b，e]；b、erespectively corresponding to the initial number and the termination number of the measuring section of the target width B of the strip steel;a k setting coefficients for the higher order term plate-shaped target curve,k=2,4,6,8，a 0 is a constant term coefficient;
step 1.2: according to the following pairiMeasuring physical position of a segmentP i And (3) carrying out standardization treatment:
；
in the above-mentioned method, the step of,x i is normalized to the firstiMeasuring a physical location at the segment;
step 1.3: and (3) carrying out standardization processing on the set coefficient and the constant term coefficient of the plate-shaped target curve according to the following steps:
；
in the formula ,setting coefficients for the normalized plate-shaped target curve,k=2,4,6,8，/>constant term coefficient normalized for a plate-shaped target curve,/->A calculation factor of the constant term coefficient standardization processing process;
step 1.4: respectively by the first standardized treatmentiMeasuring physical position of a segmentx i And normalized coefficients of the sigmoid target curve, replacing the first order item in the sigmoid target curve basic equationiMeasuring physical position of a segmentP i And the set coefficient and the constant term coefficient of the plate-shaped target curve to obtain the following standardized higher term plate-shaped target curve equation:
；
wherein ,Gas the gain factor of the gain factor,represents normalized theoretical calculations of plate shape at the i-th measurement section.
3. The method for setting a higher order term plate shape target curve based on flatness of claim 2, wherein three expression forms of the normalized higher order term plate shape target curve equation in the step 2 are:
；
in the formula ,B 1 、B 2 、B 3 andB 4 respectively the target width of the strip steelBThe 1 st, 2 nd, 3 rd and 4 th distinguishing points are obtained by inquiring production planning information;、/>、/>three expression forms of the standard high order term plate shape target curve equation.
4. The method for setting a higher order term plate-shaped target curve based on flatness according to claim 2, wherein the step 3 specifically comprises:
gain coefficientGThe range of the value of (C) is [ -50,50]Setting coefficientsa k The value range of (2) is set to be [0,20 ]]Whereink=2,4,6,8。
5. The method for setting a higher order term plate-shaped target curve based on flatness of claim 4, wherein the step 4 specifically comprises:
will bea k Set to [0,20 ]]Arbitrary value in (1), wherek=2, 4,6,8, inGTaking a plurality of values at equal intervals in the value range of (1), drawing a corresponding number of standardized high-order item plate-shaped target curves, and finding a plate-shaped theoretical value in the standardized high-order item plate-shaped target curvesIU i And (3) withGCorresponding measuring sections of equal proportion and setting the measuring sections asGIs arranged in the region of action of (a),i∈[b, e]。
6. the method for setting a higher order term plate-shaped target curve based on flatness of claim 4, wherein the step 5 specifically comprises:
order thea k One of the setting coefficients is [0,20 ]]Taking several values at medium interval, taking fixed values for other setting coefficients and gain coefficients, drawinga k The corresponding normalized higher order term plate-shaped target curves are taken as the measuring sections in the intersection points of the non-end points of the normalized higher order term plate-shaped target curvesa k In whichk=2,4,6,8。
7. The method for setting a higher order term plate-shaped target curve based on flatness of claim 5, wherein the step 6 specifically comprises:
step 6.1: value and ratio in b measurement section and e measurement section according to the normalized higher order term plate shape target curve in step 4GIn one-to-one correspondence, the standard high-order item plate-shaped target curve is a symmetrical curve, so thatGSetting the reference section asDagp 1 And meet the followingDagp 1 =b or e；
Step 6.2: will beiTake the value ofThe corresponding measuring section is set asDagp 2 And willDagp 2 Defined as the set coefficienta k Is set up in the reference section:
；
where, int is a downward rounding function,k=2,4,6,8。
8. the method for setting a higher order term plate-shaped target curve based on flatness of claim 7, wherein the step 7 specifically comprises:
step 7.1: establishing gain coefficientsGThe solution equation of (2) is:
；
wherein ,IU b the set value of the (B) is checked by the production standard of the downstream process;
step 7.2: using the calculatedGThe value and the number are takena 2 Numerical value, other setting coefficients take any fixed value in the range of the numerical value, and the numerical value is based on the target width of the strip steelBSelecting a standardized higher order term plate-shaped target curve equation of a corresponding range according to the step 2 and drawing a plurality of standardized higher order term plate-shaped target curvesC 1 And record each item of mark curveC 1 Middle inDagp 2 Theoretical value of plate shape atIU C1 ；
Step 7.3: by means ofa 2 AndIU C1 performing nonlinear regression analysis, selecting regression equation with maximum fitting goodness, and establishinga 2 Is a regression equation of (2):
；
in the formula ,f(a 2 ) To be abouta 2 A regression function of the coefficients and,A 3 、A 2 、A 1 andA 0 respectively isf(a 2 ) The third order term coefficient, the second order term coefficient, the first order term coefficient and the constant term coefficient are calculated according to regression analysis.
9. The method for setting a higher order term plate-shaped target curve based on flatness of claim 8, wherein the step 8 specifically comprises:
step 8.1: order thea 2 In order to take the maximum value within the range of values,a k drawing a standardized higher-order term plate-shaped target curve F according to the standardized higher-order term plate-shaped target curve equation of the corresponding range selected in the step 7.2 for any value less than 0.5 in the value range 1 The method comprises the steps of carrying out a first treatment on the surface of the Order thea k In order to take the maximum value within the range of values,a 2 drawing a standardized higher order term plate-shaped target curve F for any value less than 0.5 in the value range 2； wherein k=4,6,8；
Step 8.2: let F 1 and F2 At the setting reference sectionDagp 2 At a distance of D 1 Taking F 1 To the left of the symmetry axis of (a) as an analysis zone in which F is set 1 and F2 The intersection points of A and B are respectively connected to form a straight lineL 1 ；
Step 8.3: let A and B beIn the measuring sections respectively ofSeg A And (3) withSeg B Calculate F 1 and F2 Upper partSeg A And (3) withSeg B Absolute value of difference between theoretical values of plate shape at all same measuring sectionsAnd find +.>Measuring section where maximum value is locatedSeg C Will beSeg C The corresponding plate shape theoretical value is in a normalized higher term plate shape target curve F 2 The position of (a) is defined as a point C, and the passing point C is parallel toL 1 Straight line of (2)L 2 Order-makingL 1 And (3) withL 2 The distance between them isD 2 ；
Step 8.4: will beD 1 And (3) withD 2 Equally dividing into N parts, each part being respectively deltaD 1 And deltaD 2 Obtained by fitting analysisD 1 And (3) withD 2 Fitting coefficient betweenk f The method comprises the steps of carrying out a first treatment on the surface of the Definition of flatness asflaAnd its value is obtained from debugging experience, letD 2 Expressed as:
；
thenD 1 Expressed as:
；
then calculate according to the following equationf(a 2 )：
；
wherein ,IU s andk f is the set value of the downstream production process, and is obtained by solving the equationa 2 Is a numerical value of (2).
10. The method for setting a higher order term plate-shaped target curve based on flatness of claim 9, wherein the step 9 specifically comprises:
step 9.1: to be used forGValue and value ofa 2 Based on the value, leta k Taking a plurality of values, and drawing a standardized high-order term plate-shaped target curve according to the standardized high-order term plate-shaped target curve equation of the corresponding range selected in the step 7.2C 2 And record each curveC 2 Middle inDagp 2 Theoretical value of plate shape atIU C2, wherein k=4,6,8；
Step 9.2: by means ofa k Numerical valueIU C2 Performing nonlinear regression analysis and establishinga k The regression equation is:
in the formula ,f(a k ) Is thata k Is a regression function of (2);A k andC k respectively isf(a k ) Is calculated according to regression analysis; using in step 8IU s As a means off(a k ) The function value of the equation is obtained by solving the equationa k Whereink=4,6,8。
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| WO2010146615A1 (en) * | 2009-06-17 | 2010-12-23 | Thyssenkrupp Acciai Speciali Terni S.P.A. | Method for dynamically controlling flatness in steel strip rolling |
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| CN110851994A (en) * | 2019-11-21 | 2020-02-28 | 燕山大学 | Online shape target curve adjusting method for cold-rolled strip |
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