CN103510032A - Deviation value control method for cold rolling hot galvanizing coating uniformity - Google Patents

Abstract

The invention provides a deviation value control method for cold rolling hot galvanizing coating uniformity. The method comprises the steps of: 1) establishing an influence model of the knife lip opening degree on coating thickness; 2) establishing an influence efficiency function matrix determining the influence weight of each air knife lip servo motor adjustment amount on each coating; 3) solving a motor adjustment amount according to a quadratic error function minimum principle; and 4) considering the actual application features in terms of correcting the quadratic error function, when the galvanizing thickness measured value of a point deviates from most measuring points, in order to avoid the interference of an extreme value on the coating control of other areas, adding a filtering function in an error function, thus finally obtaining a needed air knife lip opening degree. The invention provides a new galvanized layer thickness calculation model suitable for industrial application, introduces the influence efficiency function matrix, enhances the coating uniformity control accuracy, and simultaneously adds the cost function and the filtering function to improve the coating error function accuracy, thereby enhancing the coating uniformity calculation accuracy, and improving the surface quality of a galvanized product.

Description

The deviate control method of cold rolling hot dip galvanizing coating uniformity coefficient

Technical field

The invention belongs to galvanizing process automatic control technology field, relate in particular to cold rolling hot dip galvanizing line zincincation and coating control techniques.

Background technology

An important technical indicator weighing galvanizing production quality is exactly thickness of coating and homogeneity thereof.Coating is too thick not only can waste the starting material such as zinc ingot metal, and can affect spot weldability, the tack of product, the use propertieies such as resistance to chalking of coating; The too thin erosion resistance that can have influence on product of coating, user generally can not accept.Therefore the level of control of coating uniformity coefficient system will directly have influence on quality product, product cost and the competitiveness of product in market of heat zinc coating plate.This has just proposed very high technical requirements and has controlled difficulty coating uniformity coefficient control techniques, to obtain even, stable zinc coating at belt steel surface, just must design a set of tight control strategy, according to the current working condition of steel, by dynamically regulating the crucial controlling factor relevant to coating uniformity coefficient, the parameters such as air pressure, air knife lip seam aperture.Wherein, air knife cutter lip transverse shapes and size, adjust and optimize as the important indicator of controlling galvanizing production even zinc layer.The existing galvanization production line unit of China is all from external introduction, the air knife of wherein controlling zinc coating thickness and uniformity coefficient is also introducing equipment entirely, as the Ke Le air knife of German FOEN air knife, Italian Da Nieli, French CLECIM dynamic air knife DAK(dynamic air knives) system.Wherein a very important feature of DAK E type air knife be can on-line control air knife cutter lip aperture, change cutter lip shape and control the uniformity coefficient with steel athwartship plane coating.The lower knife lip of air knife is fixed, and upper knife lip lip can change, and is evenly distributed with 12 cutter lip motors on upper knife lip, and the rotation of alternating current machine drives the straight line draught of leading screw, thereby changes the cutter lip shape of air knife.

The patent No. is that the Chinese patent of CN200820151950.4 adopts auxiliary air knife+' V ' type baffle plate double control strategy, the limit control device research of crossing zinc-plated problem based on steel edge portion is provided, novel air knife device scheme has been proposed, it is by changing air knife edge dam size and baffle plate and Dai Gangjian gap, studied under the conditions such as certain air pressure and strip width, baffle dimensions and the gap rule that affects on steel edge portion zinc coating thickness, its shortcoming is only to consider that cutter lip aperture is to the excessively zinc-plated restraining effect of steel edge portion, do not solve the laterally uneven problem of other position thickness of coating of band steel, but also just rest on the system emulation stage, do not drop into practical application in industry, the patent No. be the Chinese patent of CN201110143959.7 relate to a kind of prevent air knife dross for carry out the method for accurate adjustment to controlling the air knife of galvanized layer thickness, the method comprises the step of adjusting levelness between left cutter lip and right cutter lip, because datum plane Ban two ends are inserted and placed on respectively in left cutter lip and right cutter lip, therefore, the levelness between left cutter lip and right cutter lip can be directly reflected at this datum plane plate and the angle of inclination between horizontal plane that by level measurement, go out, thereby guaranteed the accuracy of follow-up Level-adjusting, shortcoming is the equalising means that it just proposes for air knife dross problem, transverse uniformity of plating is not dealt with, the patent No. is that the Chinese patent of CN200910131086.0 has been mentioned electro-galvanizing zinc coating thickness BP neural network control method and the application on PLC thereof, the electro-galvanizing zinc coating thickness BP neural network controller of design, Zinc Coating Thickness be can control accurately, effectively man-made interference, intelligent adaptive suppressed, there is good accuracy and fault-tolerance, shortcoming is single from the viewpoint of average zinc coating thickness, does not mention the horizontal thickness of coating calculating model of band steel and control method.

At present in domestic and international most of galvanization production lines, the adjusting of air knife cutter lip transverse shapes and opening degree be all online outside, by the individual manually spiral topworks of n, realize, according to knowhow, set size and the lateral variation amount of opening degree, once drop into actual production, cannot dynamically change, seriously restricted the regulating power of coating uniformity coefficient.In addition, even application DAK air knife, its effect of automatically controlling cutter lip motor change coating uniformity coefficient is also not obvious, major cause is exactly that the uniformity coefficient deviate control model of setting up exists defect, as each cutter lip motor is adjusted the weights computation model on coating impact, adopt the method for orthogonal polynomial regression, the more complicated practicality of this algorithm is strong and precision is not high, does not consider that in addition the adjustment of cutter lip is on the too sensitive characteristic of Delay Feedback reaction and the impact of Plating measurement relatively large deviation value.

Summary of the invention

The object of the invention is to overcome the existing deficiency of above-mentioned prior art, a kind of deviate control method of cold rolling hot dip galvanizing coating uniformity coefficient is provided, to improve the setting accuracy of strip steel Zn-plating process air knife cutter lip aperture, thereby improve cold-rolling galvanization board finished product coating uniformity coefficient and surface quality.

The present invention is achieved in that the deviate control method of this cold rolling hot dip galvanizing coating uniformity coefficient comprises the steps:

1) set up the affect model of cutter lip aperture on thickness of coating

The factor that affects belt steel surface zinc coating thickness is a lot, the size that can control and belt steel surface thickness of coating is affected from variable, it is generally acknowledged that thickness of coating CW is the function of strip speed LS, whiff pressure P, air knife and belt steel surface distance D and the average lip seam of cutter lip value α:

$CW=K_{1}L{S}^a{D}^b{P}^c{e}^{\frac{?{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="HDA00001788729800013.png"\; state="\{\{state\}\}">K</figure-callout>}}_2}{\mathrm{\&alpha;}}}---\left(1\right)$

In formula, a, b, c is the adaptation coefficient that regression Analysis obtains; K ₁, K ₂for empirical constant, K wherein ₂depend on coating type.

From the zinc coating thickness model of formula (1), zinc coating thickness is the index of cutter lip seam value, if layer thickness meter departs from average thickness of coating in the thickness of coating that sampling point transversely detected with steel, laterally coating error control will be adjusted a plurality of cutter lip motors change lip seam values, eliminate the thickness of coating deviation of sampling point.

2) what set up to determine that each air knife cutter lip servomotor adjustment amount affects weights to each coating affects efficiency function matrix

Based on determining that each air knife cutter lip servomotor adjustment amount affects weights to each coating, set up and affect efficiency function matrix (Influence Efficiency Function Matrix), the upper knife lip seam of air knife is adjustable, wherein, layer thickness meter measured zone quantity is n, air knife cutter lip servomotor quantity is m, and the distance between servomotor is X _a, calculation formula is as follows:

$M_{\text{ij}}=Max\left(0,m_{ij}\right)=Max\left(0,\frac{X_a?\left|P_i?X_j\right|}{X_a}\right)---\left(2\right)$

In formula, P _iit is the distance between i measurement point and m motor;

X _jit is the distance between j motor and m motor;

M _ijfor affecting the element that efficiency function matrix i is listed as, j is capable.

3) according to quadratic form error function minimum principle, solve motor adjustment amount

According to principle of optimality, define the thickness of coating error function of each measured zone, this is a multi-variable function, and variable is α _i, i ∈ 1 ... m:

$J={{\displaystyle \underset{j=1}{\overset{n}{\&Sum;}}\left[\left(me{s}_j\right)?{\displaystyle \underset{i=1}{\overset{m}{\&Sum;}}{\mathrm{\&alpha;}}_i{M}_{ij}}+c\right]}}^2---\left(3\right)$

In formula, n is layer thickness meter measured zone quantity;

M is air knife cutter lip servomotor quantity;

C is for revising constant, and the correction summation calculating equals 0, and object is to make average value measured

remain unchanged;

Mes _jbe j measured zone observed value-coating target value;

α _ibe i motor modified value.

By asking the minimum value of error function to calculate the motor adjustment amount of each air knife cutter lip servomotor, adjust α _i, i ∈ i ... m, can obtain different J, controls target and be that to make J be minimum, and error amount is minimum, α now _ibe exactly each air knife cutter lip motor adjustment amount:

$\frac{\&PartialD;J}{\&PartialD;{\mathrm{\&alpha;}}_i}=0,\mathrm{for},i=1\&CenterDot;\&CenterDot;\&CenterDot;m$

$\left[\begin{array}{c}2[{\mathrm{mes}}_1-\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i{M}_{i1}+c]M_{11}+...+2[{\mathrm{mes}}_n-\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i{M}_{\mathrm{in}}+c]M_{1n}\\ 2[{\mathrm{mes}}_1-\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i{M}_{i1}+c]M_{21}+...+2[{\mathrm{mes}}_n-\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i{M}_{\mathrm{in}}+c]M_{2n}\\ .\\ .\\ .\\ 2[{\mathrm{mes}}_1-\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i{\mathrm{<figure-callout\; id="1"\; label="M\; i"\; filenames="554878DEST\_PATH\_HDA00002037339700013.png,HDA00001788729800013.png"\; state="\{\{state\}\}">M</figure-callout>}}_i+c]{\mathrm{<figure-callout\; id="1"\; label="M\; m"\; filenames="554878DEST\_PATH\_HDA00002037339700013.png,HDA00001788729800013.png"\; state="\{\{state\}\}">M</figure-callout>}}_m+...+2[{\mathrm{mes}}_n-\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i{M}_{\mathrm{in}}+c]M_{\mathrm{mn}}\end{array}\right]=\left[\begin{array}{c}0\\ 0\\ .\\ .\\ .\\ 0\end{array}\right]\&DoubleRightArrow;$

$M_{m\&times;n}{\left[\begin{array}{c}[{\mathrm{mes}}_1-\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i{M}_{i1}+c]\\ [{\mathrm{mes}}_2-\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i{M}_{i2}+c]\\ .\\ .\\ .\\ [{\mathrm{mes}}_n-\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i{M}_{\mathrm{in}}+c]\end{array}\right]}_{n\&times;1}=\left[\begin{array}{c}0\\ 0\\ .\\ .\\ .\\ 0\end{array}\right]\&DoubleRightArrow;M_{m\&times;n[}{\left[\begin{array}{c}[{\mathrm{<figure-callout\; id="1"\; label="mes"\; filenames="554878DEST\_PATH\_HDA00002037339700013.png,HDA00001788729800013.png"\; state="\{\{state\}\}">mes</figure-callout>}}_1+c]\\ {[\mathrm{<figure-callout\; id="2"\; label="mes"\; filenames="HDA00001788729800013.png"\; state="\{\{state\}\}">mes</figure-callout>}}_2+c]\\ .\\ .\\ .\\ {[\mathrm{mes}}_n+c]\end{array}\right]-M^T\left[\begin{array}{c}{\mathrm{\&alpha;}}_1\\ {\mathrm{\&alpha;}}_2\\ .\\ .\\ .\\ {\mathrm{\&alpha;}}_m\end{array}\right]]}_{n\&times;1}={\left[\begin{array}{c}0\\ 0\\ .\\ .\\ .\\ 0\end{array}\right]}_{m\&times;1}\&DoubleRightArrow;$

$M\left[\begin{array}{c}[{\mathrm{<figure-callout\; id="1"\; label="mes"\; filenames="554878DEST\_PATH\_HDA00002037339700013.png,HDA00001788729800013.png"\; state="\{\{state\}\}">mes</figure-callout>}}_1+c]\\ [{\mathrm{<figure-callout\; id="2"\; label="mes"\; filenames="HDA00001788729800013.png"\; state="\{\{state\}\}">mes</figure-callout>}}_2+c]\\ .\\ .\\ .\\ {[\mathrm{mes}}_n+c]\end{array}\right]-{\mathrm{MM}}^T\left[\begin{array}{c}{\mathrm{\&alpha;}}_1\\ {\mathrm{\&alpha;}}_2\\ .\\ .\\ .\\ {\mathrm{\&alpha;}}_m\end{array}\right]=\left[\begin{array}{c}0\\ 0\\ .\\ .\\ .\\ 0\end{array}\right]\&DoubleRightArrow;{\mathrm{MM}}^T\left[\begin{array}{c}{\mathrm{\&alpha;}}_1\\ {\mathrm{\&alpha;}}_2\\ .\\ .\\ .\\ {\mathrm{\&alpha;}}_m\end{array}\right]=b$

Cutter lip motor adjustment amount is: $\left[\begin{array}{c}{\mathrm{\&alpha;}}_1\\ {\mathrm{\&alpha;}}_2\\ .\\ .\\ .\\ {\mathrm{\&alpha;}}_m\end{array}\right]={\left({\mathrm{MM}}^T\right)}^{-1}b---\left(4\right)$

In formula, $b=M\left[\begin{array}{c}[{\mathrm{<figure-callout\; id="1"\; label="mes"\; filenames="554878DEST\_PATH\_HDA00002037339700013.png,HDA00001788729800013.png"\; state="\{\{state\}\}">mes</figure-callout>}}_1+c]\\ [{\mathrm{<figure-callout\; id="2"\; label="mes"\; filenames="HDA00001788729800013.png"\; state="\{\{state\}\}">mes</figure-callout>}}_2+c]\\ .\\ .\\ .\\ {[\mathrm{mes}}_n+c]\end{array}\right]$ ; MM ^tfor invertible matrix (M is for affecting efficiency function matrix).

4) consider practical application characteristic modification quadratic form error function

For fear of the adjustment of air knife aperture, Delay Feedback is controlled to reaction too responsive, in above-mentioned thickness of coating error function, has increased a cost function (Cost Function), improved the robustness of deviate control model:

$C({\mathrm{\&alpha;}}_i)={\displaystyle \underset{i=1}{\overset{m}{\&Sum;}}{g}_{si}\&CenterDot;(q_i}+{\mathrm{\&alpha;}}_i{)}^2---\left(5\right)$

In formula, q _iit is the current reference position of i motor;

G _sifor waiting cost gain.

And when certain some Zinc Coating Thickness observed value is offset most measurement point, for fear of the coating in other region of disturbing influence of extremum, control, in error function, increased a filter function.

$F({\mathrm{\&alpha;}}_i)={\displaystyle \underset{i=1}{\overset{m}{\&Sum;}}{g}_{di}\&CenterDot;{\mathrm{\&alpha;}}_i^2}---\left(6\right)$

In formula, g _difor dynamic cost gain.

Finally be converted into and solve a quadratic programming problem (Quadratic Programming) and obtain required air knife aperture, (3), (5), (6) formula are integrated:

${\mathrm{<figure-callout\; id="2"\; label="J"\; filenames="HDA00001788729800013.png"\; state="\{\{state\}\}">J</figure-callout>}}_2={{\displaystyle \underset{j=1}{\overset{n}{\&Sum;}}\left[me{s}_j?{\displaystyle \underset{i=1}{\overset{m}{\&Sum;}}{\mathrm{\&alpha;}}_i{M}_{ij}\text{+c}}\right]}}^2+{\displaystyle \underset{i=1}{\overset{m}{\&Sum;}}{g}_{si}}\&CenterDot;{(q_i+{\mathrm{\&alpha;}}_i)}^2+{\displaystyle \underset{i=1}{\overset{m}{\&Sum;}}{g}_{di}\&CenterDot;{{{\mathrm{\&alpha;}}_i}^2-}^{}}--\left(7\right)$

Separate this quadratic programming problem, just can obtain required air knife lip aperture.

The deviate control method of cold rolling hot dip galvanizing coating uniformity coefficient of the present invention, do not changing under the condition of average thickness of coating, according to region coating and average coating, decide indivedual air knife lip corrections, the zinc coating thickness computation model of new adaptation industrial application is proposed, application affects the adjustment that efficiency function matrix determines each cutter lip motor coating is affected to efficiency, set up multivariable error function simultaneously, increase and control the cost function of robustness and the filter function of outlier reflection.When actual coating is low compared with target value, automatically the air knife aperture of Hui Jiang corresponding zone reduces, otherwise opens air knife aperture, realizes the automatic accurate adjustment of coating uniformity coefficient, the 2 δ values that characterize coating uniformity coefficient after input practical application reach approximately 1.1, have increased substantially the surface quality of galvanizing production.

Accompanying drawing explanation

Fig. 1 is embodiment of the present invention hot galvanizing process schematic diagram, is (a) continuous zinc coating line, (b) is air knife jeting area.

Fig. 2 is embodiment of the present invention galvanized layer thickness deviate control flow.

Fig. 3 is that embodiment of the present invention cutter lip motor is adjusted and horizontal thickness of coating relation.

Fig. 4 is embodiment of the present invention air knife motor movement horizontal coating error control flow process when saturated.

Fig. 5 is the horizontal coating error control system of embodiment of the present invention block diagram.

Fig. 6 is the relation between embodiment of the present invention air knife cutter lip aperture and whiff pressure, shearing peak value.

Fig. 7 is that embodiment of the present invention cutter lip lip seam is adjusted and thickness of coating deviation.

Embodiment

Below by embodiment, the invention will be further described.

The embodiment of the present invention be take and coldly connected pot galvanize to produce unit be example, and as shown in Figure 1, yearly capacity is 450,000 tons, and its product is towards medium-to-high grade automobile, household electrical appliances Yong Ban market.In practical application, defined the ultimate value of cutter lip motor movement: when lip seam reference value is less than 0.4mm, forbid that cutter lip motor moves downward, and only allows to move upward; When lip seam reference value is greater than 2.5mm, forbid that cutter lip motor moves upward, and only allows to move downward.Galvanized layer thickness deviate control flow is shown in Fig. 2.As shown in Figure 3, each m=12 cutter lip electric machine control of practical application upper and lower surface air knife cutter lip seam value along air knife width totally 110 thickness of coating check points, and adjacent cutter lip motor distance is 144mm.

1) zinc coating thickness model is set up

The factor that affects belt steel surface zinc coating thickness is a lot, from variable, can control and size on belt steel surface thickness of coating impact, it is generally acknowledged that thickness of coating is process section linear velocity LS, whiff pressure P, air knife apart from the distance D of belt steel surface, the function of the average lip seam of cutter lip value α:

$CW=K_{1}L{S}^a{D}^b{P}^c{e}^{\frac{?{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="HDA00001788729800013.png"\; state="\{\{state\}\}">K</figure-callout>}}_2}{\mathrm{\&alpha;}}}---\left(1\right)$

In formula, CW is average zinc coating thickness; LS is strip speed; D is air knife and band steel distance; P is air pressure; A, b, c is the adaptation coefficient that regression Analysis obtains; K ₁=1.787 is empirical constant, wherein K ₂depend on coating type.

From the zinc coating thickness model of formula (1), zinc coating thickness is the index of cutter lip lip seam value, if layer thickness meter departs from average thickness of coating in the thickness of coating that sampling point transversely detected with steel, laterally coating error control will be adjusted the lip seam value of a plurality of cutter lip motors, eliminates the thickness of coating deviation of sampling point.

2) cutter lip motor and the laterally relation of thickness of coating

As shown in Figure 3, X ₁, X ₂... X _mrepresent cutter lip motor; Distance definition between adjacent cutter lip motor is X _a; P ₁, P ₂... P _nrepresent the horizontal thickness of coating check point of band steel; m _ijrepresent that the j Ge Daochun u of motor movement unit causes i check point P _iplace's lip seam changes.

In lateral error control strategy, precondition is: the lip between adjacent cutter lip is for linear; The lip shape only affecting between j-1 and j+1 motor that changes j cutter lip motor lip can not cause lip variation between j-2 and j-1 motor and the lip variation between j+1 and j+2 motor.

If j Ge Daochun motor movement unit is u, by similar triangles relation, can obtain P _iindividual check point m _ij

$\frac{X_a}{u}=\frac{X_a?\left|P_i?X_j\right|}{m_{ij}}$

If u=1 is,

$m_{ij}=\frac{X_a?\left|P_i?X_j\right|}{X_a}$

3) affect efficiency function matrix

Affecting efficiency function matrix (Influence Efficiency Function Matrix) is mainly to determine the weights of each air knife cutter lip servomotor adjustment amount on each coating impact, and calculation formula is as follows:

$M_{\text{ij}}=Max\left(0,m_{ij}\right)=Max\left(0,\frac{X_a?\left|P_i?X_j\right|}{X_a}\right)---\left(2\right)$

In formula, P _iit is the distance between i measurement point and m motor;

X _jit is the distance between j motor and m motor;

M _ijfor affecting the element that efficiency function matrix i is listed as, j is capable.

4) quadratic form error function

According to principle of optimality, define the thickness of coating quadratic form error function of each measured zone, this is a multi-variable function, and variable is α _i, i ∈ 1 ... m:

$J={{\displaystyle \underset{j=1}{\overset{n}{\&Sum;}}\left[\left(me{s}_j\right)?{\displaystyle \underset{i=1}{\overset{m}{\&Sum;}}{\mathrm{\&alpha;}}_i{M}_{ij}}+c\right]}}^2---\left(3\right)$

In formula, n is layer thickness meter measured zone quantity;

M is air knife cutter lip servomotor quantity;

C is for revising constant, and the correction summation calculating equals 0, and object is to make average value measured

remain unchanged;

Mes _jbe the poor of j measured zone observed value and average thickness of coating;

α _ibe i motor modified value.

Cutter lip motor adjustment amount is: $\left[\begin{array}{c}{\mathrm{\&alpha;}}_1\\ {\mathrm{\&alpha;}}_2\\ .\\ .\\ .\\ {\mathrm{\&alpha;}}_m\end{array}\right]={\left({\mathrm{MM}}^T\right)}^{-1}b---\left(4\right)$

In formula, $b=M\left[\begin{array}{c}[{\mathrm{mes}}_1+c]\\ [{\mathrm{<figure-callout\; id="2"\; label="mes"\; filenames="HDA00001788729800013.png"\; state="\{\{state\}\}">mes</figure-callout>}}_2+c]\\ .\\ .\\ .\\ {[\mathrm{mes}}_n+c]\end{array}\right]$ ; MM ^tfor invertible matrix (M is for affecting efficiency function matrix).

5) cost function and filter function

For fear of the adjustment of air knife aperture, Delay Feedback is controlled to reaction too responsive, cutter lip moves to after ultimate value, if continue motion, will damage cutter lip.In such cases, in above-mentioned quadratic form error function, increase a cost function (Cost Function), improved the robustness of deviate control model:

$C({\mathrm{\&alpha;}}_i)={\displaystyle \underset{i=1}{\overset{m}{\&Sum;}}{g}_{si}\&CenterDot;(q_i}+{\mathrm{\&alpha;}}_i{)}^2---\left(5\right)$

In formula, q _iit is the current reference position of i motor;

G _sifor waiting cost gain.

And when certain some Zinc Coating Thickness observed value is offset most measurement point, for fear of the coating in other region of disturbing influence of extremum, control, in quadratic form error function, increased a filter function (Filtering Function),

$F({\mathrm{\&alpha;}}_i)={\displaystyle \underset{i=1}{\overset{m}{\&Sum;}}{g}_{di}\&CenterDot;{\mathrm{\&alpha;}}_i^2}---\left(6\right)$

In formula, g _difor dynamic cost gain.

Finally be converted into and solve a quadratic performance index (Quadratic Programming) and obtain required air knife aperture, (3), (5), (6) formula are integrated:

${\mathrm{<figure-callout\; id="2"\; label="J"\; filenames="HDA00001788729800013.png"\; state="\{\{state\}\}">J</figure-callout>}}_2={{\displaystyle \underset{j=1}{\overset{n}{\&Sum;}}\left[me{s}_j?{\displaystyle \underset{i=1}{\overset{m}{\&Sum;}}{\mathrm{\&alpha;}}_i{M}_{ij}\text{+c}}\right]}}^2+{\displaystyle \underset{i=1}{\overset{m}{\&Sum;}}{g}_{si}}\&CenterDot;{(q_i+{\mathrm{\&alpha;}}_i)}^2+{\displaystyle \underset{i=1}{\overset{m}{\&Sum;}}{g}_{di}\&CenterDot;{{{\mathrm{\&alpha;}}_i}^2}^{}-}--\left(7\right)$

Separate this quadratic programming problem, just can obtain required air knife lip aperture.

If thickness tester departs from average thickness of coating in the thickness of coating that sampling point transversely detected with steel, laterally coating error control will be adjusted a plurality of cutter lip motor lip seam values, eliminate the thickness of coating deviation of sampling point.If it is saturated that a more than cutter lip motor occurs, at this moment need to calculate the cutter lip motor priority processing of saturation ratio maximum, cutter lip motor saturation computation:

Motor saturation ratio=(motor adjustment amount)/(ultimate value-when anterior lip seam value)

As shown in Figure 4, provide saturated strategic process figure.Similar with average thickness of coating control, lateral error is controlled and is also adopted Smith predictive compensation to lag behind, and control block diagram as shown in Figure 5.Known by air knife airflow field is analyzed, as shown in Figure 6, cutter lip lip seam aperture is when 1.2mm is following, so larger on the large impact of gas flowfield pressure peak slope, aperture is when 1.2mm is above, so less on the less impact of gas flowfield pressure peak slope.By application, draw result as shown in Figure 7, adopt the thickness of coating deviate control method of optimizing, can significantly improve along the horizontal thickness of coating ability adjustment of band steel, make to reduce transverse gage deviation surface evenness control accuracy and improve.

Claims (1)

1. a deviate control method for cold rolling hot dip galvanizing coating uniformity coefficient, is characterized in that comprising the following steps:

1) set up the affect model of cutter lip aperture on thickness of coating

$CW=K_{1}L{S}^a{D}^b{P}^c{e}^{\frac{?K_2}{\mathrm{\&alpha;}}}---\left(1\right)$

In formula, CW is average zinc coating thickness; LS is strip speed; D is air knife and band steel distance; P is air pressure; α is cutter lip aperture; A, b, c is the adaptation coefficient that regression Analysis obtains; K ₁=1.787 is empirical constant, wherein K ₂depend on coating type.

2) what set up to determine that each air knife cutter lip servomotor adjustment amount affects weights to each coating affects efficiency function matrix

Layer thickness meter measured zone quantity is n, and air knife cutter lip servomotor quantity is m, and the distance between servomotor is X _a, calculation formula is as follows:

$M_{\text{ij}}=Max\left(0,m_{ij}\right)=Max\left(0,\frac{X_a?\left|P_i?X_j\right|}{X_a}\right)---\left(2\right)$

In formula, P _ibe the distance between i measurement point and m motor,

X _jbe the distance between j motor and m motor,

M _ijfor affecting the element that efficiency function matrix i is listed as, j is capable;

3) according to quadratic form error function minimum principle, solve motor adjustment amount

According to principle of optimality, define the thickness of coating error function of each measured zone, this is a multi-variable function, and variable is α _i, i ∈ 1 ... m:

$J={{\displaystyle \underset{j=1}{\overset{n}{\&Sum;}}\left[\left(me{s}_j\right)?{\displaystyle \underset{i=1}{\overset{m}{\&Sum;}}{\mathrm{\&alpha;}}_i{M}_{ij}}+c\right]}}^2---\left(3\right)$

In formula, n is layer thickness meter measured zone quantity,

M is air knife cutter lip servomotor quantity,

C is for revising constant, and the correction summation calculating equals 0, and object is to make average value measured

remain unchanged,

Mes _jbe j measured zone observed value-coating target value,

α _ibe i motor modified value;

By asking the minimum value of error function to calculate the motor adjustment amount of each air knife cutter lip servomotor, adjust α _i, i ∈ 1 ... m can obtain different J, controls target and be that to make J be minimum, and error amount is minimum, α now _ibe exactly each air knife cutter lip motor adjustment amount:

$\frac{\&PartialD;J}{\&PartialD;{\mathrm{\&alpha;}}_i}=0,\mathrm{for},i=1\&CenterDot;\&CenterDot;\&CenterDot;m$

$\left[\begin{array}{c}2[{\mathrm{mes}}_1-\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i{M}_{i1}+c]M_{11}+...+2[{\mathrm{mes}}_n-\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i{M}_{\mathrm{in}}+c]M_{1n}\\ 2[{\mathrm{mes}}_1-\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i{M}_{i1}+c]M_{21}+...+2[{\mathrm{mes}}_n-\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i{M}_{\mathrm{in}}+c]M_{2n}\\ .\\ .\\ .\\ 2[{\mathrm{mes}}_1-\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i{M}_{i1}+c]M_{m1}+...+2[{\mathrm{mes}}_n-\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i{M}_{\mathrm{in}}+c]M_{\mathrm{mn}}\end{array}\right]=\left[\begin{array}{c}0\\ 0\\ .\\ .\\ .\\ 0\end{array}\right]\&DoubleRightArrow;$

$M_{m\&times;n}{\left[\begin{array}{c}[{\mathrm{mes}}_1-\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i{M}_{i1}+c]\\ [{\mathrm{mes}}_2-\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i{M}_{i2}+c]\\ .\\ .\\ .\\ [{\mathrm{mes}}_n-\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i{M}_{\mathrm{in}}+c]\end{array}\right]}_{n\&times;1}=\left[\begin{array}{c}0\\ 0\\ .\\ .\\ .\\ 0\end{array}\right]\&DoubleRightArrow;M_{m\&times;n}[{\left[\begin{array}{c}[{\mathrm{mes}}_1+c]\\ {[\mathrm{mes}}_2+c]\\ .\\ .\\ .\\ {[\mathrm{mes}}_n+c]\end{array}\right]-M^T\left[\begin{array}{c}{\mathrm{\&alpha;}}_1\\ {\mathrm{\&alpha;}}_2\\ .\\ .\\ .\\ {\mathrm{\&alpha;}}_m\end{array}\right]]}_{n\&times;1}={\left[\begin{array}{c}0\\ 0\\ .\\ .\\ .\\ 0\end{array}\right]}_{m\&times;1}\&DoubleRightArrow;$ $M\left[\begin{array}{c}[{\mathrm{mes}}_1+c]\\ [{\mathrm{mes}}_2+c]\\ .\\ .\\ .\\ {[\mathrm{mes}}_n+c]\end{array}\right]-{\mathrm{MM}}^T\left[\begin{array}{c}{\mathrm{\&alpha;}}_1\\ {\mathrm{\&alpha;}}_2\\ .\\ .\\ .\\ {\mathrm{\&alpha;}}_m\end{array}\right]=\left[\begin{array}{c}0\\ 0\\ .\\ .\\ .\\ 0\end{array}\right]\&DoubleRightArrow;{\mathrm{MM}}^T\left[\begin{array}{c}{\mathrm{\&alpha;}}_1\\ {\mathrm{\&alpha;}}_2\\ .\\ .\\ .\\ {\mathrm{\&alpha;}}_m\end{array}\right]=b$

Cutter lip motor adjustment amount is: $\left[\begin{array}{c}{\mathrm{\&alpha;}}_1\\ {\mathrm{\&alpha;}}_2\\ .\\ .\\ .\\ {\mathrm{\&alpha;}}_m\end{array}\right]={\left({\mathrm{MM}}^T\right)}^{-1}b---\left(4\right)$

In formula, $b=M\left[\begin{array}{c}[{\mathrm{mes}}_1+c]\\ [{\mathrm{mes}}_2+c]\\ .\\ .\\ .\\ {[\mathrm{mes}}_n+c]\end{array}\right]$ ; MM ^tfor invertible matrix (M is for affecting efficiency function matrix);

4) consider practical application characteristic modification quadratic form error function

In above-mentioned thickness of coating error function, increased a cost function:

$C({\mathrm{\&alpha;}}_i)={\displaystyle \underset{i=1}{\overset{m}{\&Sum;}}{g}_{si}\&CenterDot;(q_i}+{\mathrm{\&alpha;}}_i{)}^2---\left(5\right)$

In formula, q _ibe the current reference position of i motor,

G _sifor waiting cost gain;

Coating for fear of other region of disturbing influence of extremum is controlled, and has increased a filter function in error function:

$F({\mathrm{\&alpha;}}_i)={\displaystyle \underset{i=1}{\overset{m}{\&Sum;}}{g}_{di}\&CenterDot;{\mathrm{\&alpha;}}_i^2}---\left(6\right)$

In formula, g _difor dynamic cost gain;

Finally be converted into and solve a quadratic programming problem and obtain required air knife aperture, (3), (5), (6) formula are integrated:

$J_2={{\displaystyle \underset{j=1}{\overset{n}{\&Sum;}}\left[me{s}_j?{\displaystyle \underset{i=1}{\overset{m}{\&Sum;}}{\mathrm{\&alpha;}}_i{M}_{ij}\text{+c}}\right]}}^2+{\displaystyle \underset{i=1}{\overset{m}{\&Sum;}}{g}_{si}}\&CenterDot;{(q_i+{\mathrm{\&alpha;}}_i)}^2+{\displaystyle \underset{i=1}{\overset{m}{\&Sum;}}{g}_{\mathrm{di}}\&CenterDot;{\&CenterDot;}^{}}{{\mathrm{\&alpha;}}_i}^2--\left(7\right)$

Separate this quadratic programming problem, obtain required air knife lip aperture.

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