CN101758084B - Model self-adapting sheet shape prediction and control method - Google Patents

Abstract

The invention relates to a sheet shape control method for strip rolling. A model self-adapting sheet shape prediction and control method comprises the following steps: a sheet shape decomposition method and a sheet shape control model are given, and the input signals of the sheet shape control model include a rolling force and a crown of incoming material; then a sheet shape model which includes executing mechanism characteristics is obtained according to history sheet shape actual output data, the model is dynamically corrected according to real-time rolling parameters and corresponding actual sheet shape values, a correction model is used for accurately predicting the sheet shape and determining the optimal control quantity, and a feedback path, which removes transmission time-delay of strip steel between a frame and a measuring system, is established, thus carrying out regulation of a feedback controller in real time and ensuring rapid and dynamical sheet shape control. As the sheet shape control model is corrected in real time according to actual data, constantly changing actual conditions of the sheet shape model of a rolling mill are satisfied, thus predicting the sheet shape more accurately to increase the control accuracy of the sheet shape.

Description

The sheet shape prediction and control method of model adaptation

Technical field

The present invention relates to a kind of board-shape control method of board rolling, relate in particular to a kind of sheet shape prediction and control method of model adaptation.

Background technology

Developing rapidly of modern industry to being with steel production to have higher requirement.Thickness of slab and plate shape are two important indicators weighing strip quality; Thickness deviation on the belt steel rolling direction has obtained effective control at present; And the plate shape problem of band steel does not also obtain fine solution; More and more receive production firm and user's attention, its fine or not degree direct influence is to the lumber recovery and the market competitiveness of product, so the ups and downs that board-shape control method is studied for China's steel industry have great importance.

Because the exploitation of plate shape checkout gear, and control automatically and development of computer, the control of plate shape has developed into closed loop by simple open loop control of past and has controlled automatically.Present milling train all is based on general multinomial plate shape mostly and decomposes and conventional FEEDBACK CONTROL; But general multinomial resolution model can not be eliminated influencing each other and can not the corresponding correction component of each plate shape governor motion accurately be separated (or distribute) between each component.

Have, conventional feedback control structure is not considered delivery time of between last frame and plate shape measurement mechanism, certainly existing with steel again.In fact, the control of plate shape is the detection time lag system of a quasi-representative in the process control.If the feedback that control cycle greater than time delay, can make the size of next control cycle controlled quentity controlled variable control effect (output) by rolling phase adjacent band steel in the last control cycle decides, rather than is decided by the output quantity before the several Control cycle.When high-speed rolling, detect to postpone less than control cycle, so thereby the high-gain controller can realize the loop fast response obtain good plate shape.But; When low speed (acceleration and deceleration) is rolling, plate shape detect time delay maybe several times to plate shape control cycle, the size of next like this control cycle controlled quentity controlled variable is not the plate shape feedback signal decision by rolling phase adjacent band steel; But decide by the output board shape before the several Control cycle; If adopt the high-gain controller possibly cause the control system unstable, and adopt low ride gain can cause controlling insufficient strength, can not obtain the better controlling effect.

In recent years, the problem that how to improve strip shape quality to different milling trains has dropped into a large amount of research.Researchers explore from the angle of control thought and study plate shape control problem when seeking to set up more accurate system model.Literature search to prior art is found; People such as Pu were " Proc.Intern.Conf.on Steel Rolling " (iron and steel rolling 98 years international can collection of thesis) (1998; The 124--129 page or leaf) " the State-observerdesign and verification towards developing an integrated flatness-thickness controlsystem for the 20 roll sendzimir cluster mill " that deliver on (design of 20 roller sendzimir mill strip flatness and thickness control system mode observers and checking); This article extends to nonlinear model with routine observation device and state controller and has adopted the method for dynamic optimal; But this article does not accurately separate the corresponding correction component of each executing agency, and time-delay is not handled yet for plate shape measurement.People such as Ringwood were " IEEE Trans.onControl System Technology " (IEEE periodical control systems technology) (2000; The 8th phase; The 70-86 page or leaf) " the Shape control system for sendzimir Steel Mills " that delivers on; This article is decomposed into the Cherbyshev multinomial with plate shape value quadrature, but this article is not considered time lag and controlled quentity controlled variable constraint.People such as Jelali are in United States Patent (USP) (US 6721620B2) " Multi variable flatness control system "; Introduced plate shape forecast model; Handle the plate shape measurement time-delay through model prediction plate shape; Make plate shape control dynamically to carry out fast, but actual plate shape model is with the milling train operating mode, changes like the factors such as resistance of deformation of coefficient of friction between cooling characteristics, roll and the band steel of milling train and band steel.

Conventional feedback control structure is because the existence of band steel delivery time between last frame and plate shape measurement mechanism will inevitably influence the real-time that plate shape is regulated.Can eliminate this detection time lag based on the PREDICTIVE CONTROL of model, but basic requirement of this control method is an accurate model that needs the operation of rolling, and the actual operation of rolling is constantly to change.

Summary of the invention

The object of the present invention is to provide a kind of sheet shape prediction and control method of model adaptation; This forecast Control Algorithm is revised plate shape control model through real data in real time; Satisfy the actual conditions that milling train plate shape model constantly changes, thereby carry out the prediction of plate shape more exactly to improve the control accuracy of plate shape.

The present invention is achieved in that a kind of sheet shape prediction and control method of model adaptation, at first provides the plate shape control model that a kind of plate shape pattern decomposition method and a kind of input signal comprise roll-force and supplied materials convexity; The actual inputoutput data of plate shape through history obtains a plate shape model that contains executing agency's characteristic then; And constantly this model is carried out dynamic calibration according to real-time rolling parameter and corresponding actual plate shape value; Calibration model is used for accurately predicting plate shape and confirms optimum controlled quentity controlled variable; Set up one and removed the band steel and between frame and measuring system, transmit the feedback path of time lag, thereby carry out the adjusting of feedback controller in real time, making plate shape control can dynamically carry out fast; Concrete steps are:

The first, plate shape pattern is decomposed

Based on each sense channel actual measurement plate shape value on the strip width direction; Described sense channel is a discrete point; Obtain the plate shape value of band steel on five feature locations points on the strip width direction respectively; Said plate shape value is the percentage elongation along band steel length direction, and through five values being carried out each time characteristic component that computing obtains plate shape, the size of each component value is corresponding with positive and negative actual physics meaning with belt plate shape;

The second, plate shape control model

The input signal of plate shape control model does not include only the control variables of plate shape governor motion; Like bending roller force; Roller amount, roll shifting amount of inclining and the cooling of roll surface subregion; But also comprise roll-force and supplied materials convexity, and the output of plate shape model is each time characteristic component of plate shape, promptly plate shape pattern is decomposed each ordered coefficients of gained;

The 3rd, plate shape model adaptation

Plate shape model adaptation is that fingerboard shape model coefficient utilizes the least square recursive algorithm constantly to obtain to revise according to the up-to-date model input signal corresponding to certain section strip steel with actual measurement plate shape signal;

The 4th, plate shape PREDICTIVE CONTROL

Constantly this model is carried out dynamic calibration according to real-time rolling parameter and corresponding actual plate shape value; According to Model Measured input value prediction output board shape, set up one and removed the band steel transmits time lag between frame and measuring system feedback path through the model coefficient revised; Simultaneously, in optimal algorithm, be used for confirming optimum plate shape controlled quentity controlled variable through the model coefficient of revising;

The 5th, optimal control algorithm

The target of optimal control algorithm is to eliminate plate shape deviation; Controlled quentity controlled variable influence coefficient according to continuous correction; In controlled quentity controlled variable allowed band separately, minimize performance indications; Obtain one group of optimum control amount of eliminating plate shape deviation, coordinate each controlled quentity controlled variable with the mode of a system and realize plate shape control optimization.

The plate shape model coefficient correction of plate shape model adaptation can be divided into off-line identification and two steps of online correction carry out in said the 3rd step;

(1) off-line identification

The historical data relevant to the band steel actual plate shape of same size under the identical rolling condition once accomplished the original state that algorithm obtains plate shape model coefficient recursion by least square;

(2) online correction

According to plate shape model input value and each component of degree n n output valve of plate shape of the up-to-date actual measurement of band steel, model coefficient is constantly carried out online correction through the least square recursive algorithm.

The input of forecast model of the present invention also comprises supplied materials convexity and roll-force except comprising plate shape controlled quentity controlled variable.Because: flatness defect mainly is origin material section configuration and has not matching between year roll gap shape to cause that the control of plate shape adopts different executing agencies to change has the roll gap shape of carrying to make it to be complementary with the supplied materials section configuration.Roll-force generally is used to the THICKNESS CONTROL with steel, but it is a main plate shape influence factor.From the angle of milling train, plate shape model mainly is to be used for predicting the cross direction profiles in that milling train outlet band steel longitudinal extension rate under the state of carrying is arranged, so the input of forecast model of the present invention also comprises supplied materials convexity and roll-force.

The present invention proposes a kind of simple and practical plate shape pattern decomposition method and a plate shape control model that comprises plate shape controlled quentity controlled variable and roll-force and supplied materials convexity for input accordingly; Input and output signal according to reality is constantly revised plate shape model, realizes the accurate prediction of plate shape and the dynamic optimal control of plate shape.

The present invention revises plate shape control model through real data in real time; Satisfy the actual conditions that milling train plate shape model constantly changes; And show that by model prediction in the future plate shape output is used for carrying out clearly online adjusting; Set up one and removed the band steel transmits time lag between frame and measuring system effective feedback path; Guarantee the uniformity of whole coil of strip length direction upper outlet belt plate shape quality, for improving band steel lumber recovery and strip shape quality and guaranteeing that the stability and the reliability of the operation of rolling have good practical significance.

Description of drawings

Fig. 1 is a plate shape pattern decomposing schematic representation;

Fig. 2 is a plate shape model adaptation sketch map;

Fig. 3 is a plate shape PREDICTIVE CONTROL structured flowchart;

Fig. 4 is the model coefficient self adaptive flow;

Fig. 5 is the Model Predictive Control flow process.

The specific embodiment

Present embodiment provided detailed embodiment and process, but protection scope of the present invention is not limited to following embodiment being to implement under the prerequisite with technical scheme of the present invention.

The present invention will be described for milling train to the UCM (omnipotent convex rolling mill) of six rollers for present embodiment, and the type milling train has work roll bending, the intermediate calender rolls roller, and intermediate roll shifting, depress inclining, and plate shape such as roll surface subregion cooling is regulated executing agency.Below in conjunction with accompanying drawing and specific embodiment the present invention is described further.

Referring to Fig. 3, Fig. 3 is a plate shape PREDICTIVE CONTROL structured flowchart.A kind of sheet shape prediction and control method of model adaptation all decomposes Target Board shape and actual measurement plate shape by a kind of simple and practical plate shape pattern; The plate shape signal that the coefficient of plate shape model decomposes according to the process pattern of input signal and actual measurement constantly obtains to revise, and is used to predict plate shape and is used to minimize performance indications to confirm optimum controlled quentity controlled variable; The prediction plate shape signal gained difference that feedback actual measurement plate shape signal deducts through corresponding measurement time-delay is used for the compensation model error; Take all factors into consideration control variables constraints and minimize performance indications acquisition optimum control amount.

Specify below:

One, plate shape pattern decomposition method

Referring to Fig. 1; Fig. 1 is a plate shape pattern decomposing schematic representation; Pattern is decomposed the plate shape signal according to actual measurement; Obtain the percentage elongation (five characteristic point be respectively the strip width central point and be four points of q and e apart from transmission side and fore side Edge Distance respectively) of five characteristic points on the strip width direction, right back-pushed-type (1) computing obtains each time characteristic component of plate shape.

$F=\left[\begin{array}{c}{F}_0\\ F_1\\ F_2\\ F_3\\ F_4\end{array}\right]=\left[\begin{array}{c}\left[\underset{i=1}{\overset{n}{\mathrm{\Σ}}}F\left(x_i\right)\right]/n\\ F\left(x_{\mathrm{ed}}\right)-F\left(x_{\mathrm{ew}}\right)\\ F\left(x_c\right)-[F\left(x_{\mathrm{ed}}\right)+F\left(x_{\mathrm{ew}}\right)]/2\\ F\left(x_{\mathrm{qd}}\right)-F\left(x_{\mathrm{qw}}\right)\\ F\left(x_c\right)-[F\left(x_{\mathrm{qd}}\right)+F\left(x_{\mathrm{qw}}\right)]/2\end{array}\right]---\left(1\right)$

The physical significance of each time plate shape component is as shown in table 1

Table 1 plate shape pattern is decomposed the physical significance of each component of degree n n

Symbol	Plate shape component	Physical significance
			F 0	Constant term	The vertically average percentage elongation of band steel
F 1	One component of degree n n	F 1＞0, the monolateral unrestrained F of DS side 1＜0, the monolateral wave of WS side
			F 2	Quadratic component	F 2＞0, middle unrestrained F 2＜0, bilateral wave
F 3	Cubic component	F 3＞0, the one-sided rib wave of DS side F 3＜0, the one-sided rib wave of WS side
			F 4	Four component of degree n ns	F 4＞0, complex seas F in the limit 4＜0, bilateral rib wave

Wherein, constant term is relevant with belt steel thickness control, and is irrelevant with the control of plate shape, omits.

This plate shape pattern decomposition method, its explicit physical meaning with less several characteristic amount information, just both can more accurately, intactly be described out various flatness defects common in the actual production, can simplify plate shape control model again.

Two, plate shape specification of a model

In the plate shape model of present embodiment: be input as work roll bending power, intermediate calender rolls bending roller force, intermediate calender rolls shifting amount, depress inclining amount, roll-force and supplied materials convexity; Being output as each ordered coefficients of plate shape, also is that plate shape pattern is decomposed each ordered coefficients of gained.

The linearisation of plate shape model is represented as follows:

$\left[\begin{array}{c}{F}_1\\ F_2\\ F_3\\ F_4\end{array}\right]=\left[\begin{array}{c}{K}_{\mathrm{Fw}1}\\ K_{\mathrm{Fw}2}\\ K_{\mathrm{Fw}3}\\ K_{\mathrm{Fw}4}\end{array}\right]F_w+\left[\begin{array}{c}{K}_{\mathrm{Fi}1}\\ K_{\mathrm{Fi}2}\\ K_{\mathrm{Fi}3}\\ K_{\mathrm{Fi}4}\end{array}\right]F_i+\left[\begin{array}{c}{K}_{\mathrm{Imr}1}\\ K_{\mathrm{Imr}2}\\ K_{\mathrm{Imr}3}\\ K_{\mathrm{Imr}4}\end{array}\right]I_{\mathrm{mr}}+\left[\begin{array}{c}{K}_{F_{l}1}\\ K_{F_{l}2}\\ K_{F_{l}3}\\ K_{F_{l}4}\end{array}\right]F_l+\left[\begin{array}{c}{K}_{P1}\\ K_{P2}\\ K_{P3}\\ K_{P4}\end{array}\right]P_{\mathrm{rf}}$

$+\left[\begin{array}{cccc}{K}_{C11}& K_{C12}& K_{C13}& K_{C14}\\ K_{C21}& K_{C22}& K_{C23}& K_{C24}\\ K_{C31}& K_{C32}& K_{C33}& K_{C34}\\ K_{C41}& K_{C42}& K_{C43}& K_{C44}\end{array}\right]\left[\begin{array}{c}{C}_1\\ C_2\\ C_3\\ C_4\end{array}\right]+\left[\begin{array}{c}{d}_1\\ d_2\\ d_3\\ d_4\end{array}\right]---\left(2\right)$

Wherein

F ₁, F ₂, F ₃, F ₄---each component of degree n n of belt plate shape (glacing flatness)

F _w, F _i, I _Mr, F _l, P _Rf---work roll bending power, intermediate calender rolls bending roller force, intermediate calender rolls shifting amount, depress inclining amount and roll-force

C ₁, C ₂, C ₃, C ₄---each component of degree n n of frame inlet supplied materials convexity

d ₁, d ₂, d ₃, d ₄---constant term, relevant with band steel specifications parameter, milling train specifications parameter etc., can regard four influence coefficients as, adopt same procedure to confirm initial value with other influence coefficient, and revise in real time simultaneously.

For expressing more general situation, in plate shape model, consider the effect of roll surface subregion cooling, the expression formula of formula (2) can be expressed as formula (2 '):

$\left[\begin{array}{c}{F}_1\\ F_2\\ F_3\\ F_4\end{array}\right]=\left[\begin{array}{c}{K}_{\mathrm{Fw}1}\\ K_{\mathrm{Fw}2}\\ K_{\mathrm{Fw}3}\\ K_{\mathrm{Fw}4}\end{array}\right]F_w+\left[\begin{array}{c}{K}_{\mathrm{Fi}1}\\ K_{\mathrm{Fi}2}\\ K_{\mathrm{Fi}3}\\ K_{\mathrm{Fi}4}\end{array}\right]F_i+\left[\begin{array}{c}{K}_{\mathrm{Imr}1}\\ K_{\mathrm{Imr}2}\\ K_{\mathrm{Imr}3}\\ K_{\mathrm{Imr}4}\end{array}\right]I_{\mathrm{mr}}+\left[\begin{array}{cccc}{K}_{C11}& K_{C12}& K_{C13}& K_{C14}\\ K_{C21}& K_{C22}& K_{C23}& K_{C24}\\ K_{C31}& K_{C32}& K_{C33}& K_{C34}\\ K_{C41}& K_{C42}& K_{C43}& K_{C44}\end{array}\right]\left[\begin{array}{c}{C}_1\\ C_2\\ C_3\\ C_4\end{array}\right]$

$+\left[\begin{array}{c}{K}_{F_{l}1}\\ K_{F_{l}2}\\ K_{F_{l}3}\\ K_{F_{l}4}\end{array}\right]F_l+\left[\begin{array}{c}{K}_{P1}\\ K_{P2}\\ K_{P3}\\ K_{P4}\end{array}\right]P_{\mathrm{rf}}+\left[\begin{array}{cccc}{K}_{Q11}& K_{Q12}& \·\·\·& K_{Q1n}\\ K_{Q21}& K_{Q22}& \·\·\·& K_{Q2n}\\ K_{Q31}& K_{Q32}& \·\·\·& K_{Q3n}\\ K_{Q41}& K_{Q42}& \·\·\·& K_{Q4n}\end{array}\right]\left[\begin{array}{c}{Q}_1\\ Q_2\\ \·\\ \·\\ \·\\ Q_n\end{array}\right]+\left[\begin{array}{c}{d}_1\\ d_2\\ d_3\\ d_4\end{array}\right]---\left(2^{,}\right)$

Wherein, Q ₁, Q ₂... .., Q _n---the coolant rate of each section of roll surface subregion cooling nozzle.

Need to prove; Formula (2) and (2 ') are the universal expression formulas of plate shape forecast model, in the practical application, when model input quantity when influence or influence are very not little to certain plate shape component; The model coefficient that then starts with alphabetical K accordingly can be taken as zero, to reduce the amount of calculation of model algorithm.For example, the effect of working roll symmetry bending roller force does not have influence basically to plate shape one component of degree n n, and corresponding model coefficient is zero.In addition, more than the input/output variable of all plate shape models all to a certain section strip steel, could correctly reflect the interactively between each variable like this.

Three, plate shape model self-adapting method

Referring to Fig. 2; Fig. 2 is a plate shape model adaptation sketch map; Model adaptation is that fingerboard shape model coefficient utilizes least-squares algorithm constantly to obtain to revise according to the input signal corresponding to certain section strip steel with actual measurement plate shape signal; The coefficient self adaptive flow can be simply referring to Fig. 4, simply can be divided into off-line identification and two steps of online correction to carry out.

(1) off-line identification

To the band steel actual plate shape historical data of same size under the identical rolling condition, the decomposition method of being introduced by formula (1) obtains each component of degree n n value of plate shape.For the represented plate shape model of formula (2); We establish two vector x (k) and

x (k) is the corresponding plate shape model input quantity of k section strip steel, and is each model coefficient corresponding to plate shape one component of degree n n:

$\left\{\begin{array}{c}x\left(k\right)={\left[\begin{array}{cccccccccc}{F}_w\left(k\right)& F_i\left(k\right)& I_{\mathrm{mr}}\left(k\right)& F_l\left(k\right)& P_{\mathrm{rf}}\left(k\right)& C_1\left(k\right)& C_2\left(k\right)& C_3\left(k\right)& C_4\left(k\right)& 1\end{array}\right]}^T\\ {\widehat{\mathrm{\θ}}}_1={\left[\begin{array}{cccccccccc}{K}_{\mathrm{Fw}1}& K_{\mathrm{Fi}1}& K_{\mathrm{Imr}1}& K_{\mathrm{Fl}1}& K_{P1}& K_{C11}& K_{C12}& K_{C13}& K_{C14}& d_1\end{array}\right]}^T\end{array}\right.$

(3)

Like this, plate shape one component of degree n n output valve is expressed as F ₁(k), can be described below by least square method

$F_1\left(k\right)=x^T\left(k\right){\widehat{\mathrm{\θ}}}_1+n\left(k\right)---\left(4\right)$

Wherein, n (k) is zero random noise for average.

Rolling same size band steel can get N under identical rolling condition ₀Group model input value x and output board shape value F ₁, form regression matrix respectively

With

Then

With

Expression formula respectively as follows:

$\left\{\begin{array}{c}{X}_{N_0}=\left[\begin{array}{cccccccccc}{F}_w\left(1\right)& F_i\left(1\right)& I_{\mathrm{mr}}\left(1\right)& F_l\left(1\right)& P_{\mathrm{rf}}\left(1\right)& C_1\left(1\right)& C_2\left(1\right)& C_3\left(1\right)& C_4\left(1\right)& 1\\ F_w\left(2\right)& F_i\left(2\right)& I_{\mathrm{mr}}\left(2\right)& F_l\left(2\right)& P_{\mathrm{rf}}\left(2\right)& C_1\left(2\right)& C_2\left(2\right)& C_{3l}\left(2\right)& C_4\left(2\right)& 1\\ .& .& .& .& .& .& .& .& .& .\\ .& .& .& .& .& .& .& .& .& .\\ .& .& .& .& .& .& .& .& .& .\\ F_w\left(N_0\right)& F_i\left(N_0\right)& I_{\mathrm{mr}}\left(N_0\right)& F_l\left(N_0\right)& P_{\mathrm{rf}}\left(N_0\right)& C_1\left(N_0\right)& C_2\left(N_0\right)& C_3\left(N_0\right)& C_4\left(N_0\right)& 1\end{array}\right]\\ Y_{N_0}={\left[\begin{array}{cccc}{F}_1\left(1\right)& F_1\left(2\right)& ...& F_1\left(N_0\right)\end{array}\right]}^T\end{array}\right.$

(5)

The original state of plate shape model coefficient can be tried to achieve by once accomplishing algorithm by following formula in advance:

$\left\{\begin{array}{c}P\left(0\right)={\left[X_{N_0}^T{X}_{N_0}\right]}^{-1}\\ {\widehat{\mathrm{\θ}}}_1\left(0\right)=P\left(0\right)X_{N_0}^T{Y}_{N_0}\end{array}\right.---\left(6\right)$

Wherein, data length N ₀Generally should more than or equal to

Dimension, but in order to reduce amount of calculation, N ₀Should not obtain too big.

(2) online correction

Model input value x (k) and plate shape one component of degree n n output valve F for the actual measurement of k section strip steel ₁(k), the coefficient modification method can adopt following least square recursive algorithm to realize.

$\left\{\begin{array}{c}{\widehat{\mathrm{\θ}}}_1\left(k\right)={\widehat{\mathrm{\θ}}}_1(k-1)+K\left(k\right)[F_1\left(k\right)-x^T\left(k\right){\widehat{\mathrm{\θ}}}_1(k-1)]\\ K\left(k\right)=P(k-1)x\left(k\right){\left[x^T\left(k\right)P(k-1)x\left(k\right)\right]}^{-1}\\ P\left(k\right)=[I-K\left(k\right)x^T\left(k\right)]P(k-1)\end{array}\right.---\left(7\right)$

According to identical method, can model coefficient

and

corresponding to other component of plate shape be revised simultaneously.Regularly the numerical value to P and

averages; And preserve; When rolling same size coil of strip, can directly read original state as the least square recursion.

Four, plate shape PREDICTIVE CONTROL explanation

Referring to Fig. 3; Fig. 3 is a plate shape PREDICTIVE CONTROL structured flowchart; The actual inputoutput data of plate shape through history obtains a plate shape model that contains executing agency's characteristic; Constantly this model is carried out dynamic calibration according to real-time rolling parameter and corresponding actual plate shape value, predict output board shape according to the Model Measured input value through the model coefficient of revising; Simultaneously, in optimal algorithm, be used for confirming optimum plate shape controlled quentity controlled variable through the model coefficient of revising.Its control flow can be referring to Fig. 5.

Wherein, several key variables specify as follows:

(1) actual measurement plate shape has two purposes after pattern is decomposed:

1. with the measured value of the plate shape model input signal of corresponding section strip steel model coefficient is revised;

2. deduct prediction plate shape, gained predicated error F through time lag _eBe used for the compensation model error.

(2) through the model coefficient of revising two purposes are arranged also:

1. predict output board shape F by the measured value of plate shape model input signal _p

2. be used for dynamic optimal ground and confirm each plate shape controlled quentity controlled variable.

(3) the optimum control amount of controller output has three purposes:

1. being used for plate shape controls in real time;

2. roll-force and supplied materials convex value, measured value and the actual plate shape with corresponding section strip steel is worth the model coefficient correction;

3. with the roll-force and the supplied materials convex value measured value of corresponding section strip steel plate shape value is predicted.

Five, confirm the algorithm of optimum control amount

Plate shape setting value F _r, deduct model output error F _e, deduct prediction plate shape F again _p, obtain plate shape deviation delta F.The target of optimal control algorithm is to eliminate this plate shape deviation, and the specific algorithm flow process is following:

(1) relevant with plate shape controlled quentity controlled variable model coefficient can constitute matrix K, promptly

$\left[\begin{array}{cccc}{K}_{\mathrm{Fw}1}& K_{\mathrm{Fi}1}& K_{\mathrm{Imr}1}& K_{\mathrm{Fl}1}\\ K_{\mathrm{Fw}2}& K_{\mathrm{Fi}2}& K_{\mathrm{Imr}2}& K_{\mathrm{Fl}2}\\ K_{\mathrm{Fw}3}& K_{\mathrm{Fi}3}& K_{\mathrm{Imr}3}& K_{\mathrm{Fl}3}\\ K_{\mathrm{Fw}4}& K_{\mathrm{Fi}4}& K_{\mathrm{Imr}4}& K_{\mathrm{Fl}4}\end{array}\right]---\left(8\right)$

(2) each element in the matrix K is represented that by its ranks position, place then optimal problem can be described as: in controlled quentity controlled variable allowed band separately, seek optimum controlled quentity controlled variable combination and minimize performance indications

$J=\underset{n=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\α}}_n({\mathrm{\Δ}{F}_n-\left[\begin{array}{cccc}{K}_{n,1}& K_{n,2}& K_{n,3}& K_{n,4}\end{array}\right]\left[\begin{array}{c}\mathrm{\Δ}{F}_w\\ \mathrm{\Δ}{F}_i\\ \mathrm{\Δ}{I}_{\mathrm{mr}}\\ \mathrm{\Δ}{F}_l\end{array}\right])}^2---\left(9\right)$

Wherein, Δ F _nBe each component of degree n n error of plate shape, Δ F _w, Δ F _i, Δ I _Mr, Δ F _lBe the optimum control amount increment that needs are confirmed, α _nBe each component of degree n n shared weight coefficient in performance indications.

(3) performance indications J is respectively to Δ F _w, Δ F _i, Δ I _Mr, Δ F _lAsk local derviation, and make that each derivative expression formula is zero, can get following matrix equation

$\left[\begin{array}{cccc}\underset{n=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\α}}_n{K}_{n,1}^2& \underset{n=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\α}}_n{K}_{n,1}{K}_{n,2}& \underset{n=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\α}}_n{K}_{n,1}{K}_{n,3}& \underset{n=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\α}}_n{K}_{n,1}{K}_{n,4}\\ \underset{n=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\α}}_n{K}_{n,1}{K}_{n,2}& \underset{n=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\α}}_n{K}_{n,2}^2& \underset{n=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\α}}_n{K}_{n,2}{K}_{n,3}& \underset{n=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\α}}_n{K}_{n,2}{K}_{n,4}\\ \underset{n=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\α}}_n{K}_{n,1}{K}_{n,3}& \underset{n=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\α}}_n{K}_{n,2}{K}_{n,3}& \underset{n=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\α}}_n{K}_{n,3}^2& \underset{n=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\α}}_n{K}_{n,3}{K}_{n,4}\\ \underset{n=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\α}}_n{K}_{n,1}{K}_{n,4}& \underset{n=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\α}}_n{K}_{n,2}{K}_{n,4}& \underset{n=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\α}}_n{K}_{n,3}{K}_{n,4}& \underset{n=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\α}}_n{K}_{n,4}^2\end{array}\right]\left[\begin{array}{c}\mathrm{\Δ}{F}_w\\ \mathrm{\Δ}{F}_i\\ \mathrm{\Δ}{I}_{\mathrm{mr}}\\ \mathrm{\Δ}{F}_l\end{array}\right]=\left[\begin{array}{c}\underset{n=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\α}}_n{K}_{n,1}\mathrm{\Δ}{F}_n\\ \underset{n=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\α}}_n{K}_{n,2}\mathrm{\Δ}{F}_n\\ \underset{n=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\α}}_n{K}_{n,3}\mathrm{\Δ}{F}_n\\ \underset{n=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\α}}_n{K}_{n,4}\mathrm{\Δ}{F}_n\end{array}\right]$

(10)

Like this, optimization problem just is summed up as finds the solution above matrix equation, merges into augmented matrix by following formula two coefficient matrixes.Gained diagonal of a matrix element is confirmed as pivot, be transformed to the triangle battle array through the elimination, back substitution is found the solution and can be got each optimum control amount.

(4) exceed its allowed band if verify certain controlled quentity controlled variable; Then get its corresponding maximum or minimum of a value; And deduct by the caused plate shape of this control increment variable quantity at each time of plate shape error component; Then the residue controlled quentity controlled variable being carried out optimization as stated above again and found the solution, is minimum optimum control amount in allowed band separately until obtaining making performance indications, and residue plate shape error can further adopt the roll surface subregion to cool off to eliminate.

The sheet shape prediction and control method of model adaptation of the present invention can be summarized as, and at first provides the plate shape control model that a kind of plate shape pattern decomposition method and a kind of input signal comprise roll-force and supplied materials convexity; The actual inputoutput data of plate shape through history obtains a plate shape model that contains executing agency's characteristic then; And constantly this model is carried out dynamic calibration according to real-time rolling parameter and corresponding actual plate shape value; Calibration model is used for accurately predicting plate shape and confirms optimum controlled quentity controlled variable; Set up one and removed the band steel transmits time lag between frame and measuring system feedback path; Thereby carry out the adjusting of feedback controller in real time, make the control of plate shape dynamically to carry out fast, and the operation of rolling also can be more stable.

Complex chart 4 and Fig. 5, the enforcement of plate shape PREDICTIVE CONTROL can be divided into following several main processes:

(1) the belt plate shape measured value under same size and the rolling condition is handled, the plate shape measurement value is decomposed by the plate shape pattern that the present invention introduced;

(2), make up N by plate shape controlled quentity controlled variable, roll-force and supplied materials convex value and plate shape measurement decomposition value corresponding to this section strip steel ₀The group data are right;

(3) obtain the original state of least square recursion according to formula (6), if any the self adaptation coil of strip data of same size and rolling condition, directly the reading and saving value is as original state;

(4) read the plate shape setting value F of current volume _r

(5) plate shape measurement value F _mObtain actual plate shape value F through the pattern decomposition _a

(6) according to formula (7), by actual plate shape value F _aWith plate shape controlled quentity controlled variable, roll-force and the horizontal convex value of supplied materials, the coefficient of plate shape model is revised corresponding to this section strip steel;

(7) according to revised model coefficient, by the roll-force and the horizontal convex value prediction of the corresponding section strip steel supplied materials plate shape F of plate shape controlled quentity controlled variable and actual measurement _p

(8) actual plate shape value F _a, deduct prediction plate shape F through corresponding measurement time-delay _p, the gained difference is model output error F _e

(9) plate shape setting value F _r, deduct model output error F _e, deduct prediction plate shape F again _p, obtain plate shape deviation delta F;

(10) according to revised model coefficient, consider the control variables constraint, confirm that by optimal algorithm optimum controlled quentity controlled variable is used for real-time plate shape control.

The present invention revises plate shape control model through real data in real time; Satisfy the actual conditions that milling train plate shape model constantly changes; And be used for carrying out clearly online adjusting by model prediction plate shape output; Set up one and removed the band steel transmits time lag between frame and measuring system effective feedback path; Guarantee the uniformity of whole coil of strip length direction upper outlet belt plate shape quality, for improving band steel lumber recovery and strip shape quality and guaranteeing that the stability and the reliability of the operation of rolling have good practical significance.

Claims (2)

1. the sheet shape prediction and control method of a model adaptation is characterized in that: at first provide the plate shape control model that a kind of plate shape pattern decomposition method and a kind of input signal comprise roll-force and supplied materials convexity; The actual inputoutput data of plate shape through history obtains a plate shape model that contains executing agency's characteristic then; And constantly this model is carried out dynamic calibration according to real-time rolling parameter and corresponding actual plate shape value; Calibration model is used for accurately predicting plate shape and confirms optimum controlled quentity controlled variable; Set up one and removed the band steel and between frame and measuring system, transmit the feedback path of time lag, thereby carry out the adjusting of feedback controller in real time, making plate shape control can dynamically carry out fast; Specific as follows:

The first, plate shape pattern is decomposed

According to each sense channel actual measurement plate shape value on the strip width direction; Described sense channel is a discrete point; Obtain the plate shape value of band steel on five feature locations points on the strip width direction respectively; Said plate shape value is the percentage elongation along band steel length direction, through said five plate shape values are carried out computing obtain plate shape once to four characteristic components, be shown below:

$F=\left[\begin{array}{c}{F}_0\\ F_1\\ F_2\\ F_3\\ F_4\end{array}\right]=\left[\begin{array}{c}\left[\underset{i=1}{\overset{n}{\mathrm{\Σ}}}F\left(x_i\right)\right]/n\\ F\left(x_{\mathrm{ed}}\right)-F\left(x_{\mathrm{ew}}\right)\\ F\left(x_c\right)-[F\left(x_{\mathrm{ed}}\right)+F\left(x_{\mathrm{ew}}\right)]/2\\ F\left(x_{\mathrm{qd}}\right)-F\left(x_{\mathrm{qw}}\right)\\ F\left(x_c\right)-[F\left(x_{\mathrm{qd}}\right)+F\left(x_{\mathrm{qw}}\right)]/2\end{array}\right]$

In the formula:

F ₀---the constant term of plate shape, the vertically average percentage elongation of expression band steel;

F ₁---a component of degree n n of plate shape, F ₁＞0, the monolateral wave of DS side, F ₁＜0, the monolateral wave of WS side;

F ₂---the quadratic component of plate shape, F ₂＞0, middle wave, F ₂＜0, bilateral wave;

F ₃---the cubic component of plate shape, F ₃＞0, the one-sided rib wave of DS side, F ₃＜0, the one-sided rib wave of WS side;

F ₄---four component of degree n ns of plate shape, F ₄＞0, complex seas in the limit, F ₄＜0, bilateral rib wave;

F (x _i)---x on the strip width direction _iThe plate shape value at some place,

N---plate shape sense channel sum,

F (x _Ed)---also be the plate shape value that DS lateral edges distance is ordered for e apart from transmission side on the strip width direction,

F (x _Qd)---also be the plate shape value that DS lateral edges distance is ordered for q apart from transmission side on the strip width direction,

F (x _c)---the plate shape value of central point on the strip width direction,

F (x _Qw)---also be the plate shape value that WS lateral edges distance is ordered for q apart from fore side on the strip width direction,

F (x _Ew)---also be the plate shape value that WS lateral edges distance is ordered for e apart from fore side on the strip width direction;

The second, plate shape control model

The input signal of plate shape control model comprises the bending roller force of plate shape governor motion, the roller amount of inclining, roll shifting amount and the cooling of roll surface subregion, also comprises roll-force and supplied materials convexity, and the output of plate shape model is each time characteristic component of plate shape;

The 3rd, plate shape model adaptation

Plate shape model adaptation is that fingerboard shape model coefficient utilizes the least square recursive algorithm constantly to obtain to revise according to the up-to-date model input signal corresponding to certain section strip steel with actual measurement plate shape signal;

The 4th, plate shape PREDICTIVE CONTROL

Constantly this model is carried out dynamic calibration according to real-time rolling parameter and corresponding actual plate shape value; According to Model Measured input value prediction output board shape, set up one and removed the band steel transmits time lag between frame and measuring system feedback path through the model coefficient revised; Simultaneously, in optimal algorithm, be used for confirming optimum plate shape controlled quentity controlled variable through the model coefficient of revising;

The 5th, optimal control algorithm

The target of optimal control algorithm is to eliminate plate shape deviation; Controlled quentity controlled variable influence coefficient according to continuous correction; In controlled quentity controlled variable allowed band separately, minimize performance indications; Obtain one group of optimum control amount of eliminating plate shape deviation, coordinate each controlled quentity controlled variable with the mode of a system and realize plate shape control optimization.

2. the sheet shape prediction and control method of model adaptation according to claim 1 is characterized in that: the plate shape model coefficient correction of plate shape model adaptation can be divided into off-line identification and two steps of online correction carry out in said the 3rd step;

(1) off-line identification

The historical data relevant to the band steel actual plate shape of same size under the identical rolling condition once accomplished the original state that algorithm obtains plate shape model coefficient recursion by least square;

(2) online correction

According to plate shape model input value and each component of degree n n output valve of plate shape of the up-to-date actual measurement of band steel, model coefficient is constantly carried out online correction through the least square recursive algorithm.

Images