Multivariable flatness control system

Details Multivariable flatness control system Multivariable flatness control system

2001-08-17

2004-04-13

Picard, Leo (Department: 2125)

Data processing: generic control systems or specific application

Specific application, apparatus or process

Product assembly or manufacturing

Reexamination Certificate

active

06721620

ABSTRACT:

The invention relates to a method of measuring and/or controlling the flatness of a strip during rolling.
BACKGROUND OF THE INVENTION
During strip rolling, obtaining the optimum flatness and shape of the strip represents a particular problem. In this connection, it is advantageous that the rough strip already largely has the envisaged strip profile and runs centrally into the finishing roll train. In addition, the passes in the individual stands should be carried out in such a way that a respectively uniform strip extension over the entire strip width is obtained in all the stands. Furthermore, the aim is a reduction in the strip length (in the finished product) whose flatness lies outside the tolerance. This applies in particular to the head and tail of the strip.
For this purpose, it is known to determine the length distribution of the rolled metal sheet by means of a flatness measuring system (see FIG.
1
). The various types of errors—for example central waves, edge waves, quarter waves or flatness defects of higher order—are determined by means of mathematical analysis of the measured length distribution, in order specifically to employ the suitable actuating elements for error correction.
The length distribution is represented with the aid of a conventional polynomial:
p
(
x
)=a
0
+a
1
x+a
2
x
2
+a
3
x
3
+a
4
x
4
Here, edge waves on the left-hand or right-hand side of the strip are described by the coefficients a
1
and a
3
. The coefficients a
2
and a
4
describe either symmetrical central waves or symmetrical edge waves at the left-band and right-hand side of the strip. The coefficients a
1
and a
3
, and a
2
and a
4
therefore contain common information components.
Hitherto, at least in most practical implementations of flatness control, use has primarily been made of the coefficients (also referred to below as components) a
1
and a
2
.
To control the flatness on the finishing roll line, use is mostly made of the manipulated variables relating to working-roll bending in order to control the components a
2
and a
4
, and the hydraulic settings on the operator and drive sides (pivoting) to eliminate the error components a
1
and a
3
. For the purpose of control, therefore, the coefficients a
1
and a
3
are used as the controlled variable for the pivoting, and the coefficients a
2
and a
4
are used as the controlled variable for the bending.
In some rolling stands, the axial displacement of the working rolls is primarily used to preset the roll gap contour and only in some cases, within the control loop, is used in combination with bending to correct the quarter waves. Finally, selective multizone cooling of the working rolls can permit the flatness errors of higher order to be corrected. A control system of this type is disclosed, for example, by the German Patent Application DE 197 58 466 A1.
In each case, the manipulated variables are calculated by means of a setting of the rolling force and the bending force predefined by a setup calculation. The controllers used are known PI controllers but these are not able to take the dead times of the section into account explicitly. Consequently, a weak setting of the controller gains, in particular of the I component, has to be made, in order to avoid instabilities in the control loop.
This control system is not able to satisfy the increase in quality demands on flatness, since the flatness control reaches its intended curve only after a relatively long time. This results in the fact that, firstly it is necessary to tolerate a long strip length whose flatness lies outside the tolerance. Often, however, the intended curve is not reached at all, but only to an approximation, so that large edge and center waves can be produced.
Moreover, it is disadvantageous that a
0
, a
1
, a
2
, a
3
and a
4
exert mutual influence on one another, and the dead times are not taken into account, that is to say not compensated for. Furthermore, the actuating element characteristics (influencing functions) are calculated only once for each strip and are assumed to be constant, since iterative model equations are used for the calculation.
On the basis of the classical flatness control described previously, expansions to the classical control concept have already been proposed, in order to eliminate the existing disadvantages to some extent.
Breaking down the measured flatness in the direction of influencing functions which are not orthogonal to one another is described in Schneider, A.; Kern, P.; Steffens, M.: Model Supported Profile and Flatness Control Systems, Proc. of 49° Congresso Internaciona de Tecnologia Metalurgica e de Materials—International Conference, Oct. 9-14 1994, S{overscore (a)}o Paulo, Vol. 6, p. 49/60 und McDonald, I. R.; Mason, J. D.: Advances in flatness control technology, Proc. of the Conf. on the Control of Profile and Flatness, Mar. 25-27 1996, The Institute of Materials, Birmingham, p. 161/170. Improved results can be achieved by this method, but in the case of redundant and very similar manipulated variables, because of the poor conditioning of the system (poorly invertible systems), very large manipulated variables occur. This can result in very high stress levels.
In Grimble, M. J.; Fotakis, J.: The Design of Strip shape Control Systems for Sendzimir Mills, IEEE Trans. on Automatic Control 27 (1992) no. 3, p. 656/666 und Ringwood, J. V.: Shape Control Systems for Sendzimir Steel Mills, IEEE Trans. on Control Systems Technology 8 (2000) no. 1, p. 70/86., a flatness control system for Sendzimir rolling stands with orthogonal decomposition of the flatness values into Chebyshev polynomials is proposed, in order to improve the flatness control, but in this case, dead time compensation and manipulated variable restrictions are not taken into account. In this case, the manipulated variables are determined by means of a multivariable controller. The multivariable controller is not designed to be capable of on-line dynamic optimization.
Flatness control by means of an observer and classical state controller is presented in Hoshino, I.; Kimura, H.: Observer-based multivariable control of rolling mills, Preprints of the IFAC Workshop on Automation in Mining, Mineral and Metal Processing, Sep. 1-3 1998, Cologne, p. 251/256. An expansion to nonlinear models and dynamic optimization can be found in Pu, H.: Nern, H.-J.; Roemer, R.; Nour Eldin, H. A.; Kern, P.; Jelali, M.: State-observer design and verification towards developing an integrated flatness-thickness control system for the 20 roll sendzimir cluster mill, Proc. Intern. Conf. on Steel Rolling (Steel Rolling '98), Nov. 9-11 1998, The Iron and Steel Institute of Japan, Chiba, p. 124/29 und Pu, H.; Nern, H.-J.; Nour Eldin, H. A.; Jelali M.; Totz, O.; Kern, P.: The Hardware-in-Loop simulations and on-line tests of an integrated thickness and flatness control system for the 20 rolls sendzimir cold rolling mill, Proc. Intern. Conf. on Modelling of Metal Rolling Processes, Dec. 13-15 1999, London, p. 208/16. In the case of these solutions, however, the flatness is not broken down into orthogonal polynomials. Nor are the dead times compensated for in these approaches.
Improving the flatness control by compensating for the dead time by means of a Smith predictor is described in Soda, K.; Amanuma, Y.; Tsuchii, K.; Ohno, S.; N.: Improvement in Flatness Control Response for Tandem Cold Strip Mill, Proc. Intern. Conf. on Steel Rolling (Steel Rolling '98), Nov. 9-11 1998, The Iron and Steel Institute of Japan, Chiba, p. 760/765. In this case, the predictor calculates the control variables which occur in the first sampling step after the dead time has elapsed, and therefore compensates for the dead time. Flatness is broken down along the influencing functions. In the case of redundant and very similar manipulated variables, because of the poor conditioning of the system (poorly invertible systems), very large manipulated variables occur. As a result, the plant can be excessively stressed. A classical multivariable controller (PID controller) is in

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