The invention relates to a method of measuring and/or controlling the flatness of a strip during rolling.
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 errorsxe2x80x94for example central waves, edge waves, quarter waves or flatness defects of higher orderxe2x80x94are 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)=a0+a1x+a2x2+a3x3+a4x4
Here, edge waves on the left-hand or right-hand side of the strip are described by the coefficients a1 and a3. The coefficients a2 and a4 describe either symmetrical central waves or symmetrical edge waves at the left-band and right-hand side of the strip. The coefficients a1 and a3, and a2 and a4 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) a1 and a2.
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 a2 and a4, and the hydraulic settings on the operator and drive sides (pivoting) to eliminate the error components a1 and a3. For the purpose of control, therefore, the coefficients a1 and a3 are used as the controlled variable for the pivoting, and the coefficients a2 and a4 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 a0, a1, a2, a3 and a4 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 49xc2x0 Congresso Internaciona de Tecnologia Metalurgica e de Materialsxe2x80x94International 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 integrated in the Smith predictor. There is no dynamic optimization with prediction of the course of the controlled variable going beyond the dead time. Here, a controlled variable is predicted which occurs directly in the first sampling step after the dead time.
In many conventional flatness measuring systems, measured values are supplied at predetermined sample times. When time-discrete controllers are used, for example PI controllers, it is assumed that the sampling time is constant. If the sampling time is not kept constant the control result is impaired or the control loop even becomes unstable.
Accordingly, the invention is based on the object of providing a method which permits the measurement and/or control of the flatness of a strip during rolling in a reliable manner. In addition, an apparatus for implementing this method is to be provided.
This object is achieved by a method of measuring and/or controlling the flatness of a strip during rolling, wherein the measured values are broken down into independent components, an apparatus for measuring and/or controlling the flatness of a strip for implementing the method and having a measuring system for registering the flatness deviation (measured values and a unit for breaking down the measured values into independent components; and a flatness control system that includes registering the flatness of the strip with a measuring system; breaking down the flatness errors (length distribution) into orthogonal components; an explicit on-line-capable profile and flatness model, which takes into account all the variables involved in the rolling process; an explicit on-line capable model, which calculates set points for the flatness control system; a multi-variable controller to control the flatness of the strip; a prediction of the controlled variables (flatness values), which is incorporated into the dynamic optimization, which goes beyond dead time; and interference variable feed forward, which takes account of the properties of the incoming strip, the variation in rolling force and thermal chambering. Advantageous developments form the subject of the subclaims.
Here, the invention is based on the idea of improving the flatness control according to the prior art by means of an orthogonal, model-supported multivariable flatness control system with the flatness being registered and broken down into orthogonal components. The multivariable flatness control system preferably includes determination of the manipulated variables by means of dynamic on-line optimization, taking manipulated variable restrictions into account, and prediction of the controlled variables (flatness values), which are incorporated into dynamic optimization. The prediction of the controlled variables goes beyond the dead time. In the model-based predictive approach, prediction of the controlled variables from the first sampling step after the dead time as far as a prediction horizon is used. By this means, at every time, optimal manipulated variables are calculated, even if the time constants of the individual actuating elements are considerably different. This information is preferably likewise incorporated into the dynamic optimization.
The components can advantageously be compared with values which are supplied by an on-line-capable model of the plant. The resulting difference can be used as controlled variable and subsequently compared with the intended flatness curve broken down into independent components. The resulting control difference can be fed to a multivariable controller via an optimal decoupling means.
In the method according to the invention, it is particularly advantageous that the dead time can be taken into account by the internal model control (IMC) approach. As a result, the control time can be shortened and the strip length which lies outside the tolerance range can be reduced.
By breaking down the flatness measured values into independent components, it is additionally possible for the respective flatness errors to be clearly identified which permits a considerable improvement in the quality of control.
Likewise, it is an advantage that, by means of the orthogonal breakdown of the flatness, the number and form of the necessary manipulated variables can be determined.
The method according to the invention further permits the change in the rolling force, the thermal cambering and the incoming strip properties to be taken into account during each time step by means of interference variable feedforward.
Furthermore, it has the advantage that it permits the nonlinearities of the plant to be taken into account on-line explicitly by means of an on-line-capable model of the plant which is in parallel with the section.
The method according to the invention and the associated system advantageously take into account flatness measuring systems with time variant sampling time by means of an IMC (Internal Model Control) approach with an event generator and event-triggered sample-and-hold elements.
In an advantageous embodiment, the multivariable flatness control system according to the invention comprises the following steps:
registering the flatness of the strip with a measuring system,
breaking down the flatness errors (length distribution) into orthogonal components,
an explicit, linear or nonlinear on-line-capable profile and flatness model, which takes into account all the significant variables involved in the rolling process (bending, pivoting, displacement, thermal cambering and so on);
an explicit on-line-capable model which calculates setpoints for the flatness control system,
a multivariable controller for controlling the flatness of the strip
a prediction of the controlled variables (flatness values), which is incorporated into the dynamic optimization, which goes beyond the dead time,
interference variable feedforward, which takes account of the properties of the incoming strip, the variation in rolling force and thermal cambering, and
an event-triggered sampling system for taking account of flatness measuring systems with variable sampling time.
The components can advantageously be broken down by using orthogonal polynomials, for example with the aid of Chebyshev polynomials or Gram polynomials, as described in W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery: Numerical Recipes in C, Cambridge University Press (1992) oder A. Ralston, P. Rabinowitz: A first course in numerical analysis, International series in pure applied mathematics, McGraw-Hill (1978).
The flatness of the outgoing metal sheet can be influenced by bending, pivoting and axial displacement of the rolls and by selective multizone cooling. The individual manipulated variables can be determined from the above-described control difference with the aid of a multivariable controller. At the same time, the influence of the rolling force, the incoming strip properties and thermal cambering can be compensated for by means of interference variable feedforward.