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Shape is an important quality index of cold rolling strip. Up to now, many problems in the shape control domain have not been solved satisfactorily, and a review on the research progress in the shape control domain can help to seek new breakthrough directions. In the past 10 years, researches and applications of shape control models, shape control means, shape detection technology, and shape control system have achieved significant progress. In the aspect of shape control models, the researches in the past improve the accuracy, speed and robustness of the models. The intelligentization of shape control models should be strengthened in the future. In the aspect of the shape control means, the researches in the past focus on the roll optimization, mill type selection, process optimization, local strip shape control, edge drop control, and so on. In the future, more attention should be paid to the coordination control of both strip shape and other quality indexes, and the refinement of control objective should be strengthened. In the aspects of shape detection technology and shape control system, some new types of shape detection meters and shape control systems are developed and have successfully industrial applications. In the future, the standardization of shape detection technology and shape control system should be promoted to solve the problem of compatibility. In general, the four expected development trends of shape control for cold rolling strip in the future are intelligentization, coordination, refinement, and standardization. The proposed research provides new breakthrough directions for improving shape quality.

Taper roll contours are widely applied in the single stand universal crown mill (UCM) to control the edge-drop of silicon steel, but bilateral symmetrical quarter buckles always happen in the last pass. It shows that the control on the strip profile and flatness has strong coupling nature. In this paper, the strip profile and the rolling parameters are obtained by simulations, and influences of the rolling parameters on the strip profile and flatness are revealed. The authors put forward a cantilever end model of the work roll influenced by the bending force, and analyze the rule of the influence the work roll taper curve on the additional pressure on the strip. Moreover, the rolling process characteristics of the UCM reversible rolling are expounded. One of the reasons for the coupling nature of the control on the strip profile and flatness is that, the roll taper curve increases the concentration and peak value of the additional pressure on the strip, and another is that the roll taper curve limits the lateral displacement of metal, increasing the longitudinal prolongation of metal. The optimization principle of the roll contour is determined based on the above influence mechanism.

A new strip shape control model is established to achieve the synchronizing control of complex shape defects, which can not only takes advantage of the mechanism model's strong analysis ability, but also combines with the fast online calculation function of intelligent model to reduce the poor efficiency regulation. Firstly, the dynamic target strip shape is expressed with the Legendre polynomial contained various components to describe all kinds of online shape targets, so it is easier to compare the shape control effect. Secondly, with the dynamic influence matrix and the efficiency function, some different control methods can be tightly combined in one regulation cycle to carry out the synchronous parallel control and the serial relay regulation, respectively. At the same time, by the DE‐ELM method, the intelligent shape control model can play an important role to improve the regulation efficiency of the online strip shape. On the other hand, the collaboration regulation model can make full use of all the effectiveness of each control methods according to their respective characteristics, so that the high precision of the strip shape control is able to be obtained.

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