Representation and control of the cold rolling process through artificial neural networks via sensitivity factors

The mathematical modeling of the rolling process involves several parameters that may lead to non-linear equations of difficult analytical solution. Such is the case of Alexanderʹs model [Alexander, On the theory of rolling, Proc. R. Soc. Lond. A 326 (1972) 535–563], considered one of the most complete in the rolling theory. This model requires significant computational time, which prevents its application in on-line control and supervision systems. For this reason new and efficient forms to represent this kind of process are still necessary. The only requirement is that the new representations incorporate the qualitative behavior of the process, and that they can be used in the control system design. In this paper, the representation of the cold rolling process through Neural Networks, trained with data obtained by Alexanderʹs model, is presented. Two neural networks are trained to represent the rolling process and operation. For them, the quantitative and qualitative aspects of their behaviors are verified through simulation and via sensitivity equations. These equations are based on sensitivity factors obtained by differentiating the previously trained neural networks; and for different operation points, different equations can be obtained with low computational time. On the other hand, one of the capital issues in the controller design for rolling systems is the difficulty to measure the final thickness without time delays. The time delay is a consequence of the location of the output thickness sensor that is always placed to a certain distance ahead of the roll-gap region. The representation based in sensitivity factors has predictive characteristics that will be used by the control strategy. This predictive model permits to overcome the time delay that exists in such processes and can eliminate the thickness sensor, usually based on X-ray. This model works as a virtual sensor implemented via software. Besides, this paper presents a method to determinate the appropriate adjustment for thickness control considering three possible control parameters: roll gap, front and back tensions. The method considers, as the best control action, the one that demands the smallest adjustment. Simulation results show the viability of the proposed techniques and an example of the application to a single stand rolling mill is discussed.