A near-optimum controller for cold-rolling mills†

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Abstract
This paper presents a now approach to the optimum design of cold-rolling mills. The model takes advantage of slow variation of the winding reel radius and transforms an initially non-linear system into a parametric family of linear systems. In the first stage of design procedure the ‘ three-time-scale method ’ is applied and the model is decomposed in ‘ slow ’, ‘ basic ’ and ‘ fast’ subsystems. In this way the dimensionality of the model is considerably reduced. Then the state regulator method is applied to design an optimum control. The resulting Kiccati equation is simplified by an application of ‘ e-coupling ’ and ‘ radius-embedding ’ techniques. Using this method a control program is developed for the example of an existing three-stand continuous cold rolling mill. The numerical solution of the proposed feedback controller is given.

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