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POINTWISE LINEAR QUADRATIC OPTIMAL CONTROL OF A TANDEM COLD ROLLING MILL John R. Pittner, PhD University of Pittsburgh, 2006 The tandem cold rolling of metal strip is a complex multivariable process whose control presents a significant engineering challenge. The present technology generally relies on a control structure wherein the interactive coupling between process variables is partially reduced by several single-input-single-output and single-input-multi-output control loops operating on certain variables to decompose the overall problem into several separate problems to attempt to allow independent adjustment of strip tension and thickness anywhere in the mill. However, while the existing systems generally have been successful in producing an acceptable product, their failure to completely counteract the effects of interactions between process variables has limited their capability for improvement in performance and in robustness to disturbances and uncertainties. Various techniques for improvement have been proposed and some have been implemented. Many of these techniques offer some improvements, but also have shortcomings. Therefore there is a need for a better approach. It is considered that the pointwise linear quadratic optimal control might fulfill this need. This dissertation investigates the theoretical and applied aspects of this technique for control of a tandem cold rolling mill using criteria based on practical applications. A mathematical model of the mill is developed from which nonlinear state space equations are derived. Using these equations, a pointwise linear quadratic optimal controller is developed, and its performance for variations in operating speed and product are confirmed by simulation. Robustness to disturbances and uncertainties is also confirmed by simulation. The results are compared with those using typical industry practice. |
