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Optimal multi-variable flatness control for a cold rolling mill based on a box-constraint optimisation algorithm

As the flatness control system is a multi-variable control system, the key issue for high-precision flatness is the determination of the optimal adjustments of flatness actuators. In order to determine these the first step is the establishment of a multi-variable control model in the flatness control process, by which the actual flatness control problem has been reduced to a non-linear optimisation problem with box-constraints. Around this optimisation problem, characteristics and applicability of current optimisation algorithms were analysed. Based on the coordinate descent method, a new multi-variable optimisation algorithm with global convergence was proposed. In the algorithm, the problem was transformed into a series of univariate optimisations which could be solved by sequentially searching along coordinate directions. In order to make the objective function decrease rapidly, and ensure that each iteration are carried out within the feasible region, the accelerating step method is adopted to determine the iterative step size. A series of feasible points have been obtained through a series of iterations, which make the objective function decrease gradually until the optimal solution has been obtained. Finally, the algorithm has been tested by numerical experiments with production data of actual flatness control process, and applied to the 1450 mm tandem cold mill. Numerical experiments and application show that the proposed algorithm not only can satisfy the requirements of response speed, but also have a good accuracy, which can provide a reference for the realisation of high-precision flatness control processes of cold rolled strip.