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

Abstract

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.

Numerical Analysis of Intermediate Roll Shifting–Induced Rigidity Characteristics of UCM Cold Rolling Mill

“…For an ordinary four‐high mill, such as the four‐high High Crown (HC) mill, when the structure of the mill is fixed, the vertical and transverse rigidity of the mill remain basically unchanged. The six‐high Universal Crown Control mill (UCM mill) developed by Mitsubishi‐Hitachi Metals Machinery (now Primetals Technologies Japan Ltd., Tokyo, Japan), however, adds a pair of intermediate rolls that can be moved axially on the base of the four‐high HC mill, and the vertical and transverse rigidity of the mill changes as a result of the intermediate roll shifting (IRS) value by altering the elastic deflections of the roll‐stack and the flattening state between the rolls . The IRS has greatly improved the crown and flatness control range of the mill and has given the mill stronger shape control ability.…”

Numerical simulation analysis of the rolling process based on the particle swarm hybrid algorithm

“…In the Wolfe algorithm, in each iteration, the search direction always points to an extreme point [37][38][39]. When the iteration point approaches the direction of the optimal point, the moving direction of the objective function is kept orthogonal to the gradient of the objective function [40][41][42]. However, the best descent direction is not like this.…”

Comprehensive Analysis of Metal Deformation Law Based on Numerical Simulation of Cold Rolling Process

“…The load on the roll and the elastic deformation of the roll are discretized according to the same unit. By applying the concept of influence function in mathematical physics, the deformation caused at various points of the roll body is determined when applying unit force to each unit [18] . The deformation value of each unit is obtained by superimposing the deformation caused by each unit when all loads are applied.…”