Algorithm research of the SQP method used in roll schedule calculation for Baosteel's 5m heavy plate

Loading distribution for heavy plate mill is to find optimal control solutions under the granted performance indicators and constraints including mill capacity and hypothesis of rolling models.The solutions are quite different for different performance indicators.In the article,the performance indicators and sequential quadratic programming(SQP for short below) methods employed in 5 000 mm heavy plate mill of BaoSteel are penetratingly analyzed.Generally,the SQP method is an effective and fast way to solve the nonlinear programming problems with small or medium scale constraints.Early in 1976,Han put forward the SQP method for the first time and Powell made it perfect and accomplished the algorithm in 1977.In fact, SQP method was to turn a nonlinear programming problem to a series of sub set of quadratic programming problems.In the algorithm,each iteration step is to solve one quadratic programming problem.The optimal solutions will be gradually approached after quadratic programming problems were totally solved.When solving the quadratic programming problem,the active set strategy were employed which turned the constrained quadratic programming problem to unconstrained quadratic programming problem.The active set strategy made the whole quadratic programming problem be solved by a least square problem.And finally, the matrix of the least square problem would be decomposed by Q matrix and R matrix.After Q matrix and R matrix were obtained,the optimal solutions would be finally found.For loading distribution,the performance indicators were composed by plate shape and draft of each pass.Plate shape is represented by rolling force gradually reduced pass by pass with a tunable factor.The mill capacity is another performance indicator represented by draft of each pass.For heavy plate mill,the mill capacity here is the motor moment. For heavy draft,the motor would be overloaded especially for the first several passes;for small draft,the motor would be loaded slightly.All these would not be permitted to happen when calculating the loading distribution.The mill capacity indicator made the loading of mill just be in the middle,not too much and not too low.In the article,these two performance indicators were analyzed in detail.Examples of loading distribution results with different performance indicators were given by the SQP method.When making changes to the performance indicators,there would be different solutions to the loading distribution.For the optimal solutions to the mill,there was supposed to make changes to the factors of the performance indicators or upgrade the accuracy of the mathematical models of the rolling process.