Survey Of Model Prediction Control Method Of Secondary Cooling Water Flow In Continuous Casting Under Change Of Casting Speed Based On Transient Nonlinear Convection Heat Transfer Equation

The defects of slab,such as internal cracks,surface cracks,the formation of slab bulge and rhomboidity,are associated with the unreasonable,nonuniform water flow distribution in the secondary cooling zone.The secondary cooling of the continuous casting process is realized by the secondary cooling control system.Therefore,the secondary cooling control system should be adjusted to the cooling water flow dynamically to produce the qualified slab.Secondary cooling control system has three layers:the setting layer,the basic automation layer and the equipment layer.The setting layer gives the setting value of the water flow distribution in each section of the secondary cooling zone.The regulation controller in the basic automation layer adjusts the cooling water flow by referring to the setting value,and then the cooling water flow is sprayed on the surface of slab by the vapor mist cooling device in the equipment layer to control the boundary condition of slab.Only under the condition that the setting layer gives the appropriate setting value of cooling water flow,the regulation controller can track better.At present,the parameter water distribution method is used mostly for setting the value of the cooling water flow.However,when the casting speed is changed,the parameter water distribution method can not provide the suitable setting value of cooling water flow.How to give an appropriate setting value of cooling water flow is an urgent problem to be solved when the casting speed changes in the productive process of slab at present.Therefore,in order to give the appropriate setting value of cooling water flow when the casting speed changes,this paper based on the heat transfer model of slab presents a predictive control method of the secondary cooling water flow.The model predictive control(MPC)gives the setting value of cooling water flow within future limited time by rolling-horizontal optimization method.Therefore,based on the heat transfer model,this paper makes a deep research on MPC associated with the identification of undetermined parameters in the boundary conditions and the solution of the optimization problem.The main work of this paper is summarized as follows:Firstly,the two-dimensional transient nonlinear convection heat transfer equation can describe heat transfer process of the slab,the width of which is larger than the thickness.Therefore,this paper investigates the prediction control method of secondary cooling water flow based on this equation and gives the optimization model of MPC.The main research work includes the following two aspects:1.Because the measured temperature data have the measurement error and the identification of parameters belongs to the inverse problem,which can lead to the ill-posed.The Levenberg-Marquardt(LM)algorithm can overcome this ill-posed but the LM parameter is difficult to be selected.Therefore,this paper presents a Levenberg-Marquardt(LM)algorithm based on the measurement temperature error to identify the undetermined parameter.This paper proves that this LM algorithm is locally superlinear convergent.The experimental results of industrial production and nail shooting data show that the LM algorithm based on the measurement temperature error can significantly reduce the iteration number under the same stopping criteria and the accuracy of the corrected heat transfer model has been improved by 1.7%.2,Because the solving of this MPC optimization model is time-consuming and easy to non-convergence,this paper presents a corrected adaptive step quasi-Newton method.The selection of step in this algorithm takes into consideration of the influence of two factors:cost function and Hessian matrix.This step is directly proportional to cost function and inversely proportional to square root of the maximum eigenvalue of the Hessian matrix.This paper proves that the corrected adaptive step is bounded and converges to ?max?/(1-?).The experimental results of industrial production data shows that comparing to the parameter water distribution method,the MPC taking this method as optimizer can reduce the maximum standard deviation of mid-surface temperature average value of slab reduces from 6.04? to 2.03?.Secondly,the three-dimensional transient nonlinear convection heat transfer equation can describe the heat transfer process of billet,so this paper investigates the prediction control method of secondary cooling water flow based on this equation and gives the optimization model of MPC.The main research work includes the following two aspects:1.because the LM algorithm based on the measurement temperature error needs to know the measured error and calculate inverse matrix,this paper presents a Homotopy perturbation iterative algorithm to identify the undetermined parameters.This paper proves the local linear convergence of this method and the convergence rate is O(?1/(2v+1)).The simulation experimental results show that under the same stopping criteria,compared with Landweber algorithm,this algorithm reduces the iterative number obviously.2.To reduce the running time of three-dimensional heat transfer model,this paper presents an adaptive grid method to select the number of slice and time step based on the information of precision and time.The experimental results of industrial production data shows that the MPC taking this method as optimizer can reduce the optimal cycle of MPC from 25.5s to 4.63s,which is less than the control cycle 5s.Thirdly,the three-dimensional transient nonlinear convection heat transfer equation with the casting direction of heat transfer can describe heat transfer process of slab or billet under the large change of casting speed.Therefore,this paper investigates the prediction control method of secondary cooling water flow based on this equation and gives the optimization model of MPC.The main research work includes the following two aspects:1.In order to overcome the large noise in the measurement temperature data and improve the global convergence,this paper presents a weighted least-squares phased differential evolution algorithm based on thermometry residual.This method uses the thermometry residual as input,and then the weighted value is obtained by Kernel density function,finally phased differential evolution algorithm is used to solve optimization problem.Here the phased differential evolution algorithm divides the calculated process into complete evolution and elimination-regeneration stage,which can accelerate the convergence speed.The simulation experimental results show that this method can reduce the noise influence.2.Because the solving of optimization model of MPC,which is based on three-dimensional heat transfer model with the heat conduction in casting direction,is of high computation complexity and time-consuming,this paper presents an adaptive grid quasi-Newton parallel method.This method firstly applies adaptive grid approach to determine the number of slice and time step,and then computes the space grid node temperature parallel at the control time point of the MPC,finally the corrected adaptive step quasi-Newton approach is used to solve the optimization problem of MPC.The experimental results of industrial production data shows that the MPC taking this method as optimizer can reduce the optimal cycle of MPC from 77.19s to 1.74s.It is easy to see that this method can solve the conflict between control and optimal cycle.Finally,This paper designs a software system,which can identify the undermined parameters and predict the secondary cooling water flow.This software system integrates all the methods in this paper.Furthermore,this software system provides the convenience for identifying the undermined parameters and setting value of the secondary cooling water flow.