Model Predictive Control Method Of Secondary Cooling Water Flow In Continuous Casting Steel Based On GPU

Continuous casting steel plays an indispensable role in the process of steel production and the secondary cooling zones is a decisive part of continuous casting steel.The secondary cooling water affects whether the steel is solidified evenly and the slab quality.In the actual casting steel process,it is common to take the parameter water distribution method to set the cooling water flow.However,this method cannot deal with the unsteady condition such as the casting speed fluctuation.When the casting speed varies suddenly,the parameter water distribution method may cause slab crack,casting shrinkage,and some quality defects.Taking this reason,we adapt the model predictive control(MPC)method to guarantee the slab quality,which is an advanced computer control method.According to the difference of slab size,the solidification process of slab can be abstracted into two-dimensional and three-dimensional transient heat transfer equations.The biggest difference between the two is that the latter considers the heat transfer in the width of the slab and the diffusion heat transfer in the direction of the casting speed.This paper separately performs MPC dynamic optimization control for two-dimensional transient heat transfer equation and three-dimensional transient heat transfer equation.There are two problems in the MPC optimization process.One is that the accuracy of the heat transfer coefficient in the boundary conditions affects the accuracy of the calculation of the slab temperature.The commonly used empirical formula is not accurate enough.This paper identifies the comprehensive heat transfer coefficient through the inverse problem.Second,the heat transfer equation is a second-order partial differential nonlinear equation,which is computationally intensive,but rolling optimization is a real-time process for online calculating and the real-time requirements are relatively high.How to deal with the contradiction between the two is the focus of this paper.Regarding the above research questions,the work of this paper is as follows:(1)Based on the two-dimensional steady heat transfer equation,an inverse problem optimization model is established to identify the integrated heat transfer coefficient,and an evolutionary algorithm is used to solve the optimization model.Firstly,a two-dimensional steady-state heat transfer equation and boundary conditions are established.An inverse problem optimization model is established by taking the minimum square of the deviation between the measured temperature and the calculated surface temperature of the slab.Because the Particle Swarm Optimization(PSO)has the defects of being easy to get into the local optimization,the Social Learning Particle Swarm Optimization(SL-PSO)is proposed on the basis of PSO,and the SL-PSO algorithm is proved to be convergent.The experimental results of PSO and SL-PSO are compared to solve the inverse problem,and the results show that the difference between the calculated surface temperature and the measured temperature of the slab solved by the SL-PSO algorithm is lower than that of the PSO algorithm.The convergence curve indicates that the SL-PSO algorithm has a larg e search range in the early stage of evolution and a fast convergence speed in the late stage of evolution.(2)The MPC optimization model is established based on the two-dimensional dynamic heat transfer equation and the three-dimensional dynamic heat transfer equation,and is solved by numerical method.Firstly,the boundary conditions of the two-dimensional dynamic heat transfer equation of the MPC optimization model and the boundary conditions of the three-dimensional heat transfer equation of the MPC optimization model are analyzed separately for different assumptions.Then we take Augmented Lagrangian Relaxation method(ALR)to relax constraints,and solve the MPC optimization model by the gradient descent method of precise linear search step.Finally,the comparative experiment of MPC method and parameter water distribution method under two-dimensional heat transfer model and three-dimensional heat transfer model is carried out under the variation of casting speed.Experiments show that in the control of two-dimensional transient heat transfer equation,the average surface temperature fluctuation,the fluctuation of the secondary cooling water,the maximum deviation of the surface temperature and the reference temperature,and the stabilization time are better than the control method of the parameter water distribution method.In the control of the three-dimensional transient heat transfer equation,the comparison of the surface average temperature,the center temperature,the stabilization time,the maximum deviation of the surface temperature from the reference temperature,and the fluctuation of the secondary cooling water show that the MPC control effect is better than the parameter water distribution method.(3)A two-dimensional dynamic MPC optimization and three-dimensional dynamic MPC parallel optimization algorithm software package for controlling secondary cooling water in the continuous casting steel is designed based on GPU.The dynamic heat transfer equation decides the computational time is assuming,and scrolling optimization of MPC method is online,which is contradictive.While the GPU is good at handling the advantages of large-scale computing,so we use GPU to deal with the contradiction.Firstly,the parallel method and optimization ideas under the CUDA architecture are analyzed.Then we discuss the impact of block and thread size and shared memory on performance.Finally,the experimental results verify the efficiency of MPC method in CPU and GPU.Experiments show that the parallel time of solving the two-dimensional dynamic heat transfer equation is increased by about 16 times,and the parallel time of solving the three-dimensional dynamic heat transfer equation is increased by more than 10 times,which reduces the relative time of the MPC optimization.That is,the ratio of the program running time to the simulation time.