An improved finite element meshing strategy for optimal control of chemical process

摘要

The finite element orthogonal collocation method is widely used in discrete differential algebraic equations (DAE), while the discretization strategy significantly affects the accuracy and efficiency of dynamic problem solving. A finite element meshing method with error estimation on noncollocation point is proposed. Firstly, Radau collocation points based Lagrange interpolation polynomial are used to discretize the differential equation. Then the noncollocation points are introduced to compute the error estimates of the state variables at noncollocation points. A finite element meshing method is introduced to refine the finite element, and finally develop an accurate discretization mesh for dynamic optimization problems. This approach provides a much easier solution to the DAE problem with fewer finite elements. At the same time, it can effectively control the scale of the discretized NLP problem and realize the exact solution of the corresponding dynamic problems. Through one classical control problems and a large scale reverse osmosis seawater desalination process, the numerical results show that the proposed approach is effective.