Study Of Large-Scale Process Dynamic Optimization Approach

Interest in dynamic simulation and optimization has increased significantly during the last two decades. Real world process requires dynamic modeling. Application of dynamic optimization has remarkable effect on improvement of system efficiency, reduction of energy waste, reasonable use of resource and improvement of economy profit.The most common and efficient dynamic optimization approaches are sequential approach and simultaneous approach based on nonlinear programming. Sequential approach has less optimization variables, is a feasible path approach and can use existing process simulation software. But sequential approach cannot deal with problems with state variables path constraints. Simultaneous approach can deal with state variables path constraints and only solves model equations at optimal point, but it generates a large nonlinear programming problem which requires special decomposition technique. Recently a quasi-sequential approach which combines the characteristic of both approaches was presented. On one hand, quasi-sequential approach discretizes all variables. Control variables are discretized as piecewise constant and state variables are discretized with collocation method, and state variables path constraints are added on collocation points. On the other hand, quasi-sequential approach solves model equations at each iteration, eliminates model equations and state variables which makes nonlinear programming problem including only control variables and inequality constraints.Sequential quadratic programming for nonlinear programming has two methods to deal with inequality constraints, active set method and barrier method. Efficiency of active set method relies on number of active inequality constraints, and drops significantly with increasing of active inequality constraints while efficiency of barrier method is independent with active inequality constraints. Large-scale dynamic process optimization problem usually has many active inequality constraints, therefore in this paper an interior-point quasi-sequential approach was presented. Main work in this paper includes: 1 Detail approach structure was given. Interior-point quasi-sequential approach applies two layers strategy called simulation layer and optimization layer. In simulation layer dynamic problem is discretized and model equations are solved to eliminate state variables. In optimization layer an interior-point method is applied to solve nonlinear programming problem from simulation layer.2 Based on approach structure, a software package was coded to implement interior-point quasi-sequential approach with FORTRAN. Sparse structure of Jacobian matrix was considered to improve efficiency of package. Except for free third-party sparse linear equations solver, package was coded independently from any commercial package.3 The package was used to optimize different problems to test its efficiency. Firstly a two-dimension Rosenbrock problem was presented to compare the iteration path of different optimization approaches. Then a small-scale tubular reaction problem, a middle-scale CSTR problem and a large-scale distillation system optimal control problem were presented to validate the efficiency and stability of the package. Conclusion could be drawn that interior-point quasi-sequential approach can solve large-scale dynamic optimization problems, especially optimal control problems.The paper is concluded with a summary, existing problems and prospect of future researches.