A NEW TOOL FOR SOLVING INDUSTRIAL CONTINUOUS OPTIMIZATION PROBLEMS

A numerical method is proposed to tackle the continuous optimal contro l problems involving industrial thermal processes. The latter are char acterized by their complex mathematical models. Formulated through var iational calculus using the Pontryagin maximum principle, the resultin g two-point boundary value problem is discretized with a Euler central differentiation scheme. Solution is obtained by the Newton-Raphson me thod, and Richardson extrapolation is used to increase accuracy and re fine the grid automatically as needed. The Jacobian matrix is evaluate d numerically. The program, named COMMIN, helps reduce considerably th e heavy mathematical development and the ensuing programming work, stu mbling blocks for process engineers faced with optimal control problem s. An example is worked out. This new method promises to open new poss ibilities for applications in an important class of engineering proble ms.