Simulation and optimization in technological systems with distributed parameters

The article presents a method of simulation and optimal control for rectification plants, containing technological furnaces and rectification columns. This complicated system is shown as a system with distributed parameters, as for static and dynamic modes simulation a mathematical formalism of differential equations in partial differential was applied. As a rule scientific literature deals with operation modes outcomes for single plants. Due to complicated mathematical formalism and computation investigations dealing with a number of objects with distributed parameters are infrequently. The optimal control tasks solutions for complicated plants are poorly shown in scientific literature A phenomenological approach was applied for mathematical model of heat processes in technological furnaces and separation processes in multicomponent mixtures for rectification columns. The model contains partial differential equitations for heat- and mass-exchange processes and hydrodynamics for flue gas flows in technological furnace and mass-exchange equitations for rectification column. Described processes occurs with recirculation flow interaction and heat-exchange processes' boundary conditions for rectification columns are described in ordinary derivatives. The conditions are given at the opposite ends of the plant. The optimal control modes solutions were formulated an optimal control task for desired product and necessary conditions for optimality. Due control functions are included in the main boundary derivatives, control variations in the range and on the boundary are dependent, this works on dual problem structure. Arguments of variational calculus was applied. Necessary conditions for optimality are containing original boundary-value problem conjugated relatively to the Lagrangians. Original and boundary tasks solution determines optimal control and technological processes parameters. The article gives numerical outcomes with control of flow of raw materials in debutanizer plant for sulfuric acid alkylation of isobutane with butenes. A numeric algorithm was worked out. The peculiarity of the algorithm is solving a boundary conditions tasks for some parameters at the opposite ends of the area. Moreover Lagrangians for conjugated system are given at a finite time. Optimal characteristics of heat-exchange process of desired product in the dephlagmator and cube were obtained.