MATHEMATICAL MODEL OF THE REACTOR CONTROL OF THE ELECTROCHEMICAL TREATMENT OF INDUSTRIAL WASTEWATER
Abstract
Mathematical models of changes in the concentration of components under the action of an electric current have been developed. The problem of optimal control of current strength and costs is formulated. The main principles of optimal control calculation are developed. Methods of solving the problem of identification of model parameters with application to this problem of industrial wastewater treatment are considered. The problem of optimal control of current and consumption during the treatment of industrial wastewater with an electrochemical reactor of the ELION installation is considered.
The mathematical formalization of this problem consists in the developed models of the dynamics of the concentration of components. First-order kinetics models are proposed, which describe the effect of current strength and flow rate on concentration. The model for two components takes into account the mutual influence of the concentrations of these components on each other and is non-linear.
The study of the problem of optimal control based on the principle of Pontryagin’s maximum Optimal control is the selection and implementation of the best program of actions to achieve the desired state of the controlled object (based on its certain initial state) by influencing control parameters. Pontryagin's maximum principle serves as a starting point for solving many theoretical problems of optimal control and developing appropriate numerical methods.
As a result, it is shown that the optimal control should be piecewise constant and accept in some sense minimal or maximum value. These theoretical studies are supported by a model example, which shows that piecemeal-continuous management is more acceptable than permanent. The obtained results make it possible to build quite effective methods of solving the problem of building optimal control, which allow implementation on a computer in real time.
Keywords: optimal control, maximum principle, dynamics models, component concentration, parameter identification, cost minimization, electrochemical reactor, industrial wastewater
