Optimal control of a process with discrete and continuous decision variables

The task of dynamic optimization consists of manipulating the inputs to a dynamic system (i.e., one in which the state varies with time) so that the system performs in an advantageous manner. This paper presents a systematic technique for solving the problem of optimally controlling a converter aisle in a copper smelter. The converter aisle is distinguished from the usual dynamic system in that some of the control variables occur as discrete decisions while others may vary continuously with time. In this sense, the converter aisle typifies many industrial processes. The aisle is viewed as a total system with the objective of optimizing overall performance as evaluated using a mathematical performance criterion. Typical criteria reflect total processing time and operating costs. An essential step towards optimization is the development of a mathematical model to predict the state of the system. a simple mathematical model of the converter aisle is developed and using this model, two optimization approaches are examined: direct optimization of the total system and partitioning the system into interacting subproblems. The partitioned approach is pursued in detail with techniques for solving the optimization subprobelms presented and illustrated by numerical examples.