Minimal Time Start-Up Schedules for Industrial Processes With Constraint on Transient Thermal Stress in the Apparatus

Abstract

Some industrial processes require a given variable, here called the control, to follow a prescribed time dependent path, most commonly being simply a constant. If the initial state is not on that path, then preliminary transient is necessary in which the control reaches the path and then follows it through the rest of the process. This initial transient, or start-up schedule may generate thermal, or other, stresses in the apparatus. The subject of this paper is calculating start-up schedules which reach the path in shortest possible time without the stresses exceeding the given limiting values. The above optimization problem is solved by iterative solution of a problem of minimization of terminal value (problem of Mayer) with inequality constraints on control and on output variable. The method involves a two dimensional search, the algorithm for which is provided. A sample numerical problem is solved as an illustration of the method.