Abstract
Abstract
The paper describes the calculation of the minimum amount of fuel required to warm a simple model of a batch heating plant that has an active temperature constraint on the furnace gas. The method of calculation combines optimal control theory and a direct search with a downhill simplex to place the temperatures of the multiple nodes of the load inside a target envelope. The split boundary value problem is solved by shooting. Shooting is facilitated by omitting from the plant model the thermal storage of the gas enclosed within the plant. The purpose of the calculation is to illustrate that minimizing a linear integral of fuel flow does not lead to bang-bang control and that the constraint on the gas temperature is easily handled by treating it as a control constraint.
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