On Optimum Control of Temperature Distribution in a Solid†

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Abstract
The paper describes a method of determining the switching instants for the input to a particular distiibutod-parameter system, namely a metal slab which is heated on one face and has tho opposite face insulated. The switching instants are determined on the basis of achieving a desired uniform temperature in the slab in tho shortest possible time, given certain limitations on the temperature which can be applied to the heated face. A previously known method of solving this problem was by subdividing the slab into sections and using lumped-parameter methods; tho present method makes use of a Fourier-series representation of the temperature distribution, tho input being such as to bring all the space harmonics of the error distribution to zero at the same time

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