An analysis for optimum controllers of general, linear, time-invariant multiloop systems is presented. Optimization is based on minimizing mean-square or integral-square errors for either stationary statistical or transient inputs, with limits and constraints of mean-or integral-square form. General representations of controller characteristics, stable process characteristics, and error relations are used. A method is shown of assuring stability of the multiloop system during the optimization process and casting the multiloop controlled system into an equivalent open loop so that the methods of optimum fil-ter theory can be used. General solutions are obtained for four special cases. Two examples for speed control of a turbojet engine illustrate the methods developed in this report. The data for a controlled turbo¬jet engine were in substantial agreement with the theoretical results.
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