A simple geometrical technique for determining loop frequency response bounds which achieve prescribed sensitivity specifications

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Abstract
A prerequisite to the design of a feedback system which must satisfy a prescribed sensitivity specification when its plant parameters vary within given limits is the determination of the minimum bounds on its loop frequency response for all frequencies of interest, A straight forward geometrical technique is presented which enables these bounds to be constructed using only ruler and compasses. The technique is exact for the case when the plant parameter variations can be represented by a convex polygon (the usual practical approximation) and it is far easier to apply (especially as a computer algorithm) than the trial and error approaches used previously.