Specification of the linear feedback system sensitivity function

Abstract

This paper examines the problem of designing a linear feedback system so that its response to a specified input is relatively insensitive to slow changes in system parameters. Classical feedback design techniques involve the specification of the system sensitivity function on the basis only of the forced response to a given input. A new performance criterion has been derived, in which the mean square variation of the system response is minimized. This specification of the sensitivity function results in control over the variation of both the characteristic and forced responses with system changes. The approach is based upon the assumption of a differential change in the variable system parameter, but yields workable results for large changes. It employs mathematical techniques which have been well developed for other applications in network design. The stability problem associated with high loop gains is considerably reduced when the sensitivity function is specified on the basis of this criterion.