A computational procedure based on eigenvalue sensitivity theory applicable to linear system design

Abstract

A digital computer based method for generating the sensitivities of the eigenvalues of a linear, time invariant, lumped parameter dynamic system to perturbations in its design parameters is described. The equations defining the particular system being considered must be supplied in a subroutine, and the sensitivity results are displayed in graphical form. Provision is made for treating one parameter in a special way appropriate to problems in vehicle and rotor dynamics, in which context satisfactory operation over a wide speed range is desirable, and for systematically combining parameter changes using the sensitivities generated to modify the eigenvalues in a desired manner. Although the sensitivity theory itself is based on the assumption of small design parameter perturbations, relatively large changes can be accommodated by combining small changes. It is claimed that there are many instances in which the use of the facility will be preferred to the commonly practised repetitive numerical generation of eigenvalues for different sets of design parameters.