Exact methods for modal transient response analysis including feedback control

This paper presents a modal method for the analysis of controlled structural systems that retains the uncoupled nature of the classical transient response analysis of a structure subjected to a prescribed time-varying load. The control force is expanded as a Taylor series that remains on the right side of the equations, and it does not lead to a computational approach that requires coupling between modes on the left side. Retaining a su cient number of terms in the series produces a solution to the modal equations that is accurate to machine precision. The approach is particularly attractive for large problems in which standard matrix exponential methods become computationally prohibitive. Numerical results are presented to show the accuracy and e ciency of the proposed approach for dynamic feedback compensation of a truss structure with local member modes in the controller bandwidth.