Linear time invariant approximations of linear time periodic systems

Abstract

Several methods for analysis of linear time periodic (LTP) systems have successfully been demonstrated using harmonic decompositions. One method recently examined is to create a linear time invariant (LTI) model approximation by expansion of the LTP system states into various harmonic state representations, and formulating corresponding linear time invariant models. Although this method has shown success, it relies on a second order formulation of the original LTP system. This second order formulation can prove problematic for degrees of freedom not explicitly represented in second order form. Specifically, difficulties arise when performing the harmonic decomposition of body and inflow states as well as interpretation of LTI velocities. Instead this paper will present a more generalized LTI formulation using a first order formulation for harmonic decomposition. The new first order approach is evaluated for a UH-60 rotorcraft model, and is used to show the significance of particular harmonic terms; specifically that the coupling of harmonic components of body and inflow states with the rotor states has a significant contribution to the LTI model fidelity in the prediction of vibratory hub loads.