Fidelity of Reduced Order Time Invariant Linear (LTI) Models for Integrated Flight and Rotor Control Applications

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. The LTI models are often significantly larger than the original system due to a large number of harmonic states retained in the LTI model. Using modal analysis, it has previously been shown that many of the harmonic states have little influence on the system dynamic modes and can be removed to form a smaller, reduced LTI model while still retaining high fidelity for the system dynamics. This paper will determine the input-to-output fidelity of the reduced LTI model compared to the full LTI model by evaluating the change in the input-to-output characteristics using additive uncertainty analysis and gap metric analysis. Examples are given in the paper.