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Summary: FloquetEMAJour_v4.doc, Page 1 of 11, 10/16/2008, 12:47:11 PM
Frequency-Domain Identification of Linear Time-Periodic Systems
using LTI Techniques
Matthew S. Allen
Assistant Professor
Department of Engineering Physics
University of Wisconsin-Madison
msallen@engr.wisc.edu
ABSTRACT
A variety of systems can be faithfully modeled as linear with coefficients that vary periodically with
time or Linear Time-Periodic (LTP). Examples include anisotropic rotor-bearing systems, wind turbines
and nonlinear systems linearized about a periodic trajectory. Many of these have been treated
analytically in the literature, yet few methods exist for experimentally characterizing LTP systems. This
paper presents a set of tools that can be used to identify a parametric model of an LTP system, using a
frequency domain approach and employing existing algorithms to perform parameter identification. One
of the approaches is based on lifting the response to obtain an equivalent Linear Time-Invariant (LTI)
form and the other based on Fourier series expansion. The development focuses on the pre-processing
steps needed to apply LTI identification to the measurements, the post-processing needed to reconstruct
the LTP model from the identification results, and the interpretation of the measurements. This elucidates
the similarities between LTP and LTI identification, allowing the experimentalist to transfer insight
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