Identification of High-Order Linear Time-Invariant Models from Periodic Nonlinear System Responses

This paper presents a novel step in the extension of subspace identification toward the direct identification of harmonic decomposition linear time-invariant models from nonlinear time-periodic system responses. The proposed methodology is demonstrated through examples involving the nonlinear time-periodic dynamics of a flapping-wing micro aerial vehicle. These examples focus on the identification of the vertical dynamics from various types of input-output data, including linear time-invariant, linear time-periodic, and nonlinear time-periodic input-output data. A harmonic analyzer is used to decompose the linear time-periodic and nonlinear time-periodic responses into harmonic components and introduce spurious dynamics into the identification, which make the identified model order selection challenging. A similar effect is introduced by measurement noise. The use of model order reduction and model-matching methods in the identification process is studied to recover the harmonic decomposition structure of the known system. The identified models are validated in the frequency and time domains.