Estimation of multi-input multi-output linear time-periodic models using a left matrix fraction description

摘要

In this paper, a novel multi-input multi-output (MIMO) identification tool is proposed for linear time-periodic (LTP) mechanical systems based on a left matrix fraction description. The left matrix fraction parameterization has the advantage that nonlinear mechanical parameters, such as nonlinear damping and stiffness matrices, follow directly from the estimated MIMO LTP model. The algorithm starts from the Fourier decomposition of the equation of motion. Following a total least squares (TLS) approach, the identified Fourier harmonics of the nonlinear mechanical parameters are obtained from a single broadband experiment using a singular value decomposition. We show that the TLS estimator performs quite well on noisy data. The TLS scheme is illustrated on a 2-DoF mechanical rotor supported by nonlinear fluid film bearings under periodically varying loading conditions.