System identification using IDFT for structural dynamic models

The structural vibration systems expressed with the partial differential equations are considered as the infinite-dimensional dynamic system. In multivariate control systems, it is necessary to derive the state-space reduced order model. The subspace system can be derived by eigensystem realization algorithms (ERA) with the inverse discrete Fourier transformation (IDFT) of the measured frequency response functions. The modal coordinate transformation is applied to the realization system in order to determine the natural frequencies and modal damping ratios of the subspace system. We discuss the necessary conditions of the convergence in ℋ_∞ for the approximated transfer function of the IDFT-realization system. The error bounds of the transfer function approximation are also represented in terms of the singular values of the impulse response matrices. The structural vibration test for a smart structure and the finite element model (FEM) simulation are performed to provide the records of frequency response functions