Subspace methods for frequency domain data

Subspace based methods for system identification have, during the last 10 years, matured and been accepted as important tools. Subspace based methods deliver the estimate directly in the form of a state-space realization. This is an advantage as many model based control design techniques use state-space models. Subspace algorithms have been formulated for use of both time domain as well as frequency domain data. In this tutorial contribution the class of frequency domain algorithms would be covered. Frequency domain subspace methods have been very accurate for the estimation of transfer functions of systems with a high modal density and/or poorly damped modes. The basic algorithmic structure for a frequency domain algorithm is derived. Also the numerical implementation using QR-factorization and singular value decomposition is covered. Several examples are provided including identification of flexible structures, and modeling of an acoustic path.