Identification of State-Space Models from Time and Frequency Data
Abstract: This dissertation considers the identication of linear multivariable systems using finite dimensional time-invariant state-space models.Parametrization of multivariable state-space models is considered. A full parametrization, where all elements in the state-space matrices are parameters, is introduced. A model structure with full parametrization gives two important implications; low sensitivity realizations can be used and the structural issues of multivariable canonical parametrizations are circumvented. Analysis reveals that additional estimated parameters do not increase the variance of the transfer function estimate if the resulting model class is not enlarged.Estimation and validation issues for the case of impulse response data are discussed. Identication techniques based on realization theory are linked to the prediction error method. The combination of these techniques allows for the estimation of high quality models for systems with many oscillative modes. A new model quality measure, Modal Coherence Indicator, is introduced. This indicator gives an independent quality tag for each identified mode and provides information useful for model validation and order estimation.Two applications from the aircraft and space industry are considered. Both problems are concerned with vibrational analysis of mechanical structures. The first application is from an extensive experimental vibrational study of the airframe structure of the Saab 2000 commuter aircraft. The second stems from vibrational analysis of a launcher-satellite separation system. In both applications multi-output discrete time state-space models are estimated, which are then used to derive resonant frequencies and damping ratios.New multivariable frequency domain identification algorithms are also introduced. Assuming primary data consist of uniformly spaced frequency response measurements, an identification algorithm based on realization theory is derived. The algorithm is shown to be robust against bounded noise as well as being consistent. The resulting estimate is shown to be asymptotically normal, and an explicit variance expression is determined. If data originate from an infinite dimensional system, it is shown that the estimated transfer function converges to the transfer function of the truncated balanced realization.Frequency domain subspace based algorithms are also derived and analyzed when the data consist of samples of the Fourier transform of the input and output signals. These algorithms are the frequency domain counterparts of the time domain subspace based algorithms.The frequency domain identification methods developed are applied to measured frequency data from a mechanical truss structure which exhibits many lightly damped oscillative modes. With the new methods, high quality state-space models are estimated both in continuous and discrete time.
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