On State-Space Models in System Identification

Sammanfattning: This thesis considers identification of multivariable discrete time linear systems by using time-invariant state-space models of finite dimension. A new model structure is introduced that is fully parametrized, i. e. all matrices are filled with parameters. All multivariable systems of a given order can be described within this model structure, which thereby circumvents all the interna! structural issues otherwise inherent in the multivariable state-space identification problem. An identification algorithm is presented that minimizes a regularized prediction error criterion. The algorithm adapts itself to yield models which are close to a balanced realization by means of an appropriate choice of regularization. The use of a balanced realization minimizes the transfer function sensitivity of perturbations in the parameters caused by finite word-length effects. Some analysis is pursued which shows that the proposed model structure retains the statistical properties of the standard identifiable model structures. We prove, under some weak assumptions, that the proposed identification algorithm locally converges to the set of true systems.Furthermore, system identification using impulse response measurements are discussed. The focus is on impulse response measurements from vibrating mechanical structures. The realization based algorithms by Kung or Zeiger-McEwen are linked to the prediction error minimization techniques. This work results in an identification method which yields estimated models with high quality. A numerically effective parametrization is introduced which facilitates the prediction error minimization. A distributed quality measure, the Modal Coherence Indicator (MCI), is introduced. Given a state-space modeland an impulse response, the set of MCis describes the "coherence" between the state-space model and the impulse response. 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 commuter aircraft Saab 2000. The second stems from a 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.