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UBC Theses and Dissertations

Linear continuous-time system identification and state observer design by modal analysis El-Shafey, Mohamed Hassan


A new approach to the identification problem of linear continuous-time time-invariant systems from input-output measurements is presented. Both parametric and nonparametric system models are considered. The new approach is based on the use of continuous-time functions, the modal functions, defined in terms of the system output, the output derivatives and the state variables under the assumption that the order n of the observable system is known a priori. The modal functions are obtained by linear filtering operations of the system output, the output derivatives and the state variables so that the modal functions are independent of the system instantaneous state. In this case, the modal functions are linear functions of the input exponential modes, and they contain none of the system exponential modes unlike the system general response which contains modes from both the system and the input. The filters parameters, the modal parameters are estimated using linear regression techniques. The modal functions and the modal parameters of the output and its derivatives are used to identify parametric input-output and state models of the system. The coefficients of the system characteristic polynomial are obtained by solving n algebraic equations formed from the estimates of the modal parameters. Estimates of the parameters associated with the system zeros are obtained by solving another set of linear algebraic equation. The system frequency response and step response are estimated using the output modal function. The impulse response is obtained by filtering the estimated step response using the output first derivative modal parameters. A new method is presented to obtain the system poles as the eigenvalues of a data matrix formed from the system free response. The coefficients of the system characteristic polynomial are obtained from the data matrix through a simple recursive equation. This method has some important advantages over the well known Prony's method. The state modal functions are used to obtain a minimum-time observer that gives the continuous-time system state as a direct function of input-output samples in n sampling intervals.

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