System identification via families of digital algorithms

Abstract

Digital algorithms for the implementation of time domain identification techniques which are capable of coping with the stochastic nature of their data have been proposed and investigated. These algorithms may either employ recursive or non-recursive solution strategies and they appear to have a high noise-rejection performance and yield consistent and accurate results. Alain emphasis is given to families of recursive algorithms, which have a fast rate of convergence and are based upon an integral adaptation mechanism with constant or decreasing gains and may, or may not, include a proportional adaptation mechanism. The analysis procedure is presented in an integrated manner, and makes use only of input-output sampled time data of a linear system that consists of lumped parameter or distributed parameter elements with a finite number of modes included in the system response during or after an adequate period of excitation. Through a successive model-fitting procedure the best mathematical model, defined by two characteristic polynomials, is established from which the input-output transfer function, the equation of motion, the natural frequencies and damping ratios can be obtained. The results of the present study indicate that the procedure is able to identify unstable, marginally stable, and asymptotically stable systems as well as those having closely spaced natural frequencies. Its extension to non-linear and/or non-autonomous systems is straightforward.

Notes

‡Present address : Helwan,PO Box 72,Cairo Egypt.