Iterative Pole–Zero model updating: A combined sensitivity approach

Abstract

A crucial step in the control of a weakly damped high precision motion system is having an accurate dynamic model of the system from actuators to sensors and to the unmeasured performance variables. A (reduced) Finite Element (FE) model may be a good candidate apart from the fact that it often does not sufficiently match with the real system especially when it comes to machine-to-machine variation. To improve the dynamic properties of the FE model toward the dynamic properties of a specific machine, an Iterative Pole–Zero (IPZ) model updating procedure is used that updates numerical poles and zeros of Frequency Response Functions (FRFs) toward measured poles and zeros, which can be extracted from the measured FRFs. It is assumed that in a practical situation, the model (physical) parameters that cause discrepancy with the real structure are unknown. Therefore, the updating parameters will be the eigenvalues of the stiffness and/or damping (sub)matrix. In this paper, an IPZ model updating is introduced which combines the sensitivity functions of both poles and zeros (with respect to the corresponding updating parameters) together with the cross sensitivity functions between poles and zeros. The procedure is verified first using simulated experiments of a pinned-sliding beam structure and then using non-collocated FRF measurement results from a cantilever beam setup.