Frequency Response Function Identification of Periodically Scheduled Linear Parameter-Varying Systems

For Linear Time-Invariant (LTI) systems, Frequency Response Functions (FRFs) facilitate dynamics analysis, controller design, and parametric modeling, while many practically relevant systems are in fact more accurately described by Linear Parameter-Varying (LPV) models. The aim of this paper is to develop an FRF modeling framework for periodically scheduled Single-Input Single-Output (SISO) LPV systems, that enables the identification of LPV FRF models from global experiments. This is achieved by developing an appropriate definition of the harmonic FRF for input–output LPV systems and by developing a method to compute a suitable harmonic FRF estimator. The developed approach generalizes the Empirical Transfer Function Estimate (ETFE) to the class of periodically-scheduled LPV systems, and the classical ETFE is recovered for LTI systems as a special case. The developed method is successfully used to estimate a SISO LPV FRF of an experimental motion system, thereby confirming the potential of the developed framework