On Relation Between Leakage-Free Condition and Differential Filtering Order in ETFE-Based Frequency Responce Function Estimation*

Estimation of an accurate frequency response function (FRF) of a target system is crucial to design fine servo controllers that realize fast and precise positioning control. The empirical transfer function estimation (ETFE) is the most representative and simplest FRF estimation method in terms of industrial utility. However, its applicability is limited to input and output signals of a target system measured during periodic or reciprocating operations, due to leakage errors induced by the discrete Fourier transform. Recently, an FRF estimation method combining ETFE with differential filtering has been proposed, which enables accurate FRF estimation in point-to-point motion. This paper theoretically clarifies the relationship between leakage-free condition and the differential filtering order in the ETFE-based FRF estimation framework. Furthermore, it is demonstrated through simulations that increasing the differential filtering order can broaden the input and output signals acquisition conditions that enables accurate FRF estimation.