Adaptive notch filters are local adaptive observers. (1st June 2015)

• Record Type: Journal Article
• Authors: Marino, Riccardo; Tomei, Patrizio
• Is Part Of: International journal of adaptive control and signal processing. Volume 30:Number 1(2016:Jan.)
• Page Start: 128
• Page End: 146
• Publication Date: 2015-06-01
• Subjects: notch filter -- adaptive observer -- disturbance rejection -- frequency estimation; Adaptive control systems -- Periodicals; Adaptive signal processing -- Periodicals; 629.836
• DOI: 10.1002/acs.2582
• Languages: English
• ISSNs: 0890-6327

Abstract

Summary: Several continuous‐time frequency estimators for a measured sinusoidal signal, which have been proposed in the literature, are reviewed, reinterpreted and compared both theoretically and by simulations. It is argued that adaptive notch filters are feedback algorithms that contain a local adaptive observer in the feedback loop. It is shown that the adaptive notch filter (ANF), which was originally conceived as a discrete‐time ANF, is basically equivalent to the recently proposed adapted frequency locked loop called orthogonal signal generator. They both require a sufficiently slow frequency estimation and can be interpreted as third‐order adaptive observers. They exhibit local convergence properties for the estimation errors, that is, the convergence to zero is guaranteed provided that their initial error is sufficiently small. Three adaptive observers, which were independently proposed in 2002, are third‐order frequency estimators whose estimation errors are exponentially convergent to zero from any initial condition and for any value of frequency, amplitude and phase in the measured sinusoidal signal. They have the additional advantage of not requiring the frequency estimation dynamics to be sufficiently slow. Conversely, they may be interpreted as adaptive notch filters. Second‐order frequency estimators have been proposed as well: they may be interpreted as adaptive reduced‐order observers. Copyright © 2015 John Wiley & Sons, Ltd.