Stability analysis of periodic orbit of an adaptive notch filter for frequency estimation of a periodic signal

Online frequency estimation of a sinusoidal signal is a classical problem and has many practical applications. Recently an adaptive notch filter (ANF) with global convergence property has been developed for frequency estimation of a pure sinusoidal signal. This paper addresses a modified ANF structure that can estimate the fundamental frequency of any periodic signal including pure sinusoidal signals. To prove the stability of the modified ANF, the paper introduces a new theorem that shows for any periodic signal, there exists a locally asymptotically stable periodic orbit of this ANF by which the frequency estimation becomes feasible. This alternative stability proof is simple and uses widely known mathematical tools, and therefore alleviates the problem complexity even when the input signal is a pure sinusoidal signal. A further contribution of this paper is obtaining a necessary and sufficient condition in terms of design parameters for local asymptotical stability of the modified ANF. This condition, obtained from the numerical study of Floquet multipliers of a linear time-varying periodic system, provides a strict stability region in the modified ANF design parameters space.     

Estimation of n Frequencies Using Adaptive Notch Filter

This paper introduces an adaptive structure composed of n coupled paralleled subfilters that directly estimates frequencies of multiple sinusoids. The order of differential equations governing this algorithm is 3n, where n is the number of sinusoids. Stability analysis of this algorithm is carried out based on the application of the averaging theory under the assumption of the slow adaptation. Simulation results verify the validity of the analytical issues     

Corrosion behavior of pure Mg and AZ31 magnesium alloy

Protection of Metals and Physical Chemistry of Surfaces - Purpose of this article is to study corrosion behavior of pure magnesium and AZ31 magnesium alloy in electrolyte containing different...     

An adaptive notch filter for frequency estimation of a periodic signal

Online frequency estimation of a pure sinusoidal signal is a classical problem that has many practical applications. Recently an ANF with global convergence property has been developed for this purpose. There exist some practical applications in which signals are not pure sinusoidal and contain harmonics. Therefore, online frequency estimation of periodic but not necessarily sinusoidal signals espoused by such applications becomes quite important. This note presents an alternative stability analysis for a modified ANF that permits the presence of harmonics in the incoming signal. Also, this stability analysis is simpler and alleviates the problem complexity even in the case of pure sinusoidal signal. Simulation results confirm theoretical issues.     

Time-Domain Signal Analysis Using Adaptive Notch Filter

Noise reduction and signal decomposition are among important and practical issues in time-domain signal analysis. This paper presents an adaptive notch filter (ANF) to achieve both these objectives. For noise reduction purpose, the proposed adaptive filter successfully extracts a single sinusoid of a possibly time-varying nature from a noise-corrupted signal. The paper proceeds with introducing a chain of filters which is capable of estimating the fundamental frequency of a signal composed of harmonically related sinusoids, and of decomposing it into its constituent components. The order of differential equations governing this algorithm is 2n+1, where n is the number of constituent sinusoids that should be extracted. Stability analysis of the proposed algorithm is carried out based on the application of the local averaging theory under the assumption of slow adaptation. When compared with the conventional Fourier analysis, the proposed method provides instantaneous values of the constituting components. Moreover, it is adaptive with respect to the fundamental frequency of the signal. Simulation results verify the validity of the presented algorithm and confirm its desirable transient and steady-state performances as well as its desirable noise characteristics     

A Fast and Accurate Synchronization Technique for Extraction of Symmetrical Components

This paper introduces an approach for the real-time extraction of the frequency, phase angle, and symmetrical components of the grid signal, which is of great importance for many applications in power systems such as power quality and protection. The proposed method is based on the concept of the adaptive notch filter that provides a fast and accurate estimation of the symmetrical components in the presence of frequency and amplitude variations. In addition, the system offers a high degree of immunity and insensitivity to power system disturbances, harmonics, and other types of pollutions that exist in the grid signal. The simplicity of the structure makes the method suitable for both software and hardware implementations. Moreover, this very simple and very powerful tool can be used as a synchronization technique, which further simplifies the control issues currently challenging the integration of distributed energy technologies into the electricity grid. Mathematical derivations are presented to describe the principles of operation, and experimental results confirm the validity of the analytical work.