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Electrical and Electronic Engineering, Imperial College London
Doi
Abstract
Parameter estimation of a sinusoidal signal in real-time is encountered in applications
in numerous areas of engineering. Parameters of interest are usually amplitude, frequency
and phase wherein frequency tracking is the fundamental task in sinusoidal estimation. This thesis deals with the problem of identifying a signal that comprises n (n ≥ 1) harmonics from a measurement possibly affected by structured and unstructured disturbances. The structured perturbations are modeled as a time-polynomial so as to represent, for example, bias and drift phenomena typically present in applications, whereas the unstructured disturbances are characterized as bounded perturbation. Several approaches upon different theoretical tools are presented in this thesis, and classified into two main categories: asymptotic and non-asymptotic methodologies, depending on the qualitative characteristics of the convergence behavior over time.
The first part of the thesis is devoted to the asymptotic estimators, which typically consist
in a pre-filtering module for generating a number of auxiliary signals, independent of
the structured perturbations. These auxiliary signals can be used either directly or indirectly
to estimate—in an adaptive way—the frequency, the amplitude and the phase of the
sinusoidal signals. More specifically, the direct approach is based on a simple gradient
method, which ensures Input-to-State Stability of the estimation error with respect to the
bounded-unstructured disturbances. The indirect method exploits a specific adaptive observer scheme equipped with a switching criterion allowing to properly address in a stable way the poor excitation scenarios. It is shown that the adaptive observer method can be applied for estimating multi-frequencies through an augmented but unified framework, which is a crucial advantage with respect to direct approaches. The estimators’ stability properties are also analyzed by Input-to-State-Stability (ISS) arguments.
In the second part we present a non-asymptotic estimation methodology characterized by
a distinctive feature that permits finite-time convergence of the estimates. Resorting to the
Volterra integral operators with suitably designed kernels, the measured signal is processed, yielding a set of auxiliary signals, in which the influence of the unknown initial conditions is annihilated. A sliding mode-based adaptation law, fed by the aforementioned auxiliary signals, is proposed for deadbeat estimation of the frequency and amplitude, which are dealt with in a step-by-step manner. The worst case behavior of the proposed algorithm in the presence of bounded perturbation is studied by ISS tools.
The practical characteristics of all estimation techniques are evaluated and compared
with other existing techniques by extensive simulations and experimental trials.Open Acces
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