State Estimation in Nonlinear Systems Using High-gain Observers
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Authors
Mousavi, Seyed Mohammadmoein
Date
Type
thesis
Language
eng
Keyword
Observers for nonlinear systems , Nonlinear output feedback , Nonlinear systems
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Abstract
This dissertation is concerned with state estimation in nonlinear systems represented in canonical observable form with Lipschitz nonlinearities. High gain observers (HGOs) have been shown to be quite effective for this purpose, because of their simple structure, robustness, and the advantageous property of having a design parameter (named $epsilon$ in this thesis) that can be suitably adjusted to choose the estimation error decay rate. Although increasing the HGO’s gains yields fast convergence, it can cause a substantial overshoot in transient response of the state estimations, known as the peaking phenomena. The second problem is associated with the sensitivity of the steady-state response of the observer to measurement noise. The estimates are shown to exhibit steady-state oscillations proportional to $epsilon^{-n}$ even though they remain stable in the presence of measurement noise. In this dissertation, three different observers are designed to address the main two problems of the HGOs, namely the peaking and sensitivity to noise. As for the first design, a low-power multi high-gain observer (low-power MHGO) is proposed where multiple low-power observers of order $2n-2$ are used to aggregate the advantages of the traditional HGO, low-power HGO and MHGO. The second observer combines this design with low-pass filters, and the third design uses time-varying gains with a different filter.
For all the proposed observers, it is shown that the estimation error dynamics are input-to-state stable (ISS) with respect to measurement noise with a tunable convergence rate. It is also shown that, the peaking is reduced using some design parameters. Moreover, the steady-state behaviour of the suggested observers are characterized, demonstrating the reduction of the sensitivity of the state estimates to measurement noise. Several simulation examples are used to show the effectiveness of the proposed methods compared to a standard HGO and some existing approaches in the literature.
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Proquest PhD and Master's Theses International Dissemination Agreement
Intellectual Property Guidelines at Queen's University
Copying and Preserving Your Thesis
This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owne