Fourier series based model reference adaptive control

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2014

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Gezer, Rüştü Berk

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Any signal in nature includes periodic signals with different frequencies and weightings. Therefore, any signal can be represented using summation of simple periodic functions. Representation of signals with periodic functions is called Fourier series representation. This powerful utility of the Fourier series is aimed to be used for adaptive control. In the direction of this aim, a novel approach for model reference adaptive control is proposed in this thesis. The Fourier series basedmodel reference adaptive control represents an alternative for uncertainty parametrizations used in model reference adaptive control. Commonly designed MRAC schemes use known functions of system variables or in some cases neural networks for uncertainty parametrization. In this study, these parametrization methods are replaced with Fourier series. The sine and cosine elements; which are functions of time with periods that are multipliers of precessors, are used as basis functions. An adaptation law for estimating the weightings of the periodic functions is derived using Lyapunov stability principle. The adaptive input is calculated by multiplying the periodic basis functions and the estimated weights. In this thesis, two other alternative for the proposed method are examined. These alternatives are model following control and basic model reference adaptive control that uses known functions of system variables. These controllers are designed for a sample problem. Robustness properties of the model following controller is analyzed. Performances of these controllers are inspected under defined and random disturbances, and the results are compared with the proposed controller. The performance of the Fourier series based MRAC scheme is shown to be satisfactory. The comparison of the results indicates that the proposed controller gives better disturbance rejection for the same performance level.

Subject Keywords

Fourier series., Adaptive control systems.

URI

http://etd.lib.metu.edu.tr/upload/12617685/index.pdf
https://hdl.handle.net/11511/23961

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Graduate School of Natural and Applied Sciences, Thesis

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Citation Formats

R. B. Gezer, “Fourier series based model reference adaptive control,” M.S. - Master of Science, Middle East Technical University, 2014.