Analysis of Oscillations in Linear Fractional Order Systems

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Siami, Milad | 2011

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 42406 (05)
University: Sharif University of Technology
Department: Electrical Engineering
Advisor(s): Tavazoei, Mohammad Saleh
Abstract:
This thesis studies undamped oscillations generated by marginally stable fractional order linear time invariant (LTI) systems. In this study, the concept of integral curve is developed for fractional order LTI systems. The proposed concept is obtained based on equivalent integer order linear time varying (LTV) systems. Then, an analytical approach is proposed to be used for harmonic analysis of such oscillations in marginally stable commensurate order LTI systems. Also, it is shown that the Q-semi norm of the limit sets for a trajectory of these systems can be analytically determined based on the Q-semi norm of the initial condition, where Q is a specific matrix. Moreover, this result is extended to the wider class of rational order systems. Finally, some numerical examples are presented to demonstrate the usefulness of the obtained results
Keywords:
Fractional Order System ; Harmonic Analysis ; Marginal Stability ; Oscillations