Analysis Behavior of Fractional Variable Order Systems

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Ghazisaeedi, Hamid Reza | 2015

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 47867 (05)
University: Sharif University of Technology
Department: Electrical Engineering
Advisor(s): Tavazoei, Mohammad Saleh
Abstract:
In this thesis, variable order operators as a generalization for fractional operators are introduced and their characteristics are investigated. Then fractional variable order systems are defined whose their corresponding differential equations are stated by variable order operators. Most of this research delineate some beneficial control characteristics of fractional variable order systems. The first is type number subject. In this section two important theorems are stated which are useful in determining type number in an intensive range of systems. The other important subject is norm of functions. In this part a useful theorem is presented that states a sufficient and necessary condition for finiteness of function’s norm. In continue monotonic step response theme is dealt with. This part is consist of two sufficient condition for monotonic and no monotonic of step response. The end of thesis is dedicated to VFPID controllers that can satisfy more control goals in comparison with FOPID controllers. All of theorems are verified by numerical simulation
Keywords:
Behavioral Analysis ; Fractional Calculus ; Fractional-Order Electrical Element ; Fractional Variable Order Operators ; Step Response Monotonic

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