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Controllable Fractional-Order Analogue Electronic Circuits
Dvořák, Jan ; Vávra, Jiří (oponent) ; Šimák, Boris (oponent) ; Jeřábek, Jan (vedoucí práce)
The doctoral thesis focuses on the synthesis and analysis of novel non-integer-order (fractional-order) circuit structures with electronically adjustable parameters. The main goal of the thesis is the design of new solutions of fractional-order current-mode filtering structures, fractional-order passive elements and also oscillators. The thesis contains the designs of three emulators of fractional-order elements, three filtering structures and two oscillators based on the usage of a fractional-order passive element in their circuit structure, and two general conceptions of fractional-order filters based on an approximation of the fractional-order transfer function. Based on general conceptions of the filtering structures, the fractional-order low-pass and high-pass filters are designed. The adjustability of the order, the pole frequency and in several cases also the quality factor of the proposed circuits is provided by used active elements with adjustable parameters. The features of the proposed circuits are verified by simulations using behavioural simulation models of the active elements. Several of these circuits were implemented on PCB and verified by laboratory measurement.
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Analog Implementation of Fractional-Order Elements and Their Applications
Kartci, Aslihan ; Štork, Milan (oponent) ; Machado,, José Tenreiro (oponent) ; Brančík, Lubomír (vedoucí práce)
With advancements in the theory of fractional calculus and also with widespread engineering application of fractional-order systems, analog implementation of fractional-order integrators and differentiators have received considerable attention. This is due to the fact that this powerful mathematical tool allows us to describe and model a real-world phenomenon more accurately than via classical “integer” methods. Moreover, their additional degree of freedom allows researchers to design accurate and more robust systems that would be impractical or impossible to implement with conventional capacitors. Throughout this thesis, a wide range of problems associated with analog circuit design of fractional-order systems are covered: passive component optimization of resistive-capacitive and resistive-inductive type fractional-order elements, realization of active fractional-order capacitors (FOCs), analog implementation of fractional-order integrators, robust fractional-order proportional-integral control design, investigation of different materials for FOC fabrication having ultra-wide frequency band, low phase error, possible low- and high-frequency realization of fractional-order oscillators in analog domain, mathematical and experimental study of solid-state FOCs in series-, parallel- and interconnected circuit networks. Consequently, the proposed approaches in this thesis are important considerations in beyond the future studies of fractional dynamic systems.
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Controllable Fractional-Order Analogue Electronic Circuits
Dvořák, Jan ; Vávra, Jiří (oponent) ; Šimák, Boris (oponent) ; Jeřábek, Jan (vedoucí práce)
The doctoral thesis focuses on the synthesis and analysis of novel non-integer-order (fractional-order) circuit structures with electronically adjustable parameters. The main goal of the thesis is the design of new solutions of fractional-order current-mode filtering structures, fractional-order passive elements and also oscillators. The thesis contains the designs of three emulators of fractional-order elements, three filtering structures and two oscillators based on the usage of a fractional-order passive element in their circuit structure, and two general conceptions of fractional-order filters based on an approximation of the fractional-order transfer function. Based on general conceptions of the filtering structures, the fractional-order low-pass and high-pass filters are designed. The adjustability of the order, the pole frequency and in several cases also the quality factor of the proposed circuits is provided by used active elements with adjustable parameters. The features of the proposed circuits are verified by simulations using behavioural simulation models of the active elements. Several of these circuits were implemented on PCB and verified by laboratory measurement.
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Analog Implementation of Fractional-Order Elements and Their Applications
Kartci, Aslihan ; Štork, Milan (oponent) ; Machado,, José Tenreiro (oponent) ; Brančík, Lubomír (vedoucí práce)
With advancements in the theory of fractional calculus and also with widespread engineering application of fractional-order systems, analog implementation of fractional-order integrators and differentiators have received considerable attention. This is due to the fact that this powerful mathematical tool allows us to describe and model a real-world phenomenon more accurately than via classical “integer” methods. Moreover, their additional degree of freedom allows researchers to design accurate and more robust systems that would be impractical or impossible to implement with conventional capacitors. Throughout this thesis, a wide range of problems associated with analog circuit design of fractional-order systems are covered: passive component optimization of resistive-capacitive and resistive-inductive type fractional-order elements, realization of active fractional-order capacitors (FOCs), analog implementation of fractional-order integrators, robust fractional-order proportional-integral control design, investigation of different materials for FOC fabrication having ultra-wide frequency band, low phase error, possible low- and high-frequency realization of fractional-order oscillators in analog domain, mathematical and experimental study of solid-state FOCs in series-, parallel- and interconnected circuit networks. Consequently, the proposed approaches in this thesis are important considerations in beyond the future studies of fractional dynamic systems.
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