Fractional-order Design: Devices, Circuits, And Systems

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Fractional-Order Design: Devices, Circuits, and Systems
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Contents
List of contributors
1 MOS realizations of fractional-order elements
	1.1 Introduction
	1.2 CPE/FI emulation techniques
		1.2.1 CPE/FI emulation using electronically controlled RC networks
		1.2.2 CPE/FI emulation using fractional-order integrators/differentiators
	1.3 Practical aspects
		1.3.1 Time constants and scaling factors spread reduction
		1.3.2 Reduction of the control terminals of the system
		1.3.3 Enhancement of the order range of the emulator
	1.4 Conclusions and discussion
	Acknowledgment
	References
2 A chaotic system with equilibria located on a line and its fractional-order form
	2.1 Introduction
	2.2 Model of the proposed flow and its dynamics
	2.3 Fractional-order form
	2.4 Circuit implementation
	2.5 FPGA implementation of the chaotic system
	2.6 Conclusion
	References
3 Approximation of fractional-order elements for sinusoidal oscillators
	3.1 Introduction
	3.2 R-C network-based FDs
	3.3 FDs for sinusoidal oscillators
		3.3.1 Impedance equalization-based FDs
		3.3.2 Admittance equalization-based FDs
	3.4 Performance analysis
		3.4.1 Stability analysis
		3.4.2 Sensitivity analysis using Monte Carlo simulation
		3.4.3 PSpice simulation and FoM calculation
	3.5 Conclusion and scope of future research
	References
4 Synchronization between fractional chaotic maps with different dimensions
	4.1 Introduction
	4.2 Preliminaries
	4.3 Combined synchronization of 2D fractional maps
		4.3.1 Master system and slave systems
		4.3.2 Combined scheme
	4.4 Combined synchronization of 3D fractional maps
		4.4.1 Master system and slave systems
		4.4.2 Combined scheme
	4.5 Concluding remarks and future works
	Acknowledgments
	References
5 Stabilization of different dimensional fractional chaotic maps
	5.1 Introduction
	5.2 Basic tools
		5.2.1 Caputo delta difference operator and stability
		5.2.2 Caputo h-difference operator and stability
	5.3 Stabilization of 2D fractional maps
	5.4 Stabilization of 3D fractional maps
	5.5 Summary and future works
	Acknowledgments
	References
6 Observability of speed DC motor with self-tuning fuzzy-fractional-order controller
	6.1 Introduction
	6.2 Mathematical model of DC motor
	6.3 Stability of speed estimation
	6.4 Proposed speed controller
		6.4.1 Literature review
			6.4.1.1 Riemann–Liouville fractional difference
			6.4.1.2 Caputo fractional difference
			6.4.1.3 Grunwald–Letnikov fractional difference
		6.4.2 Fractional PID controller
		6.4.3 Fractional-order PI controller
		6.4.4 Self-tuning PI fractional-order controller with fuzzy logic
	6.5 Results and discussion
		6.5.1 Test 1
		6.5.2 Test 2
		6.5.3 Test 3
		6.5.4 Test 4
	6.6 Conclusions
	References
7 Chaos control and fractional inverse matrix projective difference synchronization on parallel chaotic systems with application
	7.1 Introduction
	7.2 Preliminaries
		7.2.1 Definition
		7.2.2 Stability criterion
	7.3 The fractional inverse matrix projective difference synchronization
		7.3.1 Problem formulation
		7.3.2 System description
		7.3.3 Simulations and discussions
		7.3.4 Comparison with published literature
		7.3.5 Chaos control about the stagnation points in the presence of uncertainties and disturbances
	7.4 Illustration in secure communication
	7.5 Conclusions
	References
8 Aggregation of chaotic signal with proportional fractional derivative execution in communication and circuit simulation
	8.1 Introduction
	8.2 Fractional-order chaotic systems and their properties
		8.2.1 Lyapunov spectrum and Kaplan–Yorke dimension
		8.2.2 Dissipativity
	8.3 Analog circuit imitation
	8.4 Security analysis
	8.5 Conclusion
	References
9 CNT-based fractors in all four quadrants: design, simulation, and practical applications
	9.1 Introduction
	9.2 Fractor: definitions and state-of-the-art
		9.2.1 FOE realization: a brief survey
	9.3 A wide-CPZ, long-life, packaged CNT fractor
		9.3.1 Description of the CNT fractor
		9.3.2 Process of fabrication
		9.3.3 Electrical characterization
		9.3.4 Variation of FO parameters with time
		9.3.5 Origin of the wide CP nature in CNT fractors
	9.4 Fractors with desired specifications
		9.4.1 An RC ladder network with Foster-I topology
		9.4.2 Simulation of FO immittances with RC ladder
		9.4.3 Change in FO parameters in CNT fractor
		9.4.4 Comparison between two different fractor design techniques
	9.5 Four-quadrant FO immittances using CNT fractors
		9.5.1 Design of Type I fractors
		9.5.2 Design of Type II fractors
		9.5.3 Design of Type III fractors
		9.5.4 Tunability of fractors
	9.6 Application of four-quadrant CNT fractors
		9.6.1 Design of a high-Q factor FO resonator
		9.6.2 Hardware realization and practical tuning
	9.7 Conclusion
	9.A MATLAB program to determine RC ladder parameters for five FO specifications
	Acknowledgments
	References
10 Fractional-order systems in biological applications: estimating causal relations in a system with inner connectivity using fractional moments
	10.1 Introduction
	10.2 Related work
	10.3 Fractional moments and fractional cumulants
	10.4 Hindmarsh–Rose model
	10.5 Estimating causal relations
		10.5.1 Complex cumulants
		10.5.2 Granger causality
	10.6 Causal direction pattern recognition
		10.6.1 Clustering
		10.6.2 Convolutional neural network
	10.7 Discussion
	10.8 Conclusion
	References
11 Unitary fractional-order derivative operators for quantum computation
	11.1 Introduction
	11.2 A brief survey on geometric phase concepts in quantum computation
	11.3 Methodology
		11.3.1 Fractional calculus preliminaries
		11.3.2 Unitary fractional-order derivatives and phasor descriptions
		11.3.3 Control of multiqubit quantum interference circuits by unitary fractional-order derivatives
	11.4 Some quantum computation implications for unitary fractional-order derivative operators
		11.4.1 Modeling of quantum interference computation modes
		11.4.2 Design of a measurement probability distribution via a genetic algorithm
	11.5 Discussion and conclusions
	11.A
	References
12 Analysis and realization of fractional step filters of order (1+α)
	12.1 Introduction
	12.2 Analysis of fractional step filters
		12.2.1 First method
			12.2.1.1 Fractional step low-pass filter
			12.2.1.2 Fractional step high-pass filter
			12.2.1.3 Fractional step band-pass filter
			12.2.1.4 Fractional step all-pass filter
			12.2.1.5 Fractional step band-stop filter
		12.2.2 Second method
			12.2.2.1 Fractional step low-pass filter
			12.2.2.2 Fractional step high-pass filter
			12.2.2.3 Fractional step band-pass filter
			12.2.2.4 Fractional step all-pass filter
			12.2.2.5 Fractional step band-stop filter
	12.3 Numerical analysis and simulations of FSFs of order (1+α)
		12.3.1 Circuit simulations based on Method I
		12.3.2 Circuit simulations based on Method II
	12.4 Stability
	12.5 Sensitivity analysis
		12.5.1 Sensitivity analysis of Method I
		12.5.2 Sensitivity analysis of Method II
		12.5.3 Monte Carlo simulations
	12.6 Conclusion
	References
13 Fractional-order identification and synthesis of equivalent circuit for electrochemical system based on pulse voltammetry
	13.1 Introduction
	13.2 Experimental setup
	13.3 Fractional-order models
		13.3.1 Fractional-order transfer function
		13.3.2 Fractional-order circuit elements
	13.4 Identification of fractional-order transfer function
		13.4.1 Structure of the proposed fractional-order transfer function
		13.4.2 Parameter estimation
		13.4.3 Results: performance evaluation of the identified FOTF
	13.5 Proposed circuit with fractional-order elements
		13.5.1 Network synthesis for fractional-order circuit
		13.5.2 Analysis with fractional circuit parameters
	13.6 Principal component analysis: towards electronic tongue application
	13.7 Conclusions
	References
14 Higher-order fractional elements: realizations and applications
	14.1 Introduction
	14.2 Realization of FOEs with fractional order < 1
		14.2.1 CFE approximation-based FOC emulation
		14.2.2 FI emulation
		14.2.3 Functional block diagram-based emulation
	14.3 Realization of fractional-order element with 1 < fractional order< n
		14.3.1 IIMC-based realization
		14.3.2 GIC-based realization
		14.3.3 FBD-based realization
	14.4 Application
		14.4.1 Stability analysis
		14.4.2 Simulation and experimental results
			14.4.2.1 Functional verification of FI and FOC
			14.4.2.2 Functional verification of FOF
	14.5 Conclusion
	References
15 Fabrication of polymer nanocomposite-based fractional-order capacitor: a guide
	15.1 Introduction
		15.1.1 History
		15.1.2 Present trends in polymer NCs
			15.1.2.1 Porous polymer-based
			15.1.2.2 Ferroelectric polymer-based
			15.1.2.3 Epoxy resin-based
	15.2 Polymers
		15.2.1 Polymer NCs
		15.2.2 Polymer NC as FOC dielectric
	15.3 Ferroelectric polymers
		15.3.1 PVDF
			15.3.1.1 Dielectric properties of PVDF
			15.3.1.2 Inducing β-phase PVDF
			15.3.1.3 Ferroelectric effect
		15.3.2 Porous polymers
			15.3.2.1 Dielectric properties of PMMA
	15.4 Conductive fillers
	15.5 Methods of synthesis
		15.5.1 Intercalation
			15.5.1.1 Chemical intercalation
			15.5.1.2 Mechanical intercalation
			15.5.1.3 Melt intercalation
		15.5.2 Sol-gel method
		15.5.3 Direct mixing
		15.5.4 Melt compounding
		15.5.5 Solution blending
		15.5.6 In situ polymerization
	15.6 Percolation threshold
	15.7 Factors affecting properties of polymer NCs
		15.7.1 Alignment of the filler
		15.7.2 Dispersion of the filler
		15.7.3 Interfacial bonding between filler and the polymer matrix
	15.8 A GNS/PVDF FOC
		15.8.1 Materials and methods
		15.8.2 Results and discussion
	15.9 Conclusion
	Acknowledgments
	References
16 Design guidelines for fabrication of MWCNT-polymer based solid-state fractional capacitor
	16.1 Introduction
	16.2 Solid-state fractional capacitors
		16.2.1 Structure of the fractional capacitor
		16.2.2 Fabrication procedure
	16.3 Batch analysis of the solid-state fractional capacitors for defining the guidelines
		16.3.1 Characterization
		16.3.2 Yield rate
		16.3.3 Effect of thickness of the nanocomposite and the middle plate
	16.4 Validation of the defined guidelines
	16.5 Material characterization
		16.5.1 Details of the analysis
		16.5.2 Results from material characterization
			16.5.2.1 FTIR spectra
			16.5.2.2 SEM and TEM images
	16.6 Correlating the material characterization with the CPA of a solid-state fractional capacitor
	16.7 Conclusion
	Acknowledgments
	References
Index
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