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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