Fractional Order Systems Optimization, Control, Circuit Realizations and Applications
'Fractional Order Systems' consists of 21 contributed chapters by subject experts. Chapters offer practical solutions and novel methods for recent research problems in the multidisciplinary applications of fractional order systems, such as FPGA, circuits, memristors, control algorithms, ph...
Saved in:
| Main Authors | , , |
|---|---|
| Format | eBook |
| Language | English |
| Published |
Chantilly
Elsevier Science & Technology
2018
Academic Press |
| Edition | 1 |
| Series | Advances in nonlinear dynamics and chaos (ANDC) |
| Subjects | |
| Online Access | Get full text |
| ISBN | 9780128161524 0128161523 |
| DOI | 10.1016/C2017-0-04459-2 |
Cover
Table of Contents:
- 3.1 Fractional Derivative -- 3.2 Fractional Elements -- 3.3 Sensitivity Analysis -- 3.4 Illustrative Example -- 4 Yield Estimation -- 5 Yield Optimization -- 6 Trust Region Optimization Methods -- 6.1 Outline -- 6.2 Trust Region Method -- 6.3 Multivariate Padé Model -- 6.4 The Trust Region Subproblem -- 7 Examples -- 7.1 Low-Pass Filter -- 7.2 Band-Pass Filter -- 8 Discussion -- 9 Conclusions -- References -- Chapter 10: Survey on Two-Port Network-Based Fractional-Order Oscillators -- 1 Introduction -- 1.1 Fractional-Order Oscillator Theory -- 1.2 Two-Port Network -- 2 Prototype of Two-Port Network Three-Impedance Fractional-Order Oscillators -- 2.1 General Oscillator Structures -- 2.2 Design Procedure for Selected Impedances -- 2.2.1 Numerical Discussion -- 2.2.2 Simulation Results -- 3 Prototype of Two-Port Network Two-Impedance Fractional-Order Oscillators -- 3.1 Oscillator Structure -- 3.2 Discussion and Examples -- 3.2.1 a12 Independent of Other Matrix Parameters -- 3.2.2 a12 Dependent on Other Matrix Parameters -- 3.3 Simulation Results -- 4 Conclusion -- References -- Chapter 11: On Linear and Nonlinear Electric Circuits: A Local Fractional Calculus Approach -- 1 Introduction -- 2 Preliminary -- 3 The Nondifferentiable Elements Within LFD -- 4 The Linear LC Electric Circuit via LFD -- 4.1 The Linear Fractal LC Electric Circuit -- 4.2 Comparative Results Among the Derivative Operators -- 5 The Linear RC Electric Circuit via Local Fractional Derivatives -- 5.1 The Linear Fractal RC Electric Circuit -- 5.2 Comparative Results Among the Different Derivatives -- 6 The Nonlinear LC Electric Circuits via LFD -- 6.1 The Nonlinear Fractal LC Electric Circuits -- 6.2 Analysis of a Nonlinear Fractal LC Electric Circuit -- 7 The Nonlinear RC Electric Circuits via LFD -- 7.1 The Nonlinear Fractal RC Electric Circuits
- 7.2 Analysis of a Nonlinear Fractal RC Electric Circuit
- Front Cover -- Fractional Order Systems: Optimization, Control, Circuit Realizations and Applications -- Copyright -- Contents -- Contributors -- Preface -- About the Book -- Objectives of the Book -- Organization of the Book -- Book Features -- Audience -- Acknowledgments -- Chapter 1: Dynamics, Circuit Design, Synchronization, and Fractional-Order Form of a No-Equilibrium Chaotic System -- 1 Introduction -- 2 Description and Dynamics of the System Without Equilibrium -- 3 Antisynchronization of Two Identical Systems Without Equilibrium -- 4 Circuit Design of the System Without Equilibrium -- 5 Fractional-Order Form of the System Without Equilibrium -- 6 Conclusions -- Acknowledgments -- References -- Chapter 2: FPGA Implementation of Fractional-Order Chaotic Systems -- 1 Introduction -- 2 Fractional-Order Derivative -- 2.1 Caputo Derivative Theoretical Analysis -- 2.2 Grünwald-Letnikov's Theoretical Analysis -- 3 Implementation of Fractional-Order Derivative on FPGA -- 3.1 Caputo's Derivative Implementation -- 3.2 Grünwald-Letnikov's Implementation 1 -- 3.2.1 Hardware Architecture -- 3.3 Grünwald-Letnikov's Implementation 2 -- 3.4 Results -- 4 Fractional-Order Chaotic Systems -- 4.1 Arneodo -- 4.2 Borah Rotational Attractor -- 4.3 Chen Double and Four-Wing System -- 5 Fractional-Order Chaotic Systems FPGA Implementation -- 5.1 Arneodo FPGA Implementation -- 5.2 Borah FPGA Implementation -- 5.3 Chen Double and Four-Wing System FPGA Implementation -- 5.4 FPGA Results -- 6 Conclusion -- References -- Chapter 3: A Survey of Numerical Simulations for Multistrain Tuberculosis Models of Fractional-Order and Their Optimal Control -- 1 Introduction -- 2 A General Multistrain TB Model of Fractional-Order Derivatives -- 2.1 The Basic Reproduction Number R0 -- 2.2 Multistrain TB Model of Variable-Order Fractional Derivatives
- 3 Numerical Methods for Solving a General Multistrain TB Model -- 3.1 Standard Finite Difference Method -- 3.2 Nonstandard Finite Difference Method -- 3.3 Grünwald-Letinkov Approximation -- 4 Optimal Control of Fractional Multistrain TB Model -- 4.1 Optimality Condition for the Fractional-Order Multistrain TB Model -- 4.2 Numerical Methods for Solving FOCP -- 4.2.1 Generalized Euler Method -- 4.2.2 Iterative Optimal Control Method -- 4.3 Discussion and Numerical Experiment -- 5 Conclusions -- References -- Further Reading -- Chapter 4: Fractional-Order Models for HIV Viral and Epidemiological Dynamics -- 1 Introduction -- 2 Literature Review -- 2.1 Preliminaries -- 2.2 HIV/AIDS -- 2.3 Stability -- 2.4 Stability Analysis of a System of Fractional Differential Equations -- 3 HIV Viral Dynamics -- 3.1 Previous Models -- 3.1.1 Dynamics of HIV Infection of CD4+ T Cells -- 3.1.2 Decay Dynamics of HIV-1 Depending on the Inhibited Stages of the Viral Life Cycle -- 3.1.3 Effects of HIV Infection on CD4+ T-Cell Population Based on a Fractional-Order Model -- 3.2 The Proposed Fractional Model for Viral Dynamics -- 3.3 Stability Analysis for the Proposed Viral Dynamics Model -- 3.4 Numerical Simulations and Discussion -- 4 AIDS Epidemiological Dynamics -- 4.1 Previous Models -- 4.1.1 Differential Infectivity Model -- 4.1.2 The Staged Progression Model -- 4.1.3 Differential Infectivity and Staged Progression Model -- 4.2 The Proposed Fractional DISPR Model -- 4.3 Stability Analysis for the Proposed DISPR Model -- 4.4 Numerical Simulation and Discussion -- 5 Conclusion -- References -- Chapter 5: Biologically Inspired Optimization Algorithms for Fractional-Order Bioimpedance Models Parameters Extraction -- 1 Introduction -- 2 Fractional-Order Bioimpedance Models -- 2.1 Plant Cell -- 2.2 Cole-Impedance Model -- 2.3 The Fractional Simplified Hayden Model
- 5 Fully Integrated Fractional-Order Emulatorsin Biology -- 5.1 Human Respiratory System Model -- 5.1.1 Description of the Human Respiratory System Model -- 5.1.2 Implementation of the Human Respiratory System Model -- 5.1.3 Results of Simulation -- 5.2 Wood Tissue Model -- 5.2.1 Description of the Wood Tissue Model -- 5.2.2 Implementation of the Wood Tissue Model -- 5.2.3 Results of Simulation -- 6 Discussion -- 7 Conclusions -- References -- Further Reading -- Chapter 7: Bioimpedance Analysis Using Fractional-Order Equivalent Electrical Circuits -- 1 Introduction -- 2 Fractional-Order Circuit Models -- 2.1 Cole Impedance Model -- 3 Measurements -- 3.1 Impedance Analyzers -- 4 Determination of Fractional-Order Model Parameters -- 5 Example: Human Forearm Impedance -- 5.1 Factors Impacting Parameter Extractions -- 5.2 Comparing Parameters From Alternative Models -- 6 Alternative Measurement Techniques -- 7 Conclusion -- Appendix: MATLAB Code -- References -- Chapter 8: On the Approximation of Fractional-Order Circuit Design -- 1 Introduction -- 2 Approximation of Fractional Transfer Functions -- 2.1 Matsuda Approximation -- 2.2 Oustaloup Approximation (CRONE) -- 3 Fractional-Order Element Emulator -- 4 Fractional-Order Oscillator -- 4.1 Wien Oscillator Family -- 4.2 Numerical Solutions -- 4.3 Circuit Simulations of the Fractional-Order Oscillator -- 5 Fractional-Order Filters -- 5.1 Fractional-Order Filter Fundamentals -- 5.2 KHN Filter Design Procedure -- 5.2.1 Fractional KHN Low-Pass Filter -- 5.2.2 The Maximum and Minimum Frequencies -- 5.2.3 The Half-Power Frequency -- 5.2.4 The Right Phase Frequency -- 5.3 CCII-Based KHN Filter Simulation -- 6 Conclusion -- References -- Chapter 9: On the Fractional-Order Circuit Design: Sensitivity and Yield -- 1 Introduction -- 2 Related Work -- 3 Sensitivity Analysis on Circuits With Fractional-Order Elements
- 2.4 The Fractional Double-Shell Model -- 3 Problem Identification -- 4 Overview of Bioinspired Optimization Algorithms -- 4.1 Flower Pollination Algorithm -- 4.2 Moth-Flame Optimizer -- 4.3 Whale Optimization Algorithm -- 4.4 Characteristics of Grey Wolf Optimizer -- 4.5 Grasshopper Optimization Algorithm -- 5 Simulations and Results -- 5.1 Simulated Datasets -- 5.1.1 Cole-Impedance Model -- 5.1.2 Fractional-Order Double-Shell Model -- 5.1.3 Fractional-Order Hayden Model -- 5.2 Experimental Datasets -- 5.2.1 Cole-Impedance Model -- 5.2.2 Fractional-Order Double-Shell Model -- 5.2.3 Fractional-Order Hayden Model -- 6 Conclusion -- Acknowledgments -- References -- Chapter 6: Fractional-Order Integrated Circuits in Control Applications and Biological Modeling -- 1 Introduction -- 2 Preliminaries -- 2.1 Definition of the Fractional Laplacian Operator -- 2.2 Approximation of the Fractional Laplacian Operator -- 2.2.1 Continued Fraction Expansion -- 2.2.2 Oustaloup's Method -- 2.2.3 Comparison of Results -- 3 Method for Realizing Fractional-Order Building Blocks -- 3.1 Fractional-Order Integrators/Differentiators -- 3.1.1 Preliminaries -- 3.1.2 Inverse-Follow-the-Leader-Feedback Topologies -- 3.1.3 OTA-C Filter Topology -- 3.1.4 OTAs With Electronic Tuning -- 3.2 Fractional-Order Capacitor/Inductor Emulation -- 4 Design of Integrated Fractional-Order Controllers -- 4.1 Preliminaries -- 4.2 Design of a Fractional-Order PID Controller for a DC Motor Control -- 4.2.1 Specifications of the DC Motor Controller -- 4.2.2 OTA-C Realization of the DC Motor Controller -- 4.2.3 Results of Simulation -- 4.3 Design of Fractional-Order Controller for Brake and Throttle Control in Autonomous Vehicles -- 4.3.1 Specifications of the Brake/Throttle Controller -- 4.3.2 OTA-C Realization of the Brake/Throttle Controller -- 4.3.3 Results of Simulation