Fractional Order Systems

Optimization, Control, Circuit Realizations and Applications

Ahmad Taher Azar, Ahmed G. Radwan, Sundarapandian Vaidyanathan

• Publisher: Academic Press
• Year: 2018
• Print ISBN: 9780128161524
• eBook ISBN: 9780128163085
• Topic: Technology & Engineering
• Subtopic: Mechanical Engineering
• Index: Technology & Engineering

Fractional Order Systems: Optimization, Control, Circuit Realizations and Applications 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, photovoltaic systems, robot manipulators, oscillators, etc. This book is ideal for researchers working in the modeling and applications of both continuous-time and discrete-time dynamics and chaotic systems. Researchers from academia and industry who are working in research areas such as control engineering, electrical engineering, mechanical engineering, computer science, and information technology will find the book most informative.- Discusses multi-disciplinary applications with new fundamentals, modeling, analysis, design, realization and experimental results- Includes new circuits and systems based on the new nonlinear elements- Covers most of the linear and nonlinear fractional-order theorems that will solve many scientific issues for researchers- Closes the gap between theoretical approaches and real-world applications- Provides MATLAB® and Simulink code for many of the applications in the book

Chapter 1

Dynamics, Circuit Design, Synchronization, and Fractional-Order Form of a No-Equilibrium Chaotic System

Viet-Thanh Pham*^,†; Sundarapandian Vaidyanathan^‡; Christos Volos^§; Xiong Wang^¶; Vo Hoang Duy^|; Ahmad Taher Azar**^{,†† *} School of Electronics and Telecommunications, Hanoi University of Science and Technology, Hanoi, Vietnam
^† Division of Dynamics, Lodz University of Technology, Lodz, Poland
^‡ Research and Development Center, Vel Tech University, Chennai, India
^§ Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, Greece
^¶ Institute for Advanced Study, Shenzhen University, Shenzhen, Guangdong, P.R. China
^| Modeling Evolutionary Algorithms Simulation and Artificial Intelligence, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam
^** Faculty of Computers and Information, Benha University, Benha, Egypt
^†† School of Engineering and Applied Sciences, Nile University, Giza, Egypt

Abstract

Systems without equilibrium such as electromechanical models with rotation and electrical circuits with cylindrical phase space were studied a long time ago. However, chaotic systems without equilibrium have received significant attention recently after the introduction of hidden attractors. Interestingly, an attractor of a no-equilibrium system is hidden because its basin of attraction does not intersect with any neighborhood of an unstable fixed point. This chapter presents a 3D no-equilibrium system with hidden chaotic attractors. The fundamental qualitative properties of the proposed no-equilibrium system are discovered by using phase portraits, Poincaré map, bifurcation diagram, and Lyapunov exponents. We have designed an electronic circuit to confirm the physical implementation of the theoretical no-equilibrium system. In addition, global chaos antisynchronization of the proposed system is investigated and confirmed by numerical simulations. Finally the fractional-order form of the proposed no-equilibrium chaotic system is studied in detail.

Keywords

Chaos; Chaotic systems; Hidden attr...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Contributors
• Preface
• Acknowledgments
• Chapter 1: Dynamics, Circuit Design, Synchronization, and Fractional-Order Form of a No-Equilibrium Chaotic System
• Chapter 2: FPGA Implementation of Fractional-Order Chaotic Systems
• Chapter 3: A Survey of Numerical Simulations for Multistrain Tuberculosis Models of Fractional-Order and Their Optimal Control
• Chapter 4: Fractional-Order Models for HIV Viral and Epidemiological Dynamics
• Chapter 5: Biologically Inspired Optimization Algorithms for Fractional-Order Bioimpedance Models Parameters Extraction
• Chapter 6: Fractional-Order Integrated Circuits in Control Applications and Biological Modeling
• Chapter 7: Bioimpedance Analysis Using Fractional-Order Equivalent Electrical Circuits
• Chapter 8: On the Approximation of Fractional-Order Circuit Design
• Chapter 9: On the Fractional-Order Circuit Design: Sensitivity and Yield
• Chapter 10: Survey on Two-Port Network-Based Fractional-Order Oscillators
• Chapter 11: On Linear and Nonlinear Electric Circuits: A Local Fractional Calculus Approach
• Chapter 12: Fractional-Order Filter Design
• Chapter 13: Analog Filters With Arbitrarily Adjustable Frequency Response
• Chapter 14: Memristive Fractional-Order Nonlinear Model for Circuit Design
• Chapter 15: Estimation Methods for Fractional-Order Systems: Asymptotic Versus Nonasymptotic Approaches
• Chapter 16: Control of a Three-Link Manipulator Using Fractional-Order PID Controller
• Chapter 17: Development of a Fractional-Order PID Controller Using Adaptive Weighted PSO and Genetic Algorithms With Applications
• Chapter 18: Fractional-Order PI Controller for Permanent Magnet Synchronous Motor: A Design-Based Comparative Study
• Chapter 19: Description of the Control Strategies by A-Fractional-Order Backward Difference
• Chapter 20: Conventional, Intelligent, and Fractional-Order Control Method for Maximum Power Point Tracking of a Photovoltaic System: A Review
• Chapter 21: A BSA Tuned Fractional-Order PID Controller for Enhanced MPPT in a Photovoltaic System
• Index