New Trends in Nanotechnology and Fractional Calculus Applications

Preface

Contents

Part I New Trends in Nanotechnology

Novel Molecular Diodes Developed by Chemical Conjugation of Carbon Nanotubes with Peptide Nucleic Acid

References

Hybrid Single Walled Carbon Nanotube FETs for High Fidelity DNA Detection

1 Introduction

2 Experimental Section

2.1 SWNT Purification and Dispersion

2.2 Device Fabrication

2.3 Synthesis of SWNT-ssDNA Conjugations and Detection of Specific DNA Sequences

3 Results and Discussion

4 Conclusion

References

Towards Integrated Nanoelectronic and Photonic Devices

1 Introduction

2 Integrated Electronic Devices

2.1 Scaling of MOSFET Devices

2.2 Nanotube Transistors and Interconnects

2.3 Ultimate Integrated Devices Based on Graphene

3 Photonic Devices and Interconnects

3.1 Optical Interconnects

3.2 Photonic sources and Bragg Reflectors

3.3 Photonic Crystal Waveguides

4 Summary

References

New Noninvasive Methods for `Reading' of Random Sequences and Their Applications in Nanotechnology

1 Introduction

2 Procedure of the Optimal Linear Smoothing (POLS)

3 The Statistics of the Fractional Moments and Detection of the Statistical Proximity

4 The Universal Distribution Function of the Relative Fluctuations

5 Brief Description of Problems that Can Be Solved by These Noninvasive Methods

5.1 Comparison with Pattern Equipment and Self-Verification of the Readiness of Complex Equipment to Measurements

5.2 The Diagnosis of Deceases Based on Quantitative ``Reading'' of Noises, Which Are Registered Inside a Human Body

5.3 The Increasing of Sensitivity of Existing Spectrometers and Creation of Supersensitive Gas-Sensors and Chromatographers

5.4 Applications to Different Nanotechnologies

References

Quantum Confinement in Nanometric Structures

1 Introduction

2 2D Structures

3 1D Structures

4 0D Structures

5 Conclusions

References

Part II Techniques and Applications

Air-Fuel Ratio Control of an Internal Combustion Engine Using CRONE Control Extended to LPV Systems

1 Introduction

2 CRONE Control Principles

2.1 Template Definition

2.2 Open Loop Transfer Function Including the Template

2.3 Parameterization of Optimal Open Loop

2.4 Optimization for Optimal Open Loop Determination

2.5 Parametric Synthesis of the Controller

3 CRONE Control of LPV Systems

3.1 Principles

3.2 LPV Plant Representation

3.3 LPV CRONE Controller Structure

3.4 Objectives and Constraints

4 Lambda Control of an IC Engine

4.1 Presentation and Motivation

4.2 Model Description

4.3 Delay Approximation

4.4 Results

4.5 Simulation

5 Conclusion

References

Non Integer Order Operators Implementation via Switched Capacitors Technology

1 Circuital Implementation of Fractional Order Integrator

2 Switched Capacitors Implementation of Fractional Order Integrator

2.1 Switched Capacitors Introduction

2.2 Switched Capacitors Implementation

3 Results

4 Conclusion

References

Analysis of the Fractional Dynamics of an Ultracapacitorand Its Application to a Buck-Boost Converter

1 Introduction

2 Ultracapacitor Model

3 Buck-Boost Converter

4 Simulation Results

5 Conclusions

References

Approximation of a Fractance by a Network of Four Identical RC Cells Arranged in Gamma and a Purely Capacitive Cell

1 Introduction

2 Fractional Dynamic System

3 Forced Response

4 Free Response

5 Conclusion

References

Part III Mathematical Tools

On Deterministic Fractional Models

1 Introduction

2 Fractional Integral and Differential Operators

3 Time-Fractional Derivative: An Application of Fractional Differential Operators in Modeling Subdiffusive and Superdiffusive Problems

4 Fractional Dynamics Systems

4.1 Linear Case Using the Caputo Fractional Derivative

4.2 Quasi-Linear Case Using the Caputo Fractional Derivative

4.3 Conclusion

4.4 Examples

4.5 Applications

5 Spatial–Fractional Derivative: Anomalous Diffusion

5.1 Spatial–Fractional Diffusion Equation

6 Fractional Differential Equations and Chaos

References

A New Approach for Stability Analysis of Linear Discrete-Time Fractional-Order Systems

1 Introduction

2 Linear Discrete-Time Fractional-Order Systems

3 Asymptotic Stability

4 Numerical Example

5 Conclusion

References

Stability of Fractional-Delay Systems: A Practical Approach

1 Introduction

2 The Proposed Numerical Algorithm

3 Numerical Example

References

Comparing Numerical Methods for Solving Nonlinear Fractional Order Differential Equations

1 Introduction

2 Numerical Methods

2.1 Quadrature Method (QM)

2.2 Predictor Corrector Method (PCM)

2.3 Fixed Length Integral Principle (FLIP)

2.4 Nested Memory Principle (NMP)

2.5 Higher Order Methods (Lubich)

2.6 Kumar Agrawal Method (KAM)

3 Numerical Simulations

4 Conclusions

References

Fractional-Order Backward-Difference Definition Formula Analysis

1 Introduction

2 Mathematical Preliminaries

2.1 Notation

2.2 Fractional-Order Backward-Difference/Sum

3 Relation Between Coefficients ai()

3.1 Numerical Example

4 Coefficients ai() Values Analysis

5 Coefficients ai() Increasing Rate

6 Concluding Remarks

References

Fractional Differential Equations on Algebroids and Fractional Algebroids

1 Introduction

2 Rabinovich Equations on a Leibniz Algebroid

3 Fractional Rabinovich Equations

4 The Fractional Equations on a Fractional Leibniz Algebroid

5 Numerical Simulations and Conclusions

References

Generalized Hankel Transform and Fractional Integralson the Spaces of Generalized Functions

1 Introduction

2 Notations and Definitions

2.1 Notations

2.2 The Spaces Fp, and Their Duals

3 Fractional Integrals

4 Generalized Hankel Transform on Fp,

5 GHT of Fractional Integrals on Fp,

6 Fractional Integral of GHT on Fp,

7 Concluding Remarks

References

Some Bounds on Maximum Number of Frequencies Existing in Oscillations Produced by Linear Fractional Order Systems

1 Introduction

2 Problem Statement

3 An Upper Bound

4 A Lower Bound

5 Conclusion

References

Fractional Derivatives with Fuzzy Exponent

1 Introduction

2 Fuzzy Sets and Numbers

3 Ordered Fuzzy Numbers

4 Fuzzy Fractional Derivative

5 Conclusions

References

Game Problems for Fractional-Order Systems

1 Fractional-Order Systems

2 Game Problems

3 Example

References

Synchronization Analysis of Two Networks

1 Introduction

2 Synchronization Analysis

3 Numerical Examples

3.1 Directed Connection

3.2 Undirected Connection

4 Conclusion

References

Part IV Fractional Modelling

Modeling Ultracapacitors as Fractional-Order Systems

1 Introduction

2 Modeling and Identification

3 Experiment and Results

4 Circuit Realization

5 Conclusions

References

IPMC Actuators Non Integer Order Models

1 Introduction

2 Experimental Setup

3 Experimental Results

4 Conclusion

References

On the Implementation of a Limited Frequency Band Integrator and Application to Energetic Material Ignition Prediction

1 Introduction

2 A Model to Predict Energetic Materials Ignition

3 A Testbench for Ignition Prediction Model Validation

4 Fractional Integration Algorithm

4.1 Fractional Integration Numerical Method Specifications

4.2 Algorithm Description

5 Application to Ignition Prediction of Energetic Materials

5.1 Implementation Description

5.2 Some Rules of Thumb

5.3 Reference Signal Computation

5.4 Application and Result Analysis

6 Conclusion

References

Fractional Order Model of Beam Heating Processand Its Experimental Verification

1 Introduction

1.1 Transfer Function e(Ts) and Its Bode Diagram

2 Mathematical Description of Heating Process

3 Experimental Verification of Heating Process Model

3.1 Experimental Setup

3.2 Thermoelectric Module – Peltier Module

3.3 Modelling Results

4 Conclusion

References

Analytical Design Method for Fractional Order Controller Using Fractional Reference Model

1 Introduction

2 Fractional Order Systems

3 The Proposed Design Method

4 Illustrative Example

5 Conclusions

References

On Observability of Nonlinear Discrete-Time Fractional-Order Control Systems

1 Introduction

2 Fractional Discrete-Type Calculus

3 Observability Concepts

4 Fractional Order and Observability for Two-Dimensional Systems

References

Chaotic Fractional Order Delayed Cellular Neural Network

1 Introduction

2 Fractional Operators and its Approximation

3 Fractional Order Delayed Cellular Neural Network

4 Chaos in the Fractional Order Delayed Cellular Neural Network

5 Conclusions

References

Fractional Wavelet Transform for the Quantitative Spectral Analysis of Two-Component System

1 Introduction

2 Signal Processing Method

2.1 B-spline

2.2 Fractional B-spline

2.3 Fractional B-spline Wavelets

3 Experimental

3.1 Apparatus and Software

3.2 Preparation of Standard Solutions

3.3 Commercial Veterinary Products

4 Method Applications

4.1 Fractional Wavelet Transform of the Absorption Spectra

4.2 Calibration Graphs

4.3 Method Validation

4.4 Analysis of the Commercial Veterinary Formulation

5 Conclusions

References

Fractional Wavelet Transform and Chemometric Calibrations for the Simultaneous Determination of Amlodipineand Valsartan in Their Complex Mixture

1 Introduction

2 Experimental

2.1 Instruments and Software

2.2 Commercial Tablet Preparation

2.3 Standard Solutions

2.4 Preparation of the Commercial Tablet Samples

3 Results and Discussions

3.1 PLS Calibration Models and Prediction

3.2 Method Applications to Tablet Samples

4 Conclusions

References

Part V Fractional Control Systems

Analytical Impulse Response of Third Generation CRONE Control

1 Introduction

2 Third Generation CRONE Control

3 Analytical Response Using Residue Method

3.1 Integration upon 2 and 6 Curves

3.2 Integration upon 3 and 5 Curves

3.3 Integration upon 4 Curve

4 Poles Characterization

5 Analytical Impulse Response

6 Simulations

7 Conclusion

Appendix

References

Stability Analysis of Fractional Order Universal Adaptive Stabilization

1 Introduction

2 Preliminaries

2.1 Fractional Calculus and Mittag–Leffler Function

2.2 Nussbaum Function

3 Stability Analysis of Fractional UAS

3.1 Fractional Dynamics with Integer-Order Control Strategy

3.2 Fractional Dynamics with Fractional Control

3.3 Application of Viscoelastic and Electromagnetic Theories in UAS

4 Nussbaum Function with Mittag–Leffler Form

5 Simulations

6 Conclusion

References

Position and Velocity Control of a Servo by Using GPCof Arbitrary Real Order

1 Introduction

2 Generalized Predictive Control

2.1 Introduction

2.2 Fractional-Order Generalized Predictive Control

3 System Description

4 Controllers Design and Results

4.1 Velocity Control

4.2 Position Control

5 Conclusions

References

Decentralized CRONE Control of mxn Multivariable System with Time-Delay

1 Introduction

2 Mathematical Backgrounds

3 CRONE Control Methodology and MIMO Systems

3.1 Definition of the Diagonal Open-Loop Transfer Function Elements

3.2 Decoupling and Optimised Controller

3.3 Research of Time-Delay of Each Open-Loop

3.4 Open-Loop Transfer Matrix Optimization

3.5 Decentralized CRONE Controller

4 Application

4.1 Research of Time-Delay

4.2 Specifications

4.3 Optimisation

4.4 Results

5 Conclusion

References

Fractional Order Adaptive Control for Cogging Effect Compensation

1 Introduction

2 Fractional Order Adaptive Compensation of Cogging Effect

2.1 Motivations and Problem Formulation

2.2 Stability Analysis of Integer Order Case

2.3 Stability Analysis of the Fractional Order Case

3 Simulation Illustrations Using PMSM Position Servo System Model

3.1 Case-1: Integer Order Adaptive Compensation for Multi-Harmonics Cogging Effect

3.2 Case-2: Fractional Order Adaptive Compensation for Multi-Harmonics Cogging Effect

4 Chapter Conclusion

References

Generalized Predictive Control of Arbitrary Real Order

1 Introduction

2 Generalized Predictive Control

3 Some Mathematical Results

4 Fractional-Order Generalized Predictive Control

5 FGPC: An Application Example

6 Conclusions

References

Frequency Response Based CACSD for Fractional Order Systems

1 Introduction

2 Graphical Interface

3 Generalized Order Transfer Function

4 Illustrative Examples

4.1 Ventilatory Support in COPD Patients

4.2 Ventilation in Anesthetised Animals

5 Conclusions

References

Resonance and Stability Conditions for Fractional Transfer Functions of the Second Kind

1 Introduction

2 Stability of Fractional Transfer Functions of the Second Kind

2.1 Case || 1

2.2 Case || < 1

2.2.1 Subcase -1<0

2.2.2 Subcase 0 < 1

2.3 Summary

3 Resonance of Fractional Transfer Functions of the Second Kind

4 Open-Loop – Closed-Loop Analysis

5 Numerical Examples

5.1 Example 1

5.2 Example 2

6 Conclusion

References

Synchronization of Fractional-Order Chaotic Systemvia Adaptive PID Controller

1 Introduction

2 Adaptive PID Controller Design

3 Synchronization of Uncertain Hard Spring 6-Van der Pol Oscillator

3.1 System Description

3.2 Implementation

4 Conclusion

References

On Fractional Control Strategy for Four-Wheel-Steering Vehicle

1 Introduction

2 Improvement of Feedforward Control for 4WS Vehicle by Introducing of Fractional Derivative

2.1 Two Degrees of Freedom Vehicle Model

2.2 Fractional Order Feedforward Control Strategy

3 Yaw Feedback Control for 4WS Vehicle

3.1 Fractional Order Control Strategy with Yaw Feedback

3.2 Yaw Rate Tracking Control Strategy for 4WS Vehicle

4 Computational Simulation

5 Conclusion

References

Fractional Order Sliding Mode Controller Designfor Fractional Order Dynamic Systems

1 Introduction

2 Integer Order VSC for Integer Order Systems

3 Fractional Order VSC for Fractional Order State Space Systems

4 Two Application Examples

4.1 A Second Order System (Two State Variables)

4.2 A Third Order System (Three State Variables)

5 Concluding Remarks

References

A Fractional Order Adaptation Law for Integer Order Sliding Mode Control of a 2DOF Robot

1 Introduction

2 Robot Dynamics and the Control Problem

3 Sliding Mode Control Through a Fractional Order Adaptation Scheme

4 Simulation Results

5 Conclusions

References

Synchronization of Chaotic Nonlinear Gyros Using Fractional Order Controller

1 Introduction

2 System Description

3 Synchronization of Fractional Modelled System by Fractional PD SMC

4 Fuzzy Controller

5 Conclusion

References

Nyquist Envelope of Fractional Order Transfer Functionswith Parametric Uncertainty

1 Introduction

2 Construction of the Value Set of FOIP

3 Nyquist Envelope of FOITF

4 A Numerical Example

5 Conclusions

References

Synchronization of Gyro Systems via Fractional-Order Adaptive Controller

1 Introduction

2 Fractional Adaptive Controller Design

3 Synchronization of Uncertain Fractional-Order Gyro System

3.1 System Description

3.2 Implementation

4 Conclusion

References

Controllability and Minimum Energy Control Problemof Fractional Discrete-Time Systems

1 Introduction

2 Fractional Systems

3 Controllability

4 Minimum Energy Control

5 Concluding Remarks

References

Control of Chaos via Fractional-Order State Feedback Controller

1 Introduction

2 Stability Analysis For Fractional-Order Systems

3 Proposed Controller Design

3.1 Simple Fractional Controller

3.2 State Feedback Controller

3.3 Combination of State Feedback and Fractional-Order Controllers

3.4 The Stability Analysis

4 Implementation of Proposed Controller in Genesio-Tesi Chaotic System

5 Conclusion

References

Index