Fractional Order Systems―Control Theory and Applications: Fundamentals and Applications (Studies in Systems, Decision and Control, 364)

✍ Scribed by Omar Naifar (editor), Abdellatif Ben Makhlouf (editor)

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 224
• Category: Library

✦ Synopsis

This book aims to bring together the latest innovative knowledge, analysis, and synthesis of fractional control problems of nonlinear systems as well as some related applications. Fractional order systems (FOS) are dynamical systems that can be modelled by a fractional differential equation carried with a non-integer derivative. In the last few decades, the growth of science and engineering systems has considerably stimulated the employment of fractional calculus in many subjects of control theory, for example, in stability, stabilization, controllability, observability, observer design, and fault estimation. The application of control theory in FOS is an important issue in many engineering applications. So, to accurately describe these systems, the fractional order differential equations have been introduced.

✦ Table of Contents

Preface
Contents
On the Stability of Caputo Fractional-Order Systems: A Survey
1 Introduction
2 Preliminaries
3 Stability of Caputo Fractional Differential Equations
3.1 Stability of Nonlinear Fractional Differential equations
3.2 Special Cases
4 Conclusion
References
Observers and Observability—Theory and Literature Overview
1 Introduction
2 Observers and Observability for Continuous-Time Linear Systems
2.1 Observability
2.2 Linear Observers
3 Observability and Observers for Nonlinear Systems
3.1 Observability
3.2 The Input Problem for Observability
3.3 Nonlinear Observers
4 Conclusion
References
A Brief Overview on Fractional Order Systems in Control Theory
1 Introduction
2 Stability Theory
3 Fractional-Order Systems
3.1 Motivation
3.2 Fractional-Order Systems in the Control Theory: A State of the Art
3.3 Preliminaries
4 Observers for Nonlinear Systems
4.1 The Lipschitz Nonlinearity
4.2 The One-Sided Lipschitz Nonlinearity
4.3 The Monotone Nonlinearity
5 Fault Diagnosis in Engineering Problems
5.1 Introduction and Motivation
5.2 Fault Classification
5.3 Fault Estimation in the Literature
6 Control of Dynamic Systems
6.1 The Stabilization Problem
6.2 The Model Reference Control Problem
7 Conclusion
References
State Estimation for Fractional-Order Systems
1 Introduction and Preliminaries
1.1 Introduction
1.2 Preliminaries
2 Robust State Estimation for a Class of Linear Uncertain Fractional-Order Systems
2.1 Motivation and Problem Formulation
2.2 Robust Observer Design
2.3 Simulation Results
3 New Observer Design for Nonlinear Fractional-Order Systems
3.1 Motivation and Problem Formulation
3.2 Observer Design for Lipschitz Fractional-Order Systems
3.3 Observer Design for One-Sided Lipschitz and Quasi One-Sided Lipschitz Fractional-Order Systems
4 Full-Order Unknown Input Observer Design for Fractional One-Sided Lipschitz Systems
4.1 Motivation and Problem Formulation
4.2 Robust State Estimation in the Presence of Unknown Inputs
4.3 Simulation Results
5 Reduced-Order Unknown Input Observer Design for Fractional One-Sided Lipschitz Systems
5.1 Motivation and Problem Formulation
5.2 Robust State Estimation in the Presence of Unknown Inputs
5.3 Simulation Results
6 Conclusion
References
Observer-Based Control for Fractional-Order Systems
1 Introduction
2 Preliminaries
3 Adaptive Stabilization for a Class of Uncertain Nonlinear Fractional-Order Systems
3.1 Motivation and Problem Formulation
3.2 Observer Design and Adaptive Feedback Controller Scheme
3.3 Simulation Results
4 Model-Reference Control for Linear Fractional-Order Systems
4.1 Motivation and Problem Formulation
4.2 Model-Reference Controller Design
4.3 Simulation Results
5 Conclusion
References
Fault Estimation for Nonlinear One-Sided Lipschitz Systems
1 Introduction and Preliminaries
1.1 Introduction
1.2 Preliminaries
2 Actuator Faults and Component Faults Estimation for Integer-Order One-Sided Lipschitz Systems
2.1 Motivation and Problem Formulation
2.2 Component and Actuator Fault Estimation Strategy
2.3 Simulation Results
3 Sensor Fault Estimation for Fractional-Order Descriptor One-Sided Lipschitz Systems
3.1 Motivation
3.2 Problem Formulation
3.3 Sensor Fault Estimation Strategy
3.4 Simulation Results
4 Conclusion
References
Fractional Order CRONE and PID Controllers Design for Nonlinear Systems Based on Multimodel Approach
1 Introduction
2 Multimodel Approach Principle
2.1 Fusion Principle
2.2 Validity Computation
3 Multimodel Control of a Nonlinear System
3.1 CRONE Controller
3.2 Fractional PI Controller
4 Conclusion
References
Design of Robust Fractional Predictive Control for a Class of Uncertain Fractional Order Systems
1 Introduction
2 Fractional Order Calculus
3 Robust Fractional Predictive Control Design
4 Global Optimization
4.1 Genetic Algorithm Method
4.2 RFPC Based of Genetic Algorithm
5 Practical Application to a Fractional Thermal System
5.1 Modeling and Identification
5.2 Controller Application
6 Conclusion
References
Constant Phase Based Design of Robust Fractional PI Controller for Uncertain First Order Plus Dead Time Systems
1 Introduction
2 Problem Statement
3 Design Approach
3.1 Case of Gain Uncertainty
3.2 Case of Time Delay Uncertainty
3.3 Case of Constant Time Uncertainty
3.4 Case of Uncertainties of All Parameters
4 Numerical Example
4.1 Case of Gain Uncertainty
4.2 Case of Time Delay Uncertainty
4.3 Case of Constant Time Uncertainty
4.4 Case of Uncertainties of All Parameters
4.5 Comparative Study
5 Conclusion
References
Identification of Continuous-Time Fractional Models from Noisy Input and Output Signals
1 Notation
2 Introduction
3 Preliminaries
4 Problem Formulation
4.1 Data Generating EIV Fractional System
4.2 Model Structure for EIV Fractional System Identification
5 Fractional System Parameters Estimation
5.1 Fractional Order Ordinary Least Squares Method
5.2 Fractional Order Bias Eliminated Least Squares Method
6 Fractional Order Estimation
7 Numerical Example
7.1 Data Generating
7.2 Choice of the SVF Parameters
7.3 Comparative Study
7.4 Fractional Order Estimation
8 Application to a Real Fractional Order Electronic System
8.1 Plant Description
8.2 System Identification
9 Conclusion
References