Riccardo Caponetto, Giovanni Dongola, Luigi Fortuna, Ivo Petráš. Fractional order systems modeling and Control Applications

Монография, 2010, World Scientific Publ., Singapore, 196с.
This book is devoted to fractional order systems, their applications to modelling and control. It is based on derivatives and integrals of arbitrary (real) order, fractional differential equations and methods of their solution, approximations and implementation techniques.
The advantages of fractional calculus have been described and pointed out in the last few decades by many authors. It has been shown that the fractional order models of real systems are regularly more adequate than usually used integer order models.
Applications of these fractional order models are in many fields, as for example, rheology, mechanics, chemistry, physics, bioengineering, robotics and many others.
At the same time, fractional integrals and derivatives are also applied to the theory of control of dynamical systems, when the controlled system and/or the controller is described by fractional differential equations.
The main goal of the book is to present applications and implementations of fractional order systems. It provides only a brief theoretical introduction to fractional order system dedicating almost all the space to the modelling issue, fractional chaotic system control and fractional order
controller theory and realization.
The book is suitable for advanced undergraduates and graduate students.Acknowledgements
List of Figures
List of Tables
1. Fractional Order Systems
1.1 Fractional Order Differintegral Operator: Historical Notes
1.2 Preliminaries and Definitions
1.3 Laplace Transforms and System Representation
1.4 General Properties of the Fractional System
1.5 Impulse Response of a General Fractional System
1.6 Numerical Methods for Calculation of Fractional Derivatives and Integrals
1.7 Fractional LTI Systems
1.8 Fractional Nonlinear Systems
1.9 Stability of Fractional LTI Systems
1.10 Stability of Fractional Nonlinear Systems
2. Fractional Order PID Controller and their Stability Regions Definition
2.1 Introduction
2.2 Problem Characterization
2.3 Theory for Analyzing Systems with Time Delays
2.4Stability Regions with P I λ Dμ Controller
2.5Results
3.Fractional Order Chaotic Systems
3.1Introduction
3.2 Concept of Chua’s System
3.3 Fractional-Order Van der Pol Oscillator
3.4 Fractional-Order Duffing’s Oscillator
3.5 Fractional-Order Lorenz’s System
3.6 Fractional-Order Genesio-Tesi System
3.7 Fractional-Order Lu’s System
3.8 Fractional-Order Rossler’s System
3.9 Fractional-Order Newton-Leipnik System
3.10 Fractional-Order Lotka-Volterra System
3.11 Concept of Volta’s System
4. Field Programmable Gate Array Implementation
4.1 Numerical Fractional Integration
4.2 Gr ̈unwald-Letnikov Fractional Derivatives
4.3 The Short-Memory Principle
4.4 FPGA Hardware Implementation
5. Microprocessor Implementation and Applications
5.1 Introduction
5.2 Fractional Controller Realized by PIC Processor.
5.3 Temperature Control of a Solid by PC and PCL 812
5.4 Temperature Control of a Heater by PLC BR 2005
5.5 Concluding Remarks
6. Field Programmable Analog Array Implementation
6.1 The FPAAs Development System
6.2 Experimental Results
7. Switched Capacitor Integrated Circuit Design
7.1 Introduction
7.2 Passive and Active Filters
7.3 Switched Capacitors Filters
7.4 Design of Sampled Data Filters
7.5 Switched Capacitor Fundamental Circuits
7.6 Circuital Implementation of the Fractional Order Integrator
7.7 Switched Capacitors Implementation of Fractional Order Integrator
7.8 Results
8. Fractional Order Model of IPMC
8.1 Fractional Model Identification Introduction
8.2 Ionic Polymer Metal Composites (IPMC)
8.3 Actuation Mechanism on IPMCs
8.4 State-of-the-Art for IPMC Models
8.5 Experimental Setup
8.6 Marquardt Algorithm for the Least Squares Estimation
8.7 Fractional Models for IPMC Actuators