TY  - BOOK
AU  - Caponetto,R.
TI  - Fractional order systems: modeling and control applications 
T2  - World Scientific series on nonlinear science. Series A, Monographs and treatises
SN  - 9789814304191
AV  - QC20.7.F75 F73 2010
PY  - 2010///]
CY  - Singapore, Hackensack, NJ
PB  - World Scientific
KW  - Fractional calculus
KW  - Mathematical physics
KW  - PID controllers
KW  - Mathematical models
KW  - Field programmable gate arrays
N1  - Includes bibliographical references (pages 167-175) and index; Contents;  	Preface;  	Acknowledgments;  	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 PM Controller and their Stability Regions Definition;  	2.1 Introduction;  	2.2 Problem Characterization;  	2.3 Theory for Analyzing Systems with Time Delays;  	2.3.1 Hermite-Biehler Theorem;  	2.3.2 Pontryagin Theorem;  	2.4 Stability Regions with PIλ Dμ Controller;  	2.5 Results; 3.	Fractional Order Chaotic Systems;  	3.1 Introduction;  	3.2 Concept of Chua's System;  	3.2.1 Classical Chua's Oscillator;  	3.2.2 Chua-Hartley's Oscillator;  	3.2.3 Chua-Podlubny's Oscillator;  	3.2.4 New Fractional-Order Chua's Oscillator;  	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;  	3.11.1 Integer-Order Volta's System;  	3.11.2 Fractional-Order Volta's System; 4.	Field Programmable Gate Array Implementation;  	4.1 Numerical Fractional Integration;  	4.2 Griinwald-Letnikov Fractional Derivatives;  	4.3 The "Short-Memory" Principle;  	4.4 FPGA Hardware Implementation;  	4.4.1 FPGA Introduction;  	4.4.2 Remarks on the Fractional Differintegral Operator;  	4.4.3 FPGA Implementation of the Fractional Differintegral Operator; 5.	Microprocessor Implementation and Applications;  	5.1 Introduction;  	5.2 Fractional Controller Realized by PIC Processor;  	5.2.1 Fractional-Order Integrator;  	5.2.2 Measured Results;  	5.3 Temperature Control of a Solid by PC and PCL 812;  	5.3.1 Model of Controlled System;  	5.3.2 Controller Parameters Design and Implementation;  	5.3.3 Experimental Setup and Results;  	5.4 Temperature Control of a Heater by PLC BR 2005;  	5.4.1 Model of Controlled System;  	5.4.2 Controller Parameters Design and Implementation;  	5.4.3 Experimental Setup and Results;  	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;  	7.4.1 The Impulse Invariance Method;  	7.4.2 The Matched-z Transformation Method;  	7.4.3 Backward Euler Approximation of Derivatives;  	7.4.4 Forward Euler Approximation of Derivatives;  	7.4.5 The Bilinear Transformation Method;  	7.4.6 The Lossless Discrete Integrator Transformation;  	7.5 Switched Capacitor Fundamental Circuits;  	7.5.1 Resistor Realized by Backward Euler Transformation;  	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;  	8.7.1 Comparison Between an Integer Model and a Fractional Model of IPMC Actuators;  	8.7.2 Fractional Models for the Electrical and Electromechanical Stages of IPMC Actuators;  	Bibliography;  	Index
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