Fractional order systems : modeling and control applications / Riccardo Caponetto ... [and others].

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