Fractional-order modeling and control of dynamic systems

• Main Author: Tepljakov, Aleksei (Author)
• Format: Electronic eBook
• Language: English
• Published: Cham, Switzerland : Springer, 2017.
• Series: Springer theses.
• Subjects: Fractional calculus.; Mathematical models.; elektronické knihy; electronic books
• ISBN: 9783319529509; 9783319529493
• Physical Description: 1 online resource

This book reports on an outstanding research devoted to modeling and control of dynamic systems using fractional-order calculus. It describes the development of model-based control design methods for systems described by fractional dynamic models. More than 300 years had passed since Newton and Leib...

Table of Contents:

• Supervisor's Foreword; Parts of this thesis have been published in the following journal articles:; Acknowledgements; About the Author; Contents; Abbreviations; 1 Introduction; 1.1 State of the Art; 1.2 Motivation and Problem Statement; 1.3 Author's Contributions; 1.4 Thesis Outline; References; 2 Preliminaries; 2.1 Mathematical Basis; 2.2 Fractional-Order Models; 2.2.1 Process Models; 2.2.2 Stability Analysis; 2.2.3 Time Domain Analysis; 2.2.4 Frequency Domain Analysis; 2.3 Approximation of Fractional-Order Operators; 2.4 Fractional-Order Controllers; 2.5 Optimization Methods.
• 2.5.1 Newton-Raphson Method2.5.2 Nonlinear Least-Squares Estimation Methods; 2.5.3 Nelder-Mead Method; 2.5.4 Optimization Problems with Bounds and Constraints ; References; 3 Identification of Fractional-Order Models; 3.1 System Identification Fundamentals; 3.2 Open-Loop Identification in the Time Domain; 3.2.1 Parametric Identification; 3.2.2 Residual Analysis; 3.3 Closed-Loop Identification in the Time Domain; 3.4 Frequency Domain Identification in Automatic Tuning Applications for Process Control; 3.5 Conclusions; References; 4 Fractional-Order PID Controller Design.
• 4.1 Optimization Based Controller Design4.2 Gain and Order Scheduling; 4.3 Stabilization of Unstable Plants; 4.4 Retuning FOPID Control for Existing PID Control Loops; 4.5 Control Loop Analysis and Controller Design in the Frequency Domain #x83;; 4.5.1 Computation of Control System Characteristics; 4.5.2 FOPID Controller Design; 4.6 Conclusions; References; 5 Implementation of Fractional-Order Models and Controllers; 5.1 An Update to Carlson's Approximation Method for Analog Implementations; 5.2 Efficient Analog Implementation of Fractional-Order Models and Controllers.
• 5.2.1 Approximation Methods5.2.2 Unified Approach to Fractance Network Generation; 5.3 Digital Implementation of Fractional-Order Controllers; 5.3.1 Discrete-Time Oustaloup Filter Approximation for Embedded Applications; 5.3.2 FOPID Controller Implementation; 5.3.3 FO Lead-Lag Compensator Implementation; 5.3.4 Controller Reset Logic; 5.4 Experimental Platform for Real-Time Closed-Loop Simulations of Control Systems; 5.5 Development of a Hardware FOPID Controller Prototype; 5.5.1 Atmel AVR Microcontroller Family Based Implementation.
• 5.5.2 STMicroelectronics STM32F407 Microcontroller Family Based Implementation5.6 Conclusions; References; 6 FOMCON: Fractional-Order Modeling and Control Toolbox; 6.1 Overview of the Toolbox; 6.2 Identification Module; 6.3 Control Module; 6.4 Implementation Module; 6.5 Conclusions; References; 7 Applications of Fractional-Order Control; 7.1 Fluid Level Control in a Multi Tank System; 7.1.1 Coupled Tanks System; 7.1.2 Multi-tank System; 7.2 Retuning Control of a Magnetic Levitation System; 7.2.1 Identification of the Nonlinear Model of the MLS; 7.2.2 FOPID Controller Design for the MLS.