"Doctoral thesis accepted by Tallinn University of Technology, Tallinn, Estonia."

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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.

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 Leibniz developed a set of mathematical tools we now know as calculus. Ever since then the idea of non-integer derivatives and integrals, universally referred to as fractional calculus, has been of interest to many researchers. However, due to various issues, the usage of fractional-order models in real-life applications was limited. Advances in modern computer science made it possible to apply efficient numerical methods to the computation of fractional derivatives and integrals. This book describes novel methods developed by the author for fractional modeling and control, together with their successful application in real-world process control scenarios.