Supervisor’s Foreword	7
	Parts of this thesis have been published in the following journal articles:	8
	Acknowledgements	9
	About the Author	10
	Contents	11
	Abbreviations	14
	1 Introduction	15
	1.1 State of the Art	16
	1.2 Motivation and Problem Statement	18
	1.3 Author's Contributions	19
	1.4 Thesis Outline	20
	References	22
	2 Preliminaries	25
	2.1 Mathematical Basis	25
	2.2 Fractional-Order Models	27
	2.2.1 Process Models	28
	2.2.2 Stability Analysis	28
	2.2.3 Time Domain Analysis	29
	2.2.4 Frequency Domain Analysis	30
	2.3 Approximation of Fractional-Order Operators	31
	2.4 Fractional-Order Controllers	31
	2.5 Optimization Methods	34
	2.5.1 Newton-Raphson Method	34
	2.5.2 Nonlinear Least-Squares Estimation Methods	34
	2.5.3 Nelder-Mead Method	35
	2.5.4 Optimization Problems with Bounds and Constraints	37
	References	39
	3 Identification of Fractional-Order Models	41
	3.1 System Identification Fundamentals	41
	3.2 Open-Loop Identification in the Time Domain	43
	3.2.1 Parametric Identification	45
	3.2.2 Residual Analysis	46
	3.3 Closed-Loop Identification in the Time Domain	50
	3.4 Frequency Domain Identification in Automatic Tuning Applications for Process Control	51
	3.5 Conclusions	58
	References	59
	4 Fractional-Order PID Controller Design	61
	4.1 Optimization Based Controller Design	61
	4.2 Gain and Order Scheduling	66
	4.3 Stabilization of Unstable Plants	68
	4.4 Retuning FOPID Control for Existing PID Control Loops	70
	4.5 Control Loop Analysis and Controller Design in the Frequency Domain ƒ	74
	4.5.1 Computation of Control System Characteristics	74
	4.5.2 FOPID Controller Design	81
	4.6 Conclusions	87
	References	88
	5 Implementation of Fractional-Order Models and Controllers	91
	5.1 An Update to Carlson's Approximation Method for Analog Implementations	91
	5.2 Efficient Analog Implementation of Fractional-Order Models and Controllers	99
	5.2.1 Approximation Methods	99
	5.2.2 Unified Approach to Fractance Network Generation	102
	5.3 Digital Implementation of Fractional-Order Controllers	104
	5.3.1 Discrete-Time Oustaloup Filter Approximation for Embedded Applications	104
	5.3.2 FOPID Controller Implementation	107
	5.3.3 FO Lead-Lag Compensator Implementation	108
	5.3.4 Controller Reset Logic	109
	5.4 Experimental Platform for Real-Time Closed-Loop Simulations of Control Systems	109
	5.5 Development of a Hardware FOPID Controller Prototype	111
	5.5.1 Atmel AVR Microcontroller Family Based Implementation	111
	5.5.2 STMicroelectronics STM32F407 Microcontroller Family Based Implementation	115
	5.6 Conclusions	117
	References	118
	6 FOMCON: Fractional-Order Modeling and Control Toolbox	120
	6.1 Overview of the Toolbox	120
	6.2 Identification Module	123
	6.3 Control Module	129
	6.4 Implementation Module	132
	6.5 Conclusions	139
	References	141
	7 Applications of Fractional-Order Control	143
	7.1 Fluid Level Control in a Multi Tank System	143
	7.1.1 Coupled Tanks System	144
	7.1.2 Multi-tank System	150
	7.2 Retuning Control of a Magnetic Levitation System	155
	7.2.1 Identification of the Nonlinear Model of the MLS	158
	7.2.2 FOPID Controller Design for the MLS	160
	7.2.3 Experimental Results	161
	7.3 Control of Ion-Polymer Metal Composite Actuator	163
	7.3.1 Identification of the Actuator Model	165
	7.3.2 FOPID Control	166
	7.3.3 FOINVM Based Control	168
	7.3.4 Hardware Implementation of the Controller	168
	7.4 Conclusions	175
	7.4.1 Multi Tank System	175
	7.4.2 Magnetic Levitation System	176
	7.4.3 IPMC Actuator	176
	References	178
	8 Conclusions	180
	References	184