Intelligent Fractional Order Systems and Control : An Introduction.

Title -- Dedication -- Preface -- Contents -- Motivation for Application of Computational Intelligence Techniques to Fractional Calculus Based Control Systems -- Introduction -- References -- Applied Fractional Calculus for Computational Intelligence Researchers -- Requirement of Fractional Order Calculus -- Some Important Functions in Context of Fractional Calculus -- Gamma Function -- Beta Function -- Mittag-Leffler Function -- Miller-Ross Function -- Definitions of Fractional Differ-Integrals -- Grünwald-Letnikov (G-L) Definition -- Riemann-Liouville (R-L) Definition -- Caputo Definition -- Equivalence between the Definitions -- Some Properties of Fractional Differ-Integrals -- Laplace Transform of Fractional Differ-Integrals -- Basics of Laplace Transform -- Laplace Transform for Fractional Integrals -- Laplace Transform for Fractional Derivatives -- Fourier Transform of Fractional Differ-Integrals -- Basics of Fourier Transform -- Fourier Transform for Fractional Integrals -- Fourier Transform for Fractional Derivatives -- Realization of Fractional Order Differ-Integrators -- Continuous Time Realization -- Discrete Time Realization -- Time Domain Simulation Methods for Fractional Order Systems -- Fractional Order Systems -- Fractional Order LTI Systems -- Fractional Order Nonlinear Systems -- Stability of Fractional Order Systems -- Stability of FO LTI Systems -- Stability of FO Nonlinear Systems -- Fractional Order Controllers -- Family of Fractional Order PID Controllers -- CRONE Controllers -- Fractional Lead-Lag Compensator -- Concept of Iso-damping Using FO Controllers -- Effect of Controller Knob Variation of a Well-Tuned Control Loop -- Controller Tuning Methods for FOPID Controllers -- References -- Brief Introduction to Computational Intelligence Paradigms for Fractional Calculus Researchers -- Introduction.

Artificial Neural Networks -- Network Architecture and Training Methods -- Neural Networks in Control -- Fuzzy Logic -- Use of Fuzzy Logic in Control Applications -- Global Optimization Using Evolutionary and Swarm Algorithms -- Why Bio-inspired Algorithms over Other Conventional Techniques? -- Genetic Algorithms: Key Concepts and Attributes -- Brief Theory of Genetic Algorithms -- Genetic Programming -- Use of Bio-inspired Algorithms in Control Applications -- Synergism between Various Paradigms -- References -- Fractional Order Controller Tuning Using Swarm and Evolutionary Algorithms -- Introduction -- Optimizing a Multimodal Function with Particle Swarm Optimization -- Outline of Particle Swarm Optimization -- Optimizing a Function with PSO -- A MIMO Process Control Application Example -- Background of the Problem -- Objective Function and Optimization Algorithm -- Results and Discussions -- Application to Networked Control Systems -- Background of the Problem -- Control over Communication Network and Scope for Stochastic Optimization Based Controller Tuning -- Evolutionary Algorithms Based PID/FOPID Controller Tuning -- Simulations and Results -- MATLAB Based Simulation Study of a NCS with Packet Dropout and Variable Delay -- Optimal PID and FOPID Controller Tuning for Unstable Processes with the Consideration of Randomness in Network Induced Delays and Packet Dropouts -- Effect of Delay Distribution on the Tuned Networked FOPID Control Loops -- Validation of the Tuning Methodology for Lesser Complicated FOPTD Processes -- Summary -- References -- Multi-objective Fractional Order Controller Design with Evolutionary Algorithms -- Introduction to the Optimization Problem -- The AVR System with FO Controller -- Contradictory Objective Functions for Optimization -- Multi-objective Chaotic Non-dominated Sorting Genetic Algorithm II (NSGA-II).

Results and Discussions -- Robustness Analysis of Obtained Solutions -- Conclusions -- References -- Gain and Order Scheduling for Fractional Order Controllers -- Introduction -- A Networked Control System Application -- Problem Formulation -- Results and Discussions -- Summary -- References -- Enhancement of Fuzzy PID Controller with Fractional Calculus -- Introduction -- Review of the Existing Intelligent Tuning Techniques of FO Controllers -- New Fractional Order Fuzzy PID Controller and Its Time Domain Optimal Tuning -- Structure of Fractional Order Fuzzy PID Controller -- Membership Functions and Rule Base -- Formulation of the Objective Functions for Time Domain Optimal Controller Tuning -- Optimization Algorithm Used for the Tuning of Optimal Controllers -- Simulations and Results -- Nonlinear Process with Time Delay -- Unstable Process with Time Delay -- Comparative Performance Analysis of the Different Controllers and Few Discussions -- Conclusion -- References -- Model Reduction and Analytical Rule Extraction with Evolutionary Algorithms -- Background -- An Improved Sub-optimal Model Reduction Technique -- New Optimization Framework for Model Reduction in Nyquist Plane -- Model Reduction of a Test-Bench of Higher Order Processes -- Generation of Time Domain Optimal Controller Tuning Rule -- Controller Structure and Objective Function for Tuning -- Application of Genetic Algorithm for Optimal Controller Tuning -- Genetic Programming Based Analytical Tuning Rule Extraction for PID/PIλDμ Controllers -- Visualization of the Optimal PID/FOPID Tuning Rules -- Optimal FOPID Tuning Rules -- Optimal PID Tuning Rules -- Performance of the Analytical Tuning Rules -- Effect of Plant Perturbation on the Tuning Rules -- Summary -- References -- Model Reduction of Higher Order Systems in Fractional Order Template -- Introduction.

Reduced Order Modeling: Review of the Existing Methodologies -- New Approach towards Reduced Parameter FO Modeling of Higher Order Processes Using H2 Norm Based Method -- FO Model Reduction of Higher Order Processes Using Nyquist Based Technique -- Summary -- References -- Global Optimization Based Frequency Domain Design of Fractional Order Controllers with Iso-damping Characteristics -- Introduction -- Frequency Domain Design of PID/FOPID Controllers Using Global Optimization -- Frequency Response of the Reduced Order Process Models and Controllers -- First Order Plus Time Delay (FOPTD) Model -- Second Order Plus Time Delay (SOPTD) Model -- One Non-Integer Order Plus Time Delay (NIOPTD-I) Model -- Two Non-Integer Orders Plus Time Delay (NIOPTD-II) Model -- Integer Order Proportional Integral Derivative (IOPID) Controller -- Fractional Order Proportional Integral Derivative (FOPID) Controller -- Illustrative Examples -- Control of FOPTD Plant -- Control of NIOPTD-II Plant -- Summary -- References -- Chaos Synchronization with a Fractional Order Controller and Swarm Intelligence -- Introduction -- Master-Slave Synchronization between Two Chaotic Lu Systems -- Optimal PID and PIλDμ Controller Design for Chaos Synchronization -- Basics and Customization of Bacterial Foraging Optimization Algorithm -- Chemotaxis -- Swarming -- Reproduction -- Elimination-Dispersal -- Results and Discussions -- Conclusion -- References.

As fractional order calculus attracts interest in the control system community, this book explores the interface between CI techniques and fractional calculus, examining ways that fractional order control systems may be designed or enhanced using CI paradigms.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.