The book investigates the fractional calculus-based approaches and their benefits to adopting in complex real-time areas. Another objective is to provide initial solutions for new areas where fractional theory has yet to verify the expertise. The book focuses on the latest scientific interest and illustrates the basic idea of general fractional calculus with MATLAB codes. This book is ideal for researchers working on fractional calculus theory both in simulation and hardware. Researchers from academia and industry working or starting research in applied fractional calculus methods will find the book most useful. The scope of this book covers most of the theoretical and practical studies on linear and nonlinear systems using fractional-order integro-differential operators.
Author(s): Utkal Mehta, Kishore Bingi, Sahaj Saxena
Series: Studies in Infrastructure and Control
Publisher: Springer
Year: 2022
Language: English
Pages: 211
City: Singapore
Preface
Contents
About the Editors
1 Fractional Calculus for Multivariate Vector-Valued Function and Fractal Function
1 Introduction
2 Katugampola Fractional Integral of a Multivariate Vector-Valued Function
3 Fractional Derivative of a Fractal Function
4 Conclusion
References
2 Synchronization of Stochastic Fractional Chaotic Systems
1 Introduction
2 Preliminaries
3 Main Results
4 Examples
5 Conclusion
References
3 Fractional-Order Comb Filter Design For Power-Line Interference Removal
1 Introduction
2 Background of Fractional-Order Filter Design
3 Proposed Approach for Fractional-Order Comb Filter
4 Design and Verification
5 Conclusions
References
4 Practical Realization of Fractional-Order Notch Filter with Asymmetric Slopes and Optimized Quality Factor
1 Introduction
2 Fractional-Order Notch Filter
3 Optimizing Filter Coefficients for Real-Time Implementation
4 Simulation and Experimental Study
5 Conclusions
References
5 Fractional Order Modified IMC for Integrating Processes for Given Stability Margins and Increased Closed Loop Bandwidth
1 Introduction
2 Controller Design
2.1 Process-1
2.2 Process-2
2.3 Evaluation of Controller Parameters
2.4 Solution Philosophy
2.5 Finding beta Subscript a Baseline element of normal upper Delta Subscript aβa inΔa
2.6 Finding beta Subscript b Baseline element of normal upper Delta Subscript bβb inΔb
3 Simulation Examples
3.1 Example-1
3.2 Example-2
4 Discussions and Conclusions
References
6 Internal Model Control-Based Fractional Order Controller Design for Process Plants Satisfying Desired Gain Margin and Phase Margin
1 Introduction
1.1 Motivation to Not Approximating the Delay Term in IMC
2 Internal Model Controller
2.1 upper A Subscript mAm and phi Subscript mφm Specifications
2.2 Design Philosophy
2.3 Finding omega Subscript p Baseline element of normal upper Xi Subscript aωpinΞa
2.4 Finding omega Subscript g Baseline element of normal upper Xi Subscript bωg inΞb
2.5 Disturbance Rejection Analysis
2.6 Algorithm for Determining FO-IMC Controller Parameters
3 Simulation Studies and Experimental Validation
3.1 Example-I
3.2 Example-II
3.3 Example-III
3.4 Experimental Validation
4 Discussion and Conclusion
References
7 Novel Hybrid Iterative Learning–Fractional Predicative PI Controller for Time-Delay Systems
1 Introduction
2 Methodology
2.1 Controller Evolution
2.2 Iterative Learning Control
3 Results and Discussion
3.1 Process Model Selection
3.2 L- and Q-Filter Parameters Identification
3.3 FOPDT Process Model
3.4 SOPDT Process Model
3.5 Summary
4 Conclusion
References
8 Design of Robust Model Predictive Controller for DC Motor Using Fractional Calculus
1 Introduction
2 Modeling of DC Motors with a Fractional Order
3 Design of Fractional Model Predictive Controller (FMPC) for DC Motor Model
4 Checking the Robustness of the Response of the Fractional-Order Model
5 Conclusion
References
9 Studying Fractional-Order Controller Structures for Load Frequency Control of Interconnected Multiple Source Power System
1 Introduction
2 Concept Explanation
2.1 Chosen Application
3 Control Optimization Method
3.1 Bubble Net Attacking Method
3.2 Robust Tuning Performance Index
4 Analysis
4.1 Load Disturbance Approach—Scenario 1
4.2 Load Disturbance Approach—Scenario 2
4.3 Parameter Perturbation Approach
5 Conclusions
References
10 Hardware Implementation of the Fractional Controller on Quadrotor Aircraft
1 Introduction
2 Preliminary Concepts
3 Euler Angles Representation of 3D Rotation
4 Quadrotor Body Dynamics
5 Quadrotor Actuator Dynamics
6 Quadrotor State-Space Model
7 Quadrotor Linear Model
8 Quadrotor Transfer Functions for Control Design
9 Numeric Computation of Fractional-Order Blocks for Hardware Implementation
10 Hardware Station Setup
10.1 Hardware Experimentation Workflow Scheme
11 Analysing Experimentation results
12 Conclusions
References
11 Optimum Fractional-Order PID for Active Suspension of Quarter Car Model Control
1 Introduction
2 Mathematical Model of Quarter Car Model System
3 Brief Design of FO-PID Controller
4 Simulation Parameters
5 Results and Discussions
6 Conclusion
References
