The book presents efficient numerical methods for simulation and analysis of physical processes exhibiting fractional order (FO) dynamics. The book introduces FO system identification method to estimate parameters of a mathematical model under consideration from experimental or simulated data. A simple tuning technique, which aims to produce a robust FO PID controller exhibiting iso-damping property during re-parameterization of a plant, is devised in the book. A new numerical method to find an equivalent finite dimensional integer order system for an infinite dimensional FO system is developed in the book. The book also introduces a numerical method to solve FO optimal control problems.
- Proposes generalized triangular function operational matrices.
- Shows significant applications of triangular orthogonal functions as well as triangular strip operational matrices in simulation, identification and control of fractional order processes.
- Provides numerical methods for simulation of physical problems involving different types of weakly singular integral equations, Abel’s integral equation, fractional order integro-differential equations, fractional order differential and differential-algebraic equations, and fractional order partial differential equations.
- Suggests alternative way to do numerical computation of fractional order signals and systems and control.
- Provides source codes developed in MATLAB for each chapter, allowing the interested reader to take advantage of these codes for broadening and enhancing the scope of the book itself and developing new results.
Table of Contents
1 Mathematical Postulations
2 Numerical Method for Simulation of Physical Processes
Represented by Weakly Singular Fredholm, Volterra,
and Volterra-Fredholm Integral Equations
3 Numerical Method for Simulation of Physical Processes
Modeled by Abel’s Integral Equations
4 Numerical Method for Simulation of Physical Processes
Described by Fractional-Order Integro-Differential Equations
5 Numerical Method for Simulation of Physical Processes
Represented by Stiff and Nonstiff Fractional-Order
Differential Equations, and Differential-Algebraic Equations
6 Numerical Method for Simulation of Fractional Diffusion-Wave
7 Identification of Fractional Order Linear and Nonlinear
Systems from Experimental or Simulated Data
8 Design of Fractional Order Controllers using Triangular Strip
9 Rational Integer Order System Approximation for Irrational
Fractional Order Systems
10 Numerical Method for Solving Fractional-Order Optimal Control
Seshu Kumar Damarla was born in the year 1985 in Chirala, Prakasam, Andhra Pradesh, India. He did his B.Tech (Chemical Engineering) from Bapatla Engineering College, Bapatla, Andhra Pradesh, India (2008), and M.Tech (Chemical Engineering) from NIT Rourkela, Odisha, India (2011). Mr. Damarla submitted his Ph.D dissertation (Title of the dissertation is Developing Numerical Methods for Simulation, Identification and Control of Fractional Order Process) to NIT Rourkela, Odisha, India (2017). Mr. Damarla served as an Assistant Professor for a short duration (from 5th August 2011 to 31st December 2011) in Chemical Engineering in Maulana Azad National Institute of Technology Bhopal, Madhya Pradesh, India, and has been working as an Assistant Professor in Chemical Engineering in C.V. Raman College of Engineering, Bhubaneswar, Odisha, India. Mr. Damarla has published a couple of research articles in the internationally refereed journals to his credit and also published in the proceedings of national and international conferences. Mr. Damarla co-authored a reference textbook titled Chemometric Monitoring: Product Quality Assessment, Process Fault Detection, and Applications (CRC Press, Taylor & Francis Group, Boca Raton, Florida, United States, 2017. (ISBN 9781138746213)). Mr. Damarla has been a referee for Acta Biotheoretica (a springer publication), Journal of King Saud Science (an Elsevier publication), and Applied and Computational Mathematics (Science Publishing Group, USA). Mr. Damarla is a member of International Association of Engineers (IAENG), Fractional Calculus and Application Group, and Allahabad Mathematical Society.
Madhusree Kundu started her academic pursuits with a graduation in chemistry, with honors (University of Calcutta) followed by graduation and post-graduation in chemical engineering from the Rajabazar Science College, University of Calcutta, (1990–1992). Dr. Kundu gained experience as a process engineer at Simon Carves (I) Ltd., Kolkata (1993–1998). In the next phase of her scholarly pursuit, Dr. Kundu earned her PhD from the Indian Institute of Technology, Kharagpur (1999–2004), and started her academic profession as the faculty of the Chemical Engineering Group, BITS Pilani, Rajasthan (2004–2006). She joined the NIT Rourkela in 2007 and is continuing there as Professor in the Department of Chemical Engineering. Apart from teaching, she has focused her research activities in chemometrics along with fractional order process modeling and control, solution thermodynamics, and fluid-phase equilibria. Dr. Kundu has authored several research articles in International refereed journals and has a few book chapters, and a reference text book (Chemometric Monitoring: Product Quality Assessment, Process Fault Detection, and Applications, CRC Press, Taylor & Francis Group, Boca Raton, Florida, United States, 2017 (ISBN 9781138746213)) to her credit.