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Fractional Order Systems

Fractional Order Systems
  • Author : Ivo Petráš
  • Publsiher : MDPI
  • Release : 29 October 2019
  • ISBN : 3039216082
  • Pages : 114 pages
  • Rating : 4/5 from 21 ratings
GET THIS BOOKFractional Order Systems

Summary:
This book is focused on fractional order systems. Historically, fractional calculus has been recognized since the inception of regular calculus, with the first written reference dated in September 1695 in a letter from Leibniz to L’Hospital. Nowadays, fractional calculus has a wide area of applications in areas such as physics, chemistry, bioengineering, chaos theory, control systems engineering, and many others. In all those applications, we deal with fractional order systems in general. Moreover, fractional calculus plays an important role even in complex systems and therefore allows us to develop better descriptions of real-world phenomena. On that basis, fractional order systems are ubiquitous, as the whole real world around us is fractional. Due to this reason, it is urgent to consider almost all systems as fractional order systems. This Special Issue explores applications of such systems to control, synchronization, and various mathematical models, as for instance, MRI, long memory process, diffusion.


Fractional Order Systems

Fractional Order Systems
  • Author : Riccardo Caponetto
  • Publisher : World Scientific
  • Release : 26 February 2021
GET THIS BOOKFractional Order Systems

This book aims to propose implementations and applications of Fractional Order Systems (FOS). It is well known that FOS can be applied in control applications and systems modeling, and their effectiveness has been proven in many theoretical works and simulation routines. A further and mandatory step for FOS real world utilization is their hardware implementation and applications on real systems modeling. With this viewpoint, introductive chapters on FOS are included, on the definition of stability region of Fractional Order PID


Fractional Order Systems

Fractional Order Systems
  • Author : Ivo Petráš
  • Publisher : MDPI
  • Release : 29 October 2019
GET THIS BOOKFractional Order Systems

This book is focused on fractional order systems. Historically, fractional calculus has been recognized since the inception of regular calculus, with the first written reference dated in September 1695 in a letter from Leibniz to L’Hospital. Nowadays, fractional calculus has a wide area of applications in areas such as physics, chemistry, bioengineering, chaos theory, control systems engineering, and many others. In all those applications, we deal with fractional order systems in general. Moreover, fractional calculus plays an important role even


Fractional Order Systems

Fractional Order Systems
  • Author : Ahmad Taher Azar,Ahmed G. Radwan,Sundarapandian Vaidyanathan
  • Publisher : Academic Press
  • Release : 16 August 2018
GET THIS BOOKFractional Order Systems

Fractional Order Systems: Optimization, Control, Circuit Realizations and Applications consists of 21 contributed chapters by subject experts. Chapters offer practical solutions and novel methods for recent research problems in the multidisciplinary applications of fractional order systems, such as FPGA, circuits, memristors, control algorithms, photovoltaic systems, robot manipulators, oscillators, etc. This book is ideal for researchers working in the modeling and applications of both continuous-time and discrete-time dynamics and chaotic systems. Researchers from academia and industry who are working in research areas


Fractional-Order Control Systems

Fractional-Order Control Systems
  • Author : Dingyü Xue
  • Publisher : Walter de Gruyter GmbH & Co KG
  • Release : 10 July 2017
GET THIS BOOKFractional-Order Control Systems

This book explains the essentials of fractional calculus and demonstrates its application in control system modeling, analysis and design. It presents original research to find high-precision solutions to fractional-order differentiations and differential equations. Numerical algorithms and their implementations are proposed to analyze multivariable fractional-order control systems. Through high-quality MATLAB programs, it provides engineers and applied mathematicians with theoretical and numerical tools to design control systems. Contents Introduction to fractional calculus and fractional-order control Mathematical prerequisites Definitions and computation algorithms of


Fractional-Order Nonlinear Systems

Fractional-Order Nonlinear Systems
  • Author : Ivo Petráš
  • Publisher : Springer Science & Business Media
  • Release : 30 May 2011
GET THIS BOOKFractional-Order Nonlinear Systems

"Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study of fractional-order chaotic systems accompanied by Matlab programs for simulating their state space trajectories, which are shown in the illustrations in the book. Description of the chaotic systems is clearly presented and their analysis and numerical solution are done in an easy-to-follow manner. Simulink models for the selected fractional-order systems are also presented. The readers will understand the fundamentals of the fractional calculus, how real dynamical systems can be described


Fractional-order Systems and Controls

Fractional-order Systems and Controls
  • Author : Concepción A. Monje,YangQuan Chen,Blas M. Vinagre,Dingyu Xue,Vicente Feliu-Batlle
  • Publisher : Springer Science & Business Media
  • Release : 28 September 2010
GET THIS BOOKFractional-order Systems and Controls

Fractional-order Systems and Controls details the use of fractional calculus in the description and modeling of systems, and in a range of control design and practical applications. It is largely self-contained, covering the fundamentals of fractional calculus together with some analytical and numerical techniques and providing MATLAB® codes for the simulation of fractional-order control (FOC) systems. Many different FOC schemes are presented for control and dynamic systems problems. Practical material relating to a wide variety of applications is also provided.


Stabilization and Control of Fractional Order Systems: A Sliding Mode Approach

Stabilization and Control of Fractional Order Systems: A Sliding Mode Approach
  • Author : Bijnan Bandyopadhyay,Shyam Kamal
  • Publisher : Springer
  • Release : 22 July 2014
GET THIS BOOKStabilization and Control of Fractional Order Systems: A Sliding Mode Approach

In the last two decades fractional differential equations have been used more frequently in physics, signal processing, fluid mechanics, viscoelasticity, mathematical biology, electro chemistry and many others. It opens a new and more realistic way to capture memory dependent phenomena and irregularities inside the systems by using more sophisticated mathematical analysis. This monograph is based on the authors’ work on stabilization and control design for continuous and discrete fractional order systems. The initial two chapters and some parts of the


Mathematical Techniques of Fractional Order Systems

Mathematical Techniques of Fractional Order Systems
  • Author : Ahmad Taher Azar,Ahmed G. Radwan,Sundarapandian Vaidyanathan
  • Publisher : Elsevier
  • Release : 11 June 2018
GET THIS BOOKMathematical Techniques of Fractional Order Systems

Mathematical Techniques of Fractional Order Systems illustrates advances in linear and nonlinear fractional-order systems relating to many interdisciplinary applications, including biomedical, control, circuits, electromagnetics and security. The book covers the mathematical background and literature survey of fractional-order calculus and generalized fractional-order circuit theorems from different perspectives in design, analysis and realizations, nonlinear fractional-order circuits and systems, the fractional-order memristive circuits and systems in design, analysis, emulators, simulation and experimental results. It is primarily meant for researchers from academia and industry,


Advanced Synchronization Control and Bifurcation of Chaotic Fractional-Order Systems

Advanced Synchronization Control and Bifurcation of Chaotic Fractional-Order Systems
  • Author : Boulkroune, Abdesselem,Ladaci, Samir
  • Publisher : IGI Global
  • Release : 11 May 2018
GET THIS BOOKAdvanced Synchronization Control and Bifurcation of Chaotic Fractional-Order Systems

In the recent years, fractional-order systems have been studied by many researchers in the engineering field. It was found that many systems can be described more accurately by fractional differential equations than by integer-order models. Advanced Synchronization Control and Bifurcation of Chaotic Fractional-Order Systems is a scholarly publication that explores new developments related to novel chaotic fractional-order systems, control schemes, and their applications. Featuring coverage on a wide range of topics including chaos synchronization, nonlinear control, and cryptography, this publication


Fractional Order Signal Processing

Fractional Order Signal Processing
  • Author : Saptarshi Das,Indranil Pan
  • Publisher : Springer Science & Business Media
  • Release : 15 September 2011
GET THIS BOOKFractional Order Signal Processing

The book tries to briefly introduce the diverse literatures in the field of fractional order signal processing which is becoming an emerging topic among an interdisciplinary community of researchers. This book is aimed at postgraduate and beginning level research scholars who would like to work in the field of Fractional Order Signal processing (FOSP). The readers should have preliminary knowledge about basic signal processing techniques. Prerequisite knowledge of fractional calculus is not essential and is exposited at relevant places in


Intelligent Fractional Order Systems and Control

Intelligent Fractional Order Systems and Control
  • Author : Indranil Pan,Saptarshi Das
  • Publisher : Springer
  • Release : 23 August 2012
GET THIS BOOKIntelligent Fractional Order Systems and Control

Fractional order calculus is finding increasing interest in the control system community. Hardware realizations of fractional order controllers have sparked off a renewed zeal into the investigations of control system design in the light of fractional calculus. As such many notions of integer order LTI systems are being modified and extended to incorporate these new concepts. Computational Intelligence (CI) techniques have been applied to engineering problems to find solutions to many hitherto intractable conundrums and is a useful tool for


Fractional-order Modeling and Control of Dynamic Systems

Fractional-order Modeling and Control of Dynamic Systems
  • Author : Aleksei Tepljakov
  • Publisher : Springer
  • Release : 08 February 2017
GET THIS BOOKFractional-order Modeling and Control of Dynamic Systems

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


Fractional-order Systems and PID Controllers

Fractional-order Systems and PID Controllers
  • Author : Kishore Bingi,Rosdiazli Ibrahim,Mohd Noh Karsiti,Sabo Miya Hassan,Vivekananda Rajah Harindran
  • Publisher : Springer Nature
  • Release : 31 October 2019
GET THIS BOOKFractional-order Systems and PID Controllers

This book presents a detailed study on fractional-order, set-point, weighted PID control strategies and the development of curve-fitting-based approximation techniques for fractional-order parameters. Furthermore, in all the cases, it includes the Scilab-based commands and functions for easy implementation and better understanding, and to appeal to a wide range of readers working with the software. The presented Scilab-based toolbox is the first toolbox for fractional-order systems developed in open-source software. The toolboxes allow time and frequency domains as well as stability


Intelligent Fractional Order Systems and Control

Intelligent Fractional Order Systems and Control
  • Author : Indranil Pan,Saptarshi Das
  • Publisher : Springer
  • Release : 23 August 2012
GET THIS BOOKIntelligent Fractional Order Systems and Control

Fractional order calculus is finding increasing interest in the control system community. Hardware realizations of fractional order controllers have sparked off a renewed zeal into the investigations of control system design in the light of fractional calculus. As such many notions of integer order LTI systems are being modified and extended to incorporate these new concepts. Computational Intelligence (CI) techniques have been applied to engineering problems to find solutions to many hitherto intractable conundrums and is a useful tool for


Analysis, Modeling and Stability of Fractional Order Differential Systems 1

Analysis, Modeling and Stability of Fractional Order Differential Systems 1
  • Author : Jean-Claude Trigeassou,Nezha Maamri
  • Publisher : John Wiley & Sons
  • Release : 06 August 2019
GET THIS BOOKAnalysis, Modeling and Stability of Fractional Order Differential Systems 1

This book introduces an original fractional calculus methodology (‘the infinite state approach’) which is applied to the modeling of fractional order differential equations (FDEs) and systems (FDSs). Its modeling is based on the frequency distributed fractional integrator, while the resulting model corresponds to an integer order and infinite dimension state space representation. This original modeling allows the theoretical concepts of integer order systems to be generalized to fractional systems, with a particular emphasis on a convolution formulation.