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Fractional Order Processes: Simulation, Identification, and Control [Kõva köide]

(Department of Chemical Engineering, National Institute of Technology Rourkela, Odisha, India),
  • Formaat: Hardback, 364 pages, kõrgus x laius: 234x156 mm, kaal: 650 g, 91 Tables, black and white; 49 Illustrations, color; 9 Illustrations, black and white
  • Ilmumisaeg: 04-Sep-2018
  • Kirjastus: CRC Press
  • ISBN-10: 1138586749
  • ISBN-13: 9781138586741
Teised raamatud teemal:
Fractional Order Processes: Simulation, Identification, and ControlSuurem pilt
  • Formaat: Hardback, 364 pages, kõrgus x laius: 234x156 mm, kaal: 650 g, 91 Tables, black and white; 49 Illustrations, color; 9 Illustrations, black and white
  • Ilmumisaeg: 04-Sep-2018
  • Kirjastus: CRC Press
  • ISBN-10: 1138586749
  • ISBN-13: 9781138586741
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781138586741.html
Märksõnad:
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.

Key features











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, Abels 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.
Preface xiii
Acknowledgments xxi
About the Authors xxiii
1 Mathematical Postulations
1(34)
1.1 Special Functions
1(5)
1.1.1 Gamma Function
1(1)
1.1.2 Beta Function
2(1)
1.1.3 Mittag-Leffler Function
3(1)
1.1.4 Hypergeometric Function
3(1)
1.1.5 Error Function and Complementary Error Function
4(1)
1.1.6 Bessel Functions
5(1)
1.2 Definitions and Properties of Fractional-Order Operators
6(4)
1.2.1 Grunwald-Letnikov (GL) Fractional-Order Derivative
6(1)
1.2.2 Riemann-Liouville (RL) Fractional-Order Integral
7(1)
1.2.3 Riemann-Liouville Fractional-Order Derivative
8(1)
1.2.4 Caputo Fractional-Order Derivative
8(1)
1.2.5 Properties of GL, RL, and Caputo Fractional-Order Derivatives
9(1)
1.3 Laplace Transforms of Fractional-Order Operators
10(2)
1.4 Fractional-Order Systems
12(2)
1.5 Fractional-Order PIλ, PDμ, and PIλDμ Controller
14(1)
1.6 Triangular Orthogonal Functions
15(16)
1.6.1 Review of Block Pulse Functions
15(2)
1.6.2 Complementary Pair of Triangular Orthogonal Function Sets
17(3)
1.6.3 Expansion of Two Variable Function via TFs
20(2)
1.6.4 The TF Estimate of the First-Order Integral of Function f(t)
22(2)
1.6.5 The TF Estimate of Riemann-Liouville Fractional-Order Integral of f(t)
24(2)
1.6.6 Error Analysis
26(3)
1.6.7 MATLAB® Code for Generalized Triangular Function Operational Matrices
29(2)
1.7 Triangular Strip Operational Matrices for Classical and Fractional Derivatives
31(3)
1.7.1 Operational Matrix for Classical Derivative
31(2)
1.7.2 Operational Matrix for Fractional-Order Derivative
33(1)
1.7.3 MATLAB Code for Triangular Strip Operational Matrices
33(1)
References
34(1)
2 Numerical Method for Simulation of Physical Processes Represented by Weakly Singular Fredholm, Volterra, and Volterra-Fredholm Integral Equations
35(38)
2.1 Existence and Uniqueness of Solution
38(3)
2.2 The Proposed Numerical Method
41(4)
2.3 Convergence Analysis
45(3)
2.4 Numerical Experiments
48(13)
2.4.1 Investigation of Validity and Accuracy
48(1)
Example 2.1 The weakly singular (WS) Fredholm-Hammerstein integral equation (IE) of 2nd kind
48(2)
Example 2.2 WS linear Fredholm IE of 2nd kind
50(1)
Example 2.3 WS Fredholm-Hammerstein IE of 1st kind
50(1)
Example 2.4 WS Volterra-Fredholm-Hammerstein IE of 2nd kind
51(1)
Example 2.5 WS Volterra-Hammerstein IE of 2nd kind
51(2)
2.4.2 Numerical Stability Analysis
53(1)
Example 2.6 WS linear Volterra-Fredholm IE of 2nd kind
53(1)
2.4.3 Application of Proposed Method to Physical Process Models
54(1)
Application 2.1 Heat radiation in a semi-infinite solid
54(2)
Application 2.2 Hydrodynamics
56(2)
Application 2.3 Lighthill singular integral equation
58(3)
2.5 MATLAB® Codes for Numerical Experiments
61(8)
2.6 Summary of Deliverables
69(1)
References
70(3)
3 Numerical Method for Simulation of Physical Processes Modeled by Abel's Integral Equations
73(36)
3.1 Existence and Uniqueness of Solution
76(1)
3.2 The Proposed Numerical Method
77(3)
3.3 Convergence Analysis
80(5)
3.4 Numerical Experiments
85(11)
3.4.1 Investigation of Validity and Accuracy
85(2)
3.4.2 Numerical Stability Analysis
87(2)
3.4.3 Application to Physical Process Models Involving Abel's Integral Equations
89(1)
Application 3.1 Cyclic voltammetry for the reversible deposition of metals on a solid planar macroelectrode
89(1)
Application 3.2 Cyclic voltammetry for reversible charge transfer at a planar macroelectrode
90(1)
Application 3.3 Potential step chronoamperometry for an irreversible charge transfer at a spherical electrode
91(1)
Application 3.4 Cyclic voltammetry for an irreversible charge transfer at a spherical electrode
92(1)
Application 3.5 Cyclic voltammetry for the catalytic mechanism at a planar electrode
93(3)
3.5 MATLAB® Codes for Numerical Experiments
96(8)
3.6 Concluding Remarks
104(1)
References
104(5)
4 Numerical Method for Simulation of Physical Processes Described by Fractional-Order Integro-Differential Equations
109(26)
4.1 Existence and Uniqueness of Solution
110(2)
4.2 The Proposed Numerical Method
112(3)
4.3 Convergence Analysis
115(7)
4.4 Numerical Experiments
122(6)
Case study 4.1 Fractional-order Fredholm-Hammerstein integro-differential equation
122(1)
Case study 4.2 Fractional order Volterra-Fredholm integro-differential equation
122(1)
Case study 4.3 Fractional-order population growth model
123(3)
Case study 4.4 Fractional-order integro-differential equations in anomalous diffusion process
126(2)
4.5 MATLAB® Codes for Numerical Experiments
128(4)
References
132(3)
5 Numerical Method for Simulation of Physical Processes Represented by Stiff and Nonstiff Fractional-Order Differential Equations, and Differential-Algebraic Equations
135(56)
5.1 Existence and Uniqueness of Solution
136(2)
5.2 The Proposed Numerical Method
138(1)
5.3 Convergence Analysis
139(1)
5.4 Numerical Experiments
140(33)
5.4.1 Investigation of Validity and Accuracy
140(1)
Example 5.1 Simple linear multiorder Fractional differential equation (FDE)
140(2)
Example 5.2 Complex linear high-order FDE
142(1)
Example 5.3 Complex linear low-order FDE
143(1)
Example 5.4 Nonlinear multiorder FDE
144(1)
Example 5.5 Linear multiorder FDE with variable coefficients
144(2)
Example 5.6 Linear fractional-order differential-algebraic equation (FDAEs)
146(1)
Example 5.7 Nonlinear FDAEs
146(1)
Example 5.8 System of nonlinear FDEs
147(1)
5.4.2 Application to Physical Processes Described by FDEs and FDAEs
147(1)
Application 5.1 Bagley-Torvik equation
147(1)
Application 5.2 Two-point Bagley-Torvik equation
148(1)
Application 5.3 Plant-herbivore model
148(3)
Application 5.4 Financial mode
151(1)
Application 5.5 Epidemiological model for computer viruses
152(4)
Application 5.6 Chemical Akzo Nobel problem
156(4)
Application 5.7 Robertson's system
160(1)
Application 5.8 High Irradiance Responses (HIRES) of photo morphogenesis
160(13)
5.5 MATLAB® Codes for Numerical Experiments
173(14)
5.6 Concluding Remarks
187(1)
References
188(3)
6 Numerical Method for Simulation of Fractional Diffusion-Wave Equation
191(8)
6.1 The Proposed Numerical Method
192(4)
6.2 Convergence Analysis
196(2)
References
198(1)
7 Identification of Fractional Order Linear and Nonlinear Systems from Experimental or Simulated Data
199(36)
7.1 Fractional Order System (FOS) Identification using TFs
201(5)
7.1.1 Linear FOS Identification
201(3)
7.1.2 Nonlinear FOS Identification
204(2)
7.2 Simulation Examples
206(12)
Case study 7.1 Identification of Linear Single Input Single Output (SISO) FOS
206(1)
Case study 7.2 Identification of Linear SISO Integer Order System (IOS)
207(2)
Case study 7.3 Identification of Linear Multi-Input Single Output IOS
209(5)
Case study 7.4 Identification of Nonlinear SISO FOS
214(2)
Case study 7.5 Verification of applicability of proposed identification method for sinusoidal signal, square wave signal, Sawtooth wave signal, step signal, pseudo random binary signal
216(2)
7.3 MATLAB Codes for Simulation Examples
218(14)
7.4 Summary of
Chapter Deliverables
232(1)
References
233(2)
8 Design of Fractional Order Controllers using Triangular Strip Operational Matrices
235(48)
8.1 Triangular Strip Operational Matrices-Based Fractional Order Controller Design Method
237(5)
8.2 Constrained Nonlinear Optimization
242(1)
8.2.1 Luus-Jaakola (LJ) Multipass Optimization Method
242(2)
8.2.2 Particle Swarm Optimization Method
244
8.3 Simulation Examples
243(22)
8.3.1 Design of Robust Fractional PIλDμ Controller for a Heating Furnace System
246(10)
8.3.2 Design of Fractional Order PIλDμDμ2 Controller for Automatic Voltage Regulator System
256(7)
8.3.3 Design of Fractional Order PIλ Controller, Fractional PDμ Controller, Fractional Order PIλDμ Controller with Fractional Order Filter, and Series Form of Fractional Order PIλDμ Controller
263(2)
8.4 MATLAB Codes for Simulation Examples
265(14)
8.5 Summary of
Chapter Deliverables
279(1)
References
280(3)
9 Rational Integer Order System Approximation for Irrational Fractional Order Systems
283(28)
9.1 The Proposed Integer-Order Approximation Method
286(4)
9.2 Simulation Example
290(15)
9.3 MATLAB Codes for Simulation Example
305(3)
References
308(3)
10 Numerical Method for Solving Fractional-Order Optimal Control Problems
311(18)
10.1 The Proposed Numerical Method
312(3)
10.2 Simulation Examples
315(6)
Case study 10.1 Optimal control of linear time invariant integer order system (IOS)
316(1)
Case study 10.2 Optimal control of linear time-varying fractional-order system (FOS)
316(2)
Case study 10.3 Optimal control of nonlinear FOS
318(2)
Case study 10.4 Optimal control of two-dimensional IOS
320(1)
10.3 MATLAB® Codes for Simulation Examples
321(6)
References
327(2)
Index 329
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, (19901992). Dr. Kundu gained experience as a process engineer at Simon Carves (I) Ltd., Kolkata (19931998). In the next phase of her scholarly pursuit, Dr. Kundu earned her PhD from the Indian Institute of Technology, Kharagpur (19992004), and started her academic profession as the faculty of the Chemical Engineering Group, BITS Pilani, Rajasthan (20042006). 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.