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The Resource Functional fractional calculus for system identification and controls, Shantanu Das

Functional fractional calculus for system identification and controls, Shantanu Das

Label
Functional fractional calculus for system identification and controls
Title
Functional fractional calculus for system identification and controls
Statement of responsibility
Shantanu Das
Creator
Subject
Language
eng
Cataloging source
YDXCP
http://library.link/vocab/creatorName
Das, Shantanu
Illustrations
illustrations
Index
no index present
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/subjectName
  • Calculus
  • Fractional calculus
Label
Functional fractional calculus for system identification and controls, Shantanu Das
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages 233-239)
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 1. Introduction to fractional calculus -- 1.1 Introduction -- 1.2 Birth of fractional calculus -- 1.3 Fractional calculus a generalization of integer order calculus -- 1.4 Historical development of fractional calculus -- 1.4.1 The popular definitions of fractional derivatives/integrals in fractional calculus -- 1.5 About fractional integration derivatives and differintegration -- 1.5.1 Fractional integration Riemann-Liouville (RL) -- 1.5.2 Fractional derivatives Riemann-Liouville (RL) left hand definition (LHD) -- 1.5.3 Fractional derivatives caputo right hand definition (RHD) -- 1.5.4 Fractional differintegrals Grunwald letnikov (GL) -- 1.5.5 Composition and property -- 1.5.6 Fractional derivative for some standard function -- 1.6 Solution of fractional differential equations -- 1.7 A thought experiment -- 1.8 Quotable quotes about fractional calculus -- 1.9 Concluding comments -- 2. Functions used in fractional calculus -- 2.1 Introduction -- 2.2 Functions for the fractional calculus -- 2.2.1 Gamma function -- 2.2.2 Mittag-Leffler function -- 2.2.3 Agarwal function -- 2.2.4 Erdelyi's function -- 2.2.5 Robotnov-Hartley function -- 2.2.6 Miller-Ross function -- 2.2.7 Generalized R function and G function -- 2.3 List of Laplace and inverse Laplace transforms related to fractional calculus -- 2.4 Concluding comments -- 3. Observation of fractional calculus in physical system description -- 3.1 Introduction -- 3.2 Temperature-heat flux relationship for heat flowing in semi-infinite conductor -- 3.3 Single thermocouple junction temperature in measurement of heat flux -- 3.4 Heat transfer -- 3.5 Driving point impedance of semi-infinite Lossy Transmission Line -- 3.5.1 Practical application of the semi-infinite line in circuits -- 3.5.2 Application of fractional integral and fractional differentiator circuit in control system -- 3.6 Semi-infinite Lossless Transmission Line -- 3.7 The concept of system order and initialization function -- 3.8 Concluding comments -- 4. Concept of fractional divergence and fractional curl -- 4.1 Introduction -- 4.2 Concept of fractional divergence for particle flux -- 4.3 Fractional kinetic equation -- 4.4 Nuclear reactor neutron flux description -- 4.5 Classical constitutive neutron diffusion equation -- 4.5.1 Discussion on classical constitutive equations -- 4.5.2 Graphical explanation -- 4.5.3 About surface flux curvature -- 4.5.4 Statistical and geometrical explanation for non-local divergence -- 4.6 Fractional divergence in neutron diffusion equations -- 4.6.1 Solution of classical constitutive neutron diffusion equation (integer order) -- 4.6.2 Solution of fractional divergence based neutron diffusion equation (fractional order) -- 4.6.3 Fractional geometrical buckling and non-point reactor kinetics -- 4.7 Concept of fractional curl in electromagnetics -- 4.7.1 Duality of solutions -- 4.7.2 Fractional curl operator -- 4.7.3 Wave propagation in unbounded chiral medium -- 4.8 Concluding comments -- 5. Fractional differintegrations : insight concepts -- 5.1 Introduction -- 5.2 Symbol standardization and description for differintegration -- 5.3 Reimann-Liouville fractional differintegral -- 5.3.1 Scale transformation -- 5.3.2 Convolution --
  • 5.3.3 Practical example of RL differintegration in electrical circuit element description -- 5.4 Grunwald-Letnikov fractional differinteration -- 5.5 Unification of differintegration through binomial coefficients -- 5.6 Short memory principle : a moving start point approximation and its error -- 5.7 Matrix approach to discretize fractional differintegration and weights -- 5.8 Infinitesimal element geometrical interpretation of fractional differintegrations -- 5.8.1 Integration -- 5.8.2 Differentiation -- 5.9 Advance digital algorithms realization for fractional controls -- 5.9.1 Concept of generating function -- 5.9.2 Digital filter realization by rational function approximation for fractional operator -- 5.9.3 Filter stability consideration -- 5.10 Local fractional derivatives -- 5.11 Concluding comments -- 6. Initialized differintegrals and generalized calculus -- 6.1 Introduction -- 6.2 Notations of differintegrals -- 6.3 Requirement of initialization -- 6.4 Initialization fractional integration (Riemann-Liouvelle approach) -- 6.4.1 Terminal initialization -- 6.4.2 Side initialization -- 6.5 Initializing fractional derivative (Riemann-Liouvelle approach) -- 6.5.1 Terminal initialization -- 6.5.2 Side initialization -- 6.6 Initializing fractional differintegrals (Grunwald-Letnikov approach) -- 6.7 Properties and criteria for generalized differintegrals -- 6.7.1 Terminal charging -- 6.7.2 Side charging -- 6.8 The fundamental fractional order differential equation -- 6.8.1 The generalized impulse response function -- 6.9 Concluding comments -- 7. Generalized Laplace transform for fractional differintegrals -- 7.1 Introduction -- 7.2 Recalling Laplace transform fundamentals -- 7.3 Laplace transform of fractional integrals -- 7.3.1 Decomposition of fractional integral in integer order -- 7.3.2 Decomposition of fractional order integral in fractional order -- 7.4 Laplace transformation of fractional derivatives -- 7.4.1 Decomposition of fractional order derivative in integer order -- 7.4.2 Decomposition of fractional derivative in fractional order -- 7.4.3 Effect of terminal charging on Laplace transforms -- 7.5 Start point shift effect -- 7.5.1 Fractional integral -- 7.5.2 Fractional derivative -- 7.6 Laplace transform of initialization function -- 7.6.1 Fractional integral -- 7.6.2 Fractional derivative -- 7.7 Examples of initialization in fractional differential equations -- 7.8 Problem of scalar initialization -- 7.9 Problem of vector initialization -- 7.10 Laplace transform s [arrow] w plane for fractional controls stability -- 7.11 Rational approximations of fractional Laplace operator -- 7.11 Rational approximations of fractional Laplace operator -- 7.12 Concluding comments -- 8. Application of generalized fractional calculus in electrical circuit analysis -- 8.1 Introduction -- 8.2 Electronics operational amplifier circuits -- 8.2.1 Operational amplifier circuit with lumped components -- 8.2.2 Operational amplifier integrator with lumped element -- 8.2.3 Operational amplifier integrator with distributed element -- 8.2.4 Operational amplifier differential circuit with lumped elements -- 8.2.5 Operational amplifier differentiator with distributed element -- 8.2.6 Operational amplifier as zero-order gain with lumped components -- 8.2.7 Operational amplifier as zero-order gain with distributed elements -- 8.2.8 Operational amplifier circuit for semi-differintegration by semi-infinite lossy line -- 8.2.9 Operational amplifier circuit for semi-integrator -- 8.2.10 Operational amplifier circuit for semi-differentiator -- 8.2.11 Cascaded semi-integrators -- 8.2.12 Semi-integrator series with semi-differentiator circuit -- 8.3 Battery dynamics- 8.3.1 Battery as fractional order system -- 8.3.2 Battery charging phase -- 8.3.3 Battery discharge phase -- 8.4 Tracking filter -- 8.4.1 Observations -- 8.5 Fractional order state vector representation in circuit theory -- 8.6 Concluding comments --
  • 9. Application of generalized fractional calculus in other science and engineering fields -- 9.1 Introduction -- 9.2 Diffusion model in electrochemistry -- 9.3 Electrode-electrolyte interface impedance -- 9.4 Capacitor theory -- 9.5 Fractance circuit -- 9.6 Feedback control system -- 9.6.1 Concept of iso-dampaing -- 9.6.2 Fractional vector feedback controller -- 9.6.3 Observer in fractional control -- 9.7 Viscoelasticity (stress-strain) -- 9.8 Vibration damping system -- 9.9 Concluding comments -- 10. System order identification and control -- 10.1 Introduction -- 10.2 Fractional order systems -- 10.3 Continuous order distribution -- 10.4 Determination of order distribution from frequency domain experimental data -- 10.5 Analysis of continuous order distribution -- 10.6 Variable order system -- 10.6.1 RL definition for variable order -- 10.6.2 Laplace transforms and transfer function of variable order system -- 10.6.3 GL definition for variable order -- 10.7 Generalized PID controls -- 10.8 continuum order feedback control system -- 10.9 Time domain response of Sinusoidal inputs for fractional order operator -- 10.10 Frequency domain response of sinusoidal inputs for fractional order operator -- 10.11 Ultra-damped system response -- 10.12 Hyper-damped system response -- 10.13 Disadvantage of fractional order system -- 10.14 Concluding comments
Control code
171111242
Dimensions
24 cm
Extent
xvii, 239 pages
Isbn
9783540727026
Lccn
2007934030
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations
System control number
(OCoLC)171111242
Label
Functional fractional calculus for system identification and controls, Shantanu Das
Publication
Bibliography note
Includes bibliographical references (pages 233-239)
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 1. Introduction to fractional calculus -- 1.1 Introduction -- 1.2 Birth of fractional calculus -- 1.3 Fractional calculus a generalization of integer order calculus -- 1.4 Historical development of fractional calculus -- 1.4.1 The popular definitions of fractional derivatives/integrals in fractional calculus -- 1.5 About fractional integration derivatives and differintegration -- 1.5.1 Fractional integration Riemann-Liouville (RL) -- 1.5.2 Fractional derivatives Riemann-Liouville (RL) left hand definition (LHD) -- 1.5.3 Fractional derivatives caputo right hand definition (RHD) -- 1.5.4 Fractional differintegrals Grunwald letnikov (GL) -- 1.5.5 Composition and property -- 1.5.6 Fractional derivative for some standard function -- 1.6 Solution of fractional differential equations -- 1.7 A thought experiment -- 1.8 Quotable quotes about fractional calculus -- 1.9 Concluding comments -- 2. Functions used in fractional calculus -- 2.1 Introduction -- 2.2 Functions for the fractional calculus -- 2.2.1 Gamma function -- 2.2.2 Mittag-Leffler function -- 2.2.3 Agarwal function -- 2.2.4 Erdelyi's function -- 2.2.5 Robotnov-Hartley function -- 2.2.6 Miller-Ross function -- 2.2.7 Generalized R function and G function -- 2.3 List of Laplace and inverse Laplace transforms related to fractional calculus -- 2.4 Concluding comments -- 3. Observation of fractional calculus in physical system description -- 3.1 Introduction -- 3.2 Temperature-heat flux relationship for heat flowing in semi-infinite conductor -- 3.3 Single thermocouple junction temperature in measurement of heat flux -- 3.4 Heat transfer -- 3.5 Driving point impedance of semi-infinite Lossy Transmission Line -- 3.5.1 Practical application of the semi-infinite line in circuits -- 3.5.2 Application of fractional integral and fractional differentiator circuit in control system -- 3.6 Semi-infinite Lossless Transmission Line -- 3.7 The concept of system order and initialization function -- 3.8 Concluding comments -- 4. Concept of fractional divergence and fractional curl -- 4.1 Introduction -- 4.2 Concept of fractional divergence for particle flux -- 4.3 Fractional kinetic equation -- 4.4 Nuclear reactor neutron flux description -- 4.5 Classical constitutive neutron diffusion equation -- 4.5.1 Discussion on classical constitutive equations -- 4.5.2 Graphical explanation -- 4.5.3 About surface flux curvature -- 4.5.4 Statistical and geometrical explanation for non-local divergence -- 4.6 Fractional divergence in neutron diffusion equations -- 4.6.1 Solution of classical constitutive neutron diffusion equation (integer order) -- 4.6.2 Solution of fractional divergence based neutron diffusion equation (fractional order) -- 4.6.3 Fractional geometrical buckling and non-point reactor kinetics -- 4.7 Concept of fractional curl in electromagnetics -- 4.7.1 Duality of solutions -- 4.7.2 Fractional curl operator -- 4.7.3 Wave propagation in unbounded chiral medium -- 4.8 Concluding comments -- 5. Fractional differintegrations : insight concepts -- 5.1 Introduction -- 5.2 Symbol standardization and description for differintegration -- 5.3 Reimann-Liouville fractional differintegral -- 5.3.1 Scale transformation -- 5.3.2 Convolution --
  • 5.3.3 Practical example of RL differintegration in electrical circuit element description -- 5.4 Grunwald-Letnikov fractional differinteration -- 5.5 Unification of differintegration through binomial coefficients -- 5.6 Short memory principle : a moving start point approximation and its error -- 5.7 Matrix approach to discretize fractional differintegration and weights -- 5.8 Infinitesimal element geometrical interpretation of fractional differintegrations -- 5.8.1 Integration -- 5.8.2 Differentiation -- 5.9 Advance digital algorithms realization for fractional controls -- 5.9.1 Concept of generating function -- 5.9.2 Digital filter realization by rational function approximation for fractional operator -- 5.9.3 Filter stability consideration -- 5.10 Local fractional derivatives -- 5.11 Concluding comments -- 6. Initialized differintegrals and generalized calculus -- 6.1 Introduction -- 6.2 Notations of differintegrals -- 6.3 Requirement of initialization -- 6.4 Initialization fractional integration (Riemann-Liouvelle approach) -- 6.4.1 Terminal initialization -- 6.4.2 Side initialization -- 6.5 Initializing fractional derivative (Riemann-Liouvelle approach) -- 6.5.1 Terminal initialization -- 6.5.2 Side initialization -- 6.6 Initializing fractional differintegrals (Grunwald-Letnikov approach) -- 6.7 Properties and criteria for generalized differintegrals -- 6.7.1 Terminal charging -- 6.7.2 Side charging -- 6.8 The fundamental fractional order differential equation -- 6.8.1 The generalized impulse response function -- 6.9 Concluding comments -- 7. Generalized Laplace transform for fractional differintegrals -- 7.1 Introduction -- 7.2 Recalling Laplace transform fundamentals -- 7.3 Laplace transform of fractional integrals -- 7.3.1 Decomposition of fractional integral in integer order -- 7.3.2 Decomposition of fractional order integral in fractional order -- 7.4 Laplace transformation of fractional derivatives -- 7.4.1 Decomposition of fractional order derivative in integer order -- 7.4.2 Decomposition of fractional derivative in fractional order -- 7.4.3 Effect of terminal charging on Laplace transforms -- 7.5 Start point shift effect -- 7.5.1 Fractional integral -- 7.5.2 Fractional derivative -- 7.6 Laplace transform of initialization function -- 7.6.1 Fractional integral -- 7.6.2 Fractional derivative -- 7.7 Examples of initialization in fractional differential equations -- 7.8 Problem of scalar initialization -- 7.9 Problem of vector initialization -- 7.10 Laplace transform s [arrow] w plane for fractional controls stability -- 7.11 Rational approximations of fractional Laplace operator -- 7.11 Rational approximations of fractional Laplace operator -- 7.12 Concluding comments -- 8. Application of generalized fractional calculus in electrical circuit analysis -- 8.1 Introduction -- 8.2 Electronics operational amplifier circuits -- 8.2.1 Operational amplifier circuit with lumped components -- 8.2.2 Operational amplifier integrator with lumped element -- 8.2.3 Operational amplifier integrator with distributed element -- 8.2.4 Operational amplifier differential circuit with lumped elements -- 8.2.5 Operational amplifier differentiator with distributed element -- 8.2.6 Operational amplifier as zero-order gain with lumped components -- 8.2.7 Operational amplifier as zero-order gain with distributed elements -- 8.2.8 Operational amplifier circuit for semi-differintegration by semi-infinite lossy line -- 8.2.9 Operational amplifier circuit for semi-integrator -- 8.2.10 Operational amplifier circuit for semi-differentiator -- 8.2.11 Cascaded semi-integrators -- 8.2.12 Semi-integrator series with semi-differentiator circuit -- 8.3 Battery dynamics- 8.3.1 Battery as fractional order system -- 8.3.2 Battery charging phase -- 8.3.3 Battery discharge phase -- 8.4 Tracking filter -- 8.4.1 Observations -- 8.5 Fractional order state vector representation in circuit theory -- 8.6 Concluding comments --
  • 9. Application of generalized fractional calculus in other science and engineering fields -- 9.1 Introduction -- 9.2 Diffusion model in electrochemistry -- 9.3 Electrode-electrolyte interface impedance -- 9.4 Capacitor theory -- 9.5 Fractance circuit -- 9.6 Feedback control system -- 9.6.1 Concept of iso-dampaing -- 9.6.2 Fractional vector feedback controller -- 9.6.3 Observer in fractional control -- 9.7 Viscoelasticity (stress-strain) -- 9.8 Vibration damping system -- 9.9 Concluding comments -- 10. System order identification and control -- 10.1 Introduction -- 10.2 Fractional order systems -- 10.3 Continuous order distribution -- 10.4 Determination of order distribution from frequency domain experimental data -- 10.5 Analysis of continuous order distribution -- 10.6 Variable order system -- 10.6.1 RL definition for variable order -- 10.6.2 Laplace transforms and transfer function of variable order system -- 10.6.3 GL definition for variable order -- 10.7 Generalized PID controls -- 10.8 continuum order feedback control system -- 10.9 Time domain response of Sinusoidal inputs for fractional order operator -- 10.10 Frequency domain response of sinusoidal inputs for fractional order operator -- 10.11 Ultra-damped system response -- 10.12 Hyper-damped system response -- 10.13 Disadvantage of fractional order system -- 10.14 Concluding comments
Control code
171111242
Dimensions
24 cm
Extent
xvii, 239 pages
Isbn
9783540727026
Lccn
2007934030
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations
System control number
(OCoLC)171111242

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