Functional fractional calculus for system identification and controls: with ... 11 tables
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| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2008
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 233 - 239 |
| Physical Description: | XVII, 239 S. graph. Darst. 24 cm |
| ISBN: | 9783540727026 3540727027 |
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MARC
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| 245 | 1 | 0 | |a Functional fractional calculus for system identification and controls |b with ... 11 tables |c Shantanu Das |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2008 | |
| 300 | |a XVII, 239 S. |b graph. Darst. |c 24 cm | ||
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| 500 | |a Literaturverz. S. 233 - 239 | ||
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| adam_text | SHANTANU DAS FUNCTIONAL FRACTIONAL CALCULUS FOR SYSTEM IDENTIFICATION
AND CONTROLS WITH 68 FIGURES AND 11 TABLES 4Y SPRINGER CONTENTS 1
INTRODUCTION TO FRACTIONAL CALCULUS 1 1.1 INTRODUCTION 1 1.2 BIRTH OF
FRACTIONAL CALCULUS 1 1.3 FRACTIONAL CALCULUS A GENERALIZATION OF
INTEGER ORDER CALCULUS 2 1.4 HISTORICAL DEVELOPMENT OF FRACTIONAL
CALCULUS 3 1.4.1 THE POPULAR DEFINITIONS OF FRACTIONAL
DERIVATIVES/INTEGRALS IN FRACTIONAL CALCULUS 7 1.5 ABOUT FRACTIONAL
INTEGRATION DERIVATIVES AND DIFFERINTEGRATION 9 1.5.1 FRACTIONAL
INTEGRATION RIEMANN-LIOUVILLE (RL) 9 1.5.2 FRACTIONAL DERIVATIVES
RIEMANN-LIOUVILLE (RL) LEFT HAND DEFINITION (LHD) 10 1.5.3 FRACTIONAL
DERIVATIVES CAPUTO RIGHT HAND DEFINITION (RHD) .. 10 1.5.4 FRACTIONAL
DIFFERINTEGRALS GRUNWALD LETNIKOV (GL) 12 1.5.5 COMPOSITION AND PROPERTY
14 1.5.6 FRACTIONAL DERIVATIVE FOR SOME STANDARD FUNCTION 15 1.6
SOLUTION OF FRACTIONAL DIFFERENTIAL EQUATIONS 16 1.7 A THOUGHT
EXPERIMENT.... 16 1.8 QUOTABLE QUOTES ABOUT FRACTIONAL CALCULUS 17 1.9
CONCLUDING COMMENTS 18 2 FUNCTIONS USED IN FRACTIONAL CALCULUS 19 2.1
INTRODUCTION 19 2.2 FUNCTIONS FOR THE FRACTIONAL CALCULUS 19 2.2.1 GAMMA
FUNCTION 19 2.2.2 MITTAG-LEFFLER FUNCTION .* 22 2.2.3 AGARWAL FUNCTION
27 2.2.4 ERDELYI S FUNCTION 27 2.2.5 ROBOTNOV-HARTLEY FUNCTION 27 2.2.6
MILLER-ROSS FUNCTION 27 2.2.7 GENERALIZED R FUNCTION AND G FUNCTION 28
2.3 LIST OF LAPLACE AND INVERSE LAPLACE TRANSFORMS RELATED TO FRACTIONAL
CALCULUS .. /: 30 2.4 CONCLUDING COMMENTS 33 XIV CONTENTS 3 OBSERVATION
OF FRACTIONAL CALCULUS IN PHYSICAL SYSTEM DESCRIPTION ... 35 3.1
INTRODUCTION 35 3.2 TEMPERATURE-HEAT FLUX RELATIONSHIP FOR HEAT FLOWING
IN SEMI-INFINITE CONDUCTOR 35 3.3 SINGLE THERMOCOUPLE JUNCTION
TEMPERATURE IN MEASUREMENT OF HEAT FLUX 38 3.4 HEAT TRANSFER 40 3.5
DRIVING POINT IMPEDANCE OF SEMI-INFINITE LOSSY TRANSMISSION LINE ... 43
3.5.1 PRACTICAL APPLICATION OF THE SEMI-INFINITE LINE IN CIRCUITS 49
3.5.2 APPLICATION OF FRACTIONAL INTEGRAL AND FRACTIONAL DIFFERENTIATOR
CIRCUIT IN CONTROL SYSTEM 52 3.6 SEMI-INFINITE LOSSLESS TRANSMISSION
LINE 54 3.7 THE CONCEPT OF SYSTEM ORDER AND INITIALIZATION FUNCTION 60
3.8 CONCLUDING COMMENTS 61 4 CONCEPT OF FRACTIONAL DIVERGENCE AND
FRACTIONAL CURL 63 4.1 INTRODUCTION 63 4.2 CONCEPT OF FRACTIONAL
DIVERGENCE FOR PARTICLE FLUX 63 4.3 FRACTIONAL KINETIC EQUATION 65 4.4
NUCLEAR REACTOR NEUTRON FLUX DESCRIPTION 67 4.5 CLASSICAL CONSTITUTIVE
NEUTRON DIFFUSION EQUATION 67 4.5.1 DISCUSSION ON CLASSICAL CONSTITUTIVE
EQUATIONS 68 4.5.2 GRAPHICAL EXPLANATION 69 4.5.3 ABOUT SURFACE FLUX
CURVATURE 69 4.5.4 STATISTICAL AND GEOMETRICAL EXPLANATION FOR NON-LOCAL
DIVERGENCE 70 4.6 FRACTIONAL DIVERGENCE IN NEUTRON DIFFUSION EQUATIONS
71 4.6.1 SOLUTION OF CLASSICAL CONSTITUTIVE NEUTRON DIFFUSION EQUATION
(INTEGER ORDER) 73 4.6.2 SOLUTION OF FRACTIONAL DIVERGENCE BASED NEUTRON
DIFFUSION EQUATION (FRACTIONAL ORDER) 74 4.6.3 FRACTIONAL GEOMETRICAL
BUCKLING AND NON-POINT REACTOR KINETICS 76 4.7 CONCEPT OF FRACTIONAL
CURL IN ELECTROMAGNETICS 76 4.7.1 DUALITY OF SOLUTIONS 77 4.7.2
FRACTIONAL CURL OPERATOR ^ 77 4.7.3 WAVE PROPAGATION IN UNBOUNDED CHIRAL
MEDIUM 77 4.8 CONCLUDING COMMENTS 79 5 FRACTIONAL DIFFERINTEGRATIONS:
INSIGHT CONCEPTS 81 5.1 INTRODUCTION 81 5.2 SYMBOL STANDARDIZATION AND
DESCRIPTION FOR DIFFERINTEGRATION 81 5.3 REIMANN-LIOUVILLE FRACTIONAL
DIFFERINTEGRAL 82 5.3.1 SCALE TRANSFORMATION 82 5.3.2 CONVOLUTION 85
CONTENTS XV 5.3.3 PRACTICAL EXAMPLE OF RL DIFFERINTEGRATION IN
ELECTRICAL CIRCUIT ELEMENT DESCRIPTION 87 5.4 GRUNWALD-LETNIKOV
FRACTIONAL DIFFERINTERATION 90 5.5 UNIFICATION OF DIFFERINTEGRATION
THROUGH BINOMIAL COEFFICIENTS 92 5.6 SHORT MEMORY PRINCIPLE: A MOVING
START POINT APPROXIMATION AND ITS ERROR 95 5.7 MATRIX APPROACH TO
DISCRETIZE FRACTIONAL DIFFERINTEGRATION AND WEIGHTS 97 5.8 INFINITESIMAL
ELEMENT GEOMETRICAL INTERPRETATION OF FRACTIONAL DIFFERINTEGRATIONS 98
5.8.1 INTEGRATION 99 5.8.2 DIFFERENTIATION 100 5.9 ADVANCE DIGITAL
ALGORITHMS REALIZATION FOR FRACTIONAL CONTROLS 102 5.9.1 CONCEPT OF
GENERATING FUNCTION 102 5.9.2 DIGITAL FILTER REALIZATION BY RATIONAL
FUNCTION APPROXIMATION FOR FRACTIONAL OPERATOR 103 5.9.3 FILTER
STABILITY CONSIDERATION 106 5.10 LOCAL FRACTIONAL DERIVATIVES 106 5.11
CONCLUDING COMMENTS 107 6 INITIALIZED DIFFERINTEGRALS AND GENERALIZED
CALCULUS 109 6.1 INTRODUCTION 109 6.2 NOTATIONS OF DIFFERINTEGRALS 110
6.3 REQUIREMENT OF INITIALIZATION 110 6.4 INITIALIZATION FRACTIONAL
INTEGRATION (RIEMANN-LIOUVILLE APPROACH) 112 6.4.1 TERMINAL
INITIALIZATION . 113 6.4.2 SIDE INITIALIZATION 114 6.5 INITIALIZING
FRACTIONAL DERIVATIVE (RIEMANN-LIOUVELLE APPROACH) 115 6.5.1 TERMINAL
INITIALIZATION 116 6.5.2 SIDE INITIALIZATION 117 6.6 INITIALIZING
FRACTIONAL DIFFERINTEGRALS (GRUNWALD-LETNIKOV APPROACH) .118 6.7
PROPERTIES AND CRITERIA FOR GENERALIZED DIFFERINTEGRALS 119 6.7.1
TERMINAL CHARGING 121 6.7.2 SIDE CHARGING 122 6.8 THE FUNDAMENTAL
FRACTIONAL ORDER DIFFERENTIAL EQUATION 122 6.8.1 THE GENERALIZED IMPULSE
RESPONSE FUNCTIOFF 123 6.9 CONCLUDING COMMENTS 127 7 GENERALIZED LAPLACE
TRANSFORM FOR FRACTIONAL DIFFERINTEGRALS 129 7.1 INTRODUCTION 129 7.2
RECALLING LAPLACE TRANSFORM FUNDAMENTALS 129 7.3 LAPLACE TRANSFORM OF
FRACTIONAL INTEGRALS 131 7.3.1 DECOMPOSITION OF FRACTIONAL INTEGRAL IN
INTEGER ORDER 132 7.3.2 DECOMPOSITION OF FRACTIONAL ORDER INTEGRAL IN
FRACTIONAL ORDER 135 XVI CONTENTS 7.4 LAPLACE TRANSFORMATION OF
FRACTIONAL DERIVATIVES 136 7.4.1 DECOMPOSITION OF FRACTIONAL ORDER
DERIVATIVE IN INTEGER ORDER 138 7.4.2 DECOMPOSITION OF FRACTIONAL
DERIVATIVE IN FRACTIONAL ORDER ... 141 7.4.3 EFFECT OF TERMINAL CHARGING
ON LAPLACE TRANSFORMS 142 7.5 START POINT SHIFT EFFECT 143 7.5.1
FRACTIONAL INTEGRAL 143 7.5.2 FRACTIONAL DERIVATIVE ; 143 7.6 LAPLACE
TRANSFORM OF INITIALIZATION FUNCTION 144 7.6.1 FRACTIONAL INTEGRAL 144
7.6.2 FRACTIONAL DERIVATIVE 144 7.7 EXAMPLES OF INITIALIZATION IN
FRACTIONAL DIFFERENTIAL EQUATIONS 144 7.8 PROBLEM OF SCALAR
INITIALIZATION 147 7.9 PROBLEM OF VECTOR INITIALIZATION 149 7.10 LAPLACE
TRANSFORM S * * W PLANE FOR FRACTIONAL CONTROLS STABILITY 151 7.11
RATIONAL APPROXIMATIONS OF FRACTIONAL LAPLACE OPERATOR 153 7.12
CONCLUDING COMMENTS 155 8 APPLICATION OF GENERALIZED FRACTIONAL CALCULUS
IN ELECTRICAL CIRCUIT ANALYSIS 157 8.1 INTRODUCTION 157 8.2 ELECTRONICS
OPERATIONAL AMPLIFIER CIRCUITS 157 8.2.1 OPERATIONAL AMPLIFIER CIRCUIT
WITH LUMPED COMPONENTS 157 8.2.2 OPERATIONAL AMPLIFIER INTEGRATOR WITH
LUMPED ELEMENT 158 8.2.3 OPERATIONAL AMPLIFIER INTEGRATOR WITH
DISTRIBUTED ELEMENT .... 159 8.2.4 OPERATIONAL AMPLIFIER DIFFERENTIAL
CIRCUIT WITH LUMPED ELEMENTS 161 8.2.5 OPERATIONAL AMPLIFIER
DIFFERENTIATOR WITH DISTRIBUTED ELEMENT. 162 8.2.6 OPERATIONAL AMPLIFIER
AS ZERO-ORDER GAIN WITH LUMPED COMPONENTS 163 8.2.7 OPERATIONAL
AMPLIFIER AS ZERO-ORDER GAIN WITH DISTRIBUTED ELEMENTS 163 8.2.8
OPERATIONAL AMPLIFIER CIRCUIT FOR SEMI-DIFFERINTEGRATION BY
SEMI-INFINITE LOSSY LINE 164 8.2.9 OPERATIONAL AMPLIFIER CIRCUIT FOR
SEMI-INTEGRATOR 165 8.2.10 OPERATIONAL AMPLIFIER CIRCUIT FOR
SEMI-DIFFERENTIATOR 166 8.2.11 CASCADED SEMI-INTEGRATORS 167 8.2.12
SEMI-INTEGRATOR SERIES WITH SEMI-DIFFERENTIATOR CIRCUIT 167 8.3 BATTERY
DYNAMICS 168 8.3.1 BATTERY AS FRACTIONAL ORDER SYSTEM 168 8.3.2 BATTERY
CHARGING PHASE 168 8.3.3 BATTERY DISCHARGE PHASE 172 8.4 TRACKING FILTER
174 8.4.1 OBSERVATIONS 176 8.5 FRACTIONAL ORDER STATE VECTOR
REPRESENTATION IN CIRCUIT THEORY 177 8.6 CONCLUDING COMMENTS 180
CONTENTS XVII 9 APPLICATION OF GENERALIZED FRACTIONAL CALCULUS IN OTHER
SCIENCE AND ENGINEERING FIELDS 181 9.1 INTRODUCTION 181 9.2 DIFFUSION
MODEL IN ELECTROCHEMISTRY 181 9.3 ELECTRODE-ELECTROLYTE INTERFACE
IMPEDANCE 182 9.4 CAPACITOR THEORY 184 9.5 FRACTANCE CIRCUIT 185 9.6
FEEDBACK CONTROL SYSTEM 187 9.6.1 CONCEPT OF ISO-DAMPING 194 9.6.2
FRACTIONAL VECTOR FEEDBACK CONTROLLER 196 9.6.3 OBSERVER IN FRACTIONAL
VECTOR SYSTEM 197 9.6.4 MODERN ASPECTS OF FRACTIONAL CONTROL 199 9.7
VISCOELASTICITY (STRESS-STRAIN) 200 9.8 VIBRATION DAMPING SYSTEM 202 9.9
CONCLUDING COMMENTS 204 10 SYSTEM ORDER IDENTIFICATION AND CONTROL 205
10.1 INTRODUCTION 205 10.2 FRACTIONAL ORDER SYSTEMS 205 10.3 CONTINUOUS
ORDER DISTRIBUTION 207 10.4 DETERMINATION OF ORDER DISTRIBUTION FROM
FREQUENCY DOMAIN EXPERIMENTAL DATA 209 10.5 ANALYSIS OF CONTINUOUS ORDER
DISTRIBUTION 211 10.6 VARIABLE ORDER SYSTEM 220 10.6.1 RL DEFINITION FOR
VARIABLE ORDER 220 10.6.2 LAPLACE TRANSFORMS AND. TRANSFER FUNCTION OF
VARIABLE ORDER SYSTEM 222 10.6.3 GL DEFINITION FOR VARIABLE ORDER 223
10.7 GENERALIZED PID CONTROLS ( . 224 10.8 CONTINUUM ORDER FEEDBACK
CONTROL SYSTEM 226 10.9 TIME DOMAIN RESPONSE OF SINUSOIDAL INPUTS FOR
FRACTIONAL ORDER OPERATOR 228 10.10 FREQUENCY DOMAIN RESPONSE OF
SINUSOIDAL INPUTS FOR FRACTIONAL ORDER OPERATOR 229 10.11 ULTRA-DAMPED
SYSTEM RESPONSE 229 10.12 HYPER-DAMPED SYSTEM RESPONSE 230 10.13
DISADVANTAGE OF FRACTIONAL ORDER SYSTEM 231 10.14 CONCLUDING COMMENTS F
232 BIBLIOGRAPHY 233
|
| adam_txt |
SHANTANU DAS FUNCTIONAL FRACTIONAL CALCULUS FOR SYSTEM IDENTIFICATION
AND CONTROLS WITH 68 FIGURES AND 11 TABLES 4Y SPRINGER CONTENTS 1
INTRODUCTION TO FRACTIONAL CALCULUS 1 1.1 INTRODUCTION 1 1.2 BIRTH OF
FRACTIONAL CALCULUS 1 1.3 FRACTIONAL CALCULUS A GENERALIZATION OF
INTEGER ORDER CALCULUS 2 1.4 HISTORICAL DEVELOPMENT OF FRACTIONAL
CALCULUS 3 1.4.1 THE POPULAR DEFINITIONS OF FRACTIONAL
DERIVATIVES/INTEGRALS IN FRACTIONAL CALCULUS 7 1.5 ABOUT FRACTIONAL
INTEGRATION DERIVATIVES AND DIFFERINTEGRATION 9 1.5.1 FRACTIONAL
INTEGRATION RIEMANN-LIOUVILLE (RL) 9 1.5.2 FRACTIONAL DERIVATIVES
RIEMANN-LIOUVILLE (RL) LEFT HAND DEFINITION (LHD) 10 1.5.3 FRACTIONAL
DERIVATIVES CAPUTO RIGHT HAND DEFINITION (RHD) . 10 1.5.4 FRACTIONAL
DIFFERINTEGRALS GRUNWALD LETNIKOV (GL) 12 1.5.5 COMPOSITION AND PROPERTY
14 1.5.6 FRACTIONAL DERIVATIVE FOR SOME STANDARD FUNCTION 15 1.6
SOLUTION OF FRACTIONAL DIFFERENTIAL EQUATIONS 16 1.7 A THOUGHT
EXPERIMENT." 16 1.8 QUOTABLE QUOTES ABOUT FRACTIONAL CALCULUS 17 1.9
CONCLUDING COMMENTS 18 2 FUNCTIONS USED IN FRACTIONAL CALCULUS 19 2.1
INTRODUCTION 19 2.2 FUNCTIONS FOR THE FRACTIONAL CALCULUS 19 2.2.1 GAMMA
FUNCTION 19 2.2.2 MITTAG-LEFFLER FUNCTION .* 22 2.2.3 AGARWAL FUNCTION
27 2.2.4 ERDELYI'S FUNCTION 27 2.2.5 ROBOTNOV-HARTLEY FUNCTION 27 2.2.6
MILLER-ROSS FUNCTION 27 2.2.7 GENERALIZED R FUNCTION AND G FUNCTION 28
2.3 LIST OF LAPLACE AND INVERSE LAPLACE TRANSFORMS RELATED TO FRACTIONAL
CALCULUS . /: 30 2.4 CONCLUDING COMMENTS 33 XIV CONTENTS 3 OBSERVATION
OF FRACTIONAL CALCULUS IN PHYSICAL SYSTEM DESCRIPTION . 35 3.1
INTRODUCTION 35 3.2 TEMPERATURE-HEAT FLUX RELATIONSHIP FOR HEAT FLOWING
IN SEMI-INFINITE CONDUCTOR 35 3.3 SINGLE THERMOCOUPLE JUNCTION
TEMPERATURE IN MEASUREMENT OF HEAT FLUX 38 3.4 HEAT TRANSFER 40 3.5
DRIVING POINT IMPEDANCE OF SEMI-INFINITE LOSSY TRANSMISSION LINE . 43
3.5.1 PRACTICAL APPLICATION OF THE SEMI-INFINITE LINE IN CIRCUITS 49
3.5.2 APPLICATION OF FRACTIONAL INTEGRAL AND FRACTIONAL DIFFERENTIATOR
CIRCUIT IN CONTROL SYSTEM 52 3.6 SEMI-INFINITE LOSSLESS TRANSMISSION
LINE 54 3.7 THE CONCEPT OF SYSTEM ORDER AND INITIALIZATION FUNCTION 60
3.8 CONCLUDING COMMENTS 61 4 CONCEPT OF FRACTIONAL DIVERGENCE AND
FRACTIONAL CURL 63 4.1 INTRODUCTION 63 4.2 CONCEPT OF FRACTIONAL
DIVERGENCE FOR PARTICLE FLUX 63 4.3 FRACTIONAL KINETIC EQUATION 65 4.4
NUCLEAR REACTOR NEUTRON FLUX DESCRIPTION 67 4.5 CLASSICAL CONSTITUTIVE
NEUTRON DIFFUSION EQUATION 67 4.5.1 DISCUSSION ON CLASSICAL CONSTITUTIVE
EQUATIONS 68 4.5.2 GRAPHICAL EXPLANATION 69 4.5.3 ABOUT SURFACE FLUX
CURVATURE 69 4.5.4 STATISTICAL AND GEOMETRICAL EXPLANATION FOR NON-LOCAL
DIVERGENCE 70 4.6 FRACTIONAL DIVERGENCE IN NEUTRON DIFFUSION EQUATIONS
71 4.6.1 SOLUTION OF CLASSICAL CONSTITUTIVE NEUTRON DIFFUSION EQUATION
(INTEGER ORDER) 73 4.6.2 SOLUTION OF FRACTIONAL DIVERGENCE BASED NEUTRON
DIFFUSION EQUATION (FRACTIONAL ORDER) 74 4.6.3 FRACTIONAL GEOMETRICAL
BUCKLING AND NON-POINT REACTOR KINETICS 76 4.7 CONCEPT OF FRACTIONAL
CURL IN ELECTROMAGNETICS 76 4.7.1 DUALITY OF SOLUTIONS 77 4.7.2
FRACTIONAL CURL OPERATOR ^ 77 4.7.3 WAVE PROPAGATION IN UNBOUNDED CHIRAL
MEDIUM 77 4.8 CONCLUDING COMMENTS 79 5 FRACTIONAL DIFFERINTEGRATIONS:
INSIGHT CONCEPTS 81 5.1 INTRODUCTION 81 5.2 SYMBOL STANDARDIZATION AND
DESCRIPTION FOR DIFFERINTEGRATION 81 5.3 REIMANN-LIOUVILLE FRACTIONAL
DIFFERINTEGRAL 82 5.3.1 SCALE TRANSFORMATION 82 5.3.2 CONVOLUTION 85
CONTENTS XV 5.3.3 PRACTICAL EXAMPLE OF RL DIFFERINTEGRATION IN
ELECTRICAL CIRCUIT ELEMENT DESCRIPTION 87 5.4 GRUNWALD-LETNIKOV
FRACTIONAL DIFFERINTERATION 90 5.5 UNIFICATION OF DIFFERINTEGRATION
THROUGH BINOMIAL COEFFICIENTS 92 5.6 SHORT MEMORY PRINCIPLE: A MOVING
START POINT APPROXIMATION AND ITS ERROR 95 5.7 MATRIX APPROACH TO
DISCRETIZE FRACTIONAL DIFFERINTEGRATION AND WEIGHTS 97 5.8 INFINITESIMAL
ELEMENT GEOMETRICAL INTERPRETATION OF FRACTIONAL DIFFERINTEGRATIONS 98
5.8.1 INTEGRATION 99 5.8.2 DIFFERENTIATION 100 5.9 ADVANCE DIGITAL
ALGORITHMS REALIZATION FOR FRACTIONAL CONTROLS 102 5.9.1 CONCEPT OF
GENERATING FUNCTION 102 5.9.2 DIGITAL FILTER REALIZATION BY RATIONAL
FUNCTION APPROXIMATION FOR FRACTIONAL OPERATOR 103 5.9.3 FILTER
STABILITY CONSIDERATION 106 5.10 LOCAL FRACTIONAL DERIVATIVES 106 5.11
CONCLUDING COMMENTS 107 6 INITIALIZED DIFFERINTEGRALS AND GENERALIZED
CALCULUS 109 6.1 INTRODUCTION 109 6.2 NOTATIONS OF DIFFERINTEGRALS 110
6.3 REQUIREMENT OF INITIALIZATION 110 6.4 INITIALIZATION FRACTIONAL
INTEGRATION (RIEMANN-LIOUVILLE APPROACH) 112 6.4.1 TERMINAL
INITIALIZATION '. 113 6.4.2 SIDE INITIALIZATION 114 6.5 INITIALIZING
FRACTIONAL DERIVATIVE (RIEMANN-LIOUVELLE APPROACH) 115 6.5.1 TERMINAL
INITIALIZATION 116 6.5.2 SIDE INITIALIZATION 117 6.6 INITIALIZING
FRACTIONAL DIFFERINTEGRALS (GRUNWALD-LETNIKOV APPROACH) .118 6.7
PROPERTIES AND CRITERIA FOR GENERALIZED DIFFERINTEGRALS 119 6.7.1
TERMINAL CHARGING 121 6.7.2 SIDE CHARGING 122 6.8 THE FUNDAMENTAL
FRACTIONAL ORDER DIFFERENTIAL EQUATION 122 6.8.1 THE GENERALIZED IMPULSE
RESPONSE FUNCTIOFF 123 6.9 CONCLUDING COMMENTS 127 7 GENERALIZED LAPLACE
TRANSFORM FOR FRACTIONAL DIFFERINTEGRALS 129 7.1 INTRODUCTION 129 7.2
RECALLING LAPLACE TRANSFORM FUNDAMENTALS 129 7.3 LAPLACE TRANSFORM OF
FRACTIONAL INTEGRALS 131 7.3.1 DECOMPOSITION OF FRACTIONAL INTEGRAL IN
INTEGER ORDER 132 7.3.2 DECOMPOSITION OF FRACTIONAL ORDER INTEGRAL IN
FRACTIONAL ORDER 135 XVI CONTENTS 7.4 LAPLACE TRANSFORMATION OF
FRACTIONAL DERIVATIVES 136 7.4.1 DECOMPOSITION OF FRACTIONAL ORDER
DERIVATIVE IN INTEGER ORDER 138 7.4.2 DECOMPOSITION OF FRACTIONAL
DERIVATIVE IN FRACTIONAL ORDER . 141 7.4.3 EFFECT OF TERMINAL CHARGING
ON LAPLACE TRANSFORMS 142 7.5 START POINT SHIFT EFFECT 143 7.5.1
FRACTIONAL INTEGRAL 143 7.5.2 FRACTIONAL DERIVATIVE ; 143 7.6 LAPLACE
TRANSFORM OF INITIALIZATION FUNCTION 144 7.6.1 FRACTIONAL INTEGRAL 144
7.6.2 FRACTIONAL DERIVATIVE 144 7.7 EXAMPLES OF INITIALIZATION IN
FRACTIONAL DIFFERENTIAL EQUATIONS 144 7.8 PROBLEM OF SCALAR
INITIALIZATION 147 7.9 PROBLEM OF VECTOR INITIALIZATION 149 7.10 LAPLACE
TRANSFORM S * * W PLANE FOR FRACTIONAL CONTROLS STABILITY 151 7.11
RATIONAL APPROXIMATIONS OF FRACTIONAL LAPLACE OPERATOR 153 7.12
CONCLUDING COMMENTS 155 8 APPLICATION OF GENERALIZED FRACTIONAL CALCULUS
IN ELECTRICAL CIRCUIT ANALYSIS 157 8.1 INTRODUCTION 157 8.2 ELECTRONICS
OPERATIONAL AMPLIFIER CIRCUITS 157 8.2.1 OPERATIONAL AMPLIFIER CIRCUIT
WITH LUMPED COMPONENTS 157 8.2.2 OPERATIONAL AMPLIFIER INTEGRATOR WITH
LUMPED ELEMENT 158 8.2.3 OPERATIONAL AMPLIFIER INTEGRATOR WITH
DISTRIBUTED ELEMENT . 159 8.2.4 OPERATIONAL AMPLIFIER DIFFERENTIAL
CIRCUIT WITH LUMPED ELEMENTS 161 8.2.5 OPERATIONAL AMPLIFIER
DIFFERENTIATOR WITH DISTRIBUTED ELEMENT. 162 8.2.6 OPERATIONAL AMPLIFIER
AS ZERO-ORDER GAIN WITH LUMPED COMPONENTS 163 8.2.7 OPERATIONAL
AMPLIFIER AS ZERO-ORDER GAIN WITH DISTRIBUTED ELEMENTS 163 8.2.8
OPERATIONAL AMPLIFIER CIRCUIT FOR SEMI-DIFFERINTEGRATION BY
SEMI-INFINITE LOSSY LINE 164 8.2.9 OPERATIONAL AMPLIFIER CIRCUIT FOR
SEMI-INTEGRATOR 165 8.2.10 OPERATIONAL AMPLIFIER CIRCUIT FOR
SEMI-DIFFERENTIATOR 166 8.2.11 CASCADED SEMI-INTEGRATORS 167 8.2.12
SEMI-INTEGRATOR SERIES WITH SEMI-DIFFERENTIATOR CIRCUIT 167 8.3 BATTERY
DYNAMICS 168 8.3.1 BATTERY AS FRACTIONAL ORDER SYSTEM 168 8.3.2 BATTERY
CHARGING PHASE 168 8.3.3 BATTERY DISCHARGE PHASE 172 8.4 TRACKING FILTER
174 8.4.1 OBSERVATIONS 176 8.5 FRACTIONAL ORDER STATE VECTOR
REPRESENTATION IN CIRCUIT THEORY 177 8.6 CONCLUDING COMMENTS 180
CONTENTS XVII 9 APPLICATION OF GENERALIZED FRACTIONAL CALCULUS IN OTHER
SCIENCE AND ENGINEERING FIELDS 181 9.1 INTRODUCTION 181 9.2 DIFFUSION
MODEL IN ELECTROCHEMISTRY 181 9.3 ELECTRODE-ELECTROLYTE INTERFACE
IMPEDANCE 182 9.4 CAPACITOR THEORY 184 9.5 FRACTANCE CIRCUIT 185 9.6
FEEDBACK CONTROL SYSTEM 187 9.6.1 CONCEPT OF ISO-DAMPING 194 9.6.2
FRACTIONAL VECTOR FEEDBACK CONTROLLER 196 9.6.3 OBSERVER IN FRACTIONAL
VECTOR SYSTEM 197 9.6.4 MODERN ASPECTS OF FRACTIONAL CONTROL 199 9.7
VISCOELASTICITY (STRESS-STRAIN) 200 9.8 VIBRATION DAMPING SYSTEM 202 9.9
CONCLUDING COMMENTS 204 10 SYSTEM ORDER IDENTIFICATION AND CONTROL 205
10.1 INTRODUCTION 205 10.2 FRACTIONAL ORDER SYSTEMS 205 10.3 CONTINUOUS
ORDER DISTRIBUTION 207 10.4 DETERMINATION OF ORDER DISTRIBUTION FROM
FREQUENCY DOMAIN EXPERIMENTAL DATA 209 10.5 ANALYSIS OF CONTINUOUS ORDER
DISTRIBUTION 211 10.6 VARIABLE ORDER SYSTEM 220 10.6.1 RL DEFINITION FOR
VARIABLE ORDER 220 10.6.2 LAPLACE TRANSFORMS AND. TRANSFER FUNCTION OF
VARIABLE ORDER SYSTEM 222 10.6.3 GL DEFINITION FOR VARIABLE ORDER 223
10.7 GENERALIZED PID CONTROLS ( . 224 10.8 CONTINUUM ORDER FEEDBACK
CONTROL SYSTEM 226 10.9 TIME DOMAIN RESPONSE OF SINUSOIDAL INPUTS FOR
FRACTIONAL ORDER OPERATOR 228 10.10 FREQUENCY DOMAIN RESPONSE OF
SINUSOIDAL INPUTS FOR FRACTIONAL ORDER OPERATOR 229 10.11 ULTRA-DAMPED
SYSTEM RESPONSE 229 10.12 HYPER-DAMPED SYSTEM RESPONSE 230 10.13
DISADVANTAGE OF FRACTIONAL ORDER SYSTEM 231 10.14 CONCLUDING COMMENTS F
232 BIBLIOGRAPHY 233 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Das, Shantanu |
| author_facet | Das, Shantanu |
| author_role | aut |
| author_sort | Das, Shantanu |
| author_variant | s d sd |
| building | Verbundindex |
| bvnumber | BV023388315 |
| classification_rvk | SK 490 |
| ctrlnum | (OCoLC)634194447 (DE-599)DNB983914656 |
| dewey-full | 515.83 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.83 |
| dewey-search | 515.83 |
| dewey-sort | 3515.83 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV023388315 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:18:54Z |
| indexdate | 2024-07-09T21:17:28Z |
| institution | BVB |
| isbn | 9783540727026 3540727027 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016571292 |
| oclc_num | 634194447 |
| open_access_boolean | |
| owner | DE-703 |
| owner_facet | DE-703 |
| physical | XVII, 239 S. graph. Darst. 24 cm |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| spelling | Das, Shantanu Verfasser aut Functional fractional calculus for system identification and controls with ... 11 tables Shantanu Das Berlin [u.a.] Springer 2008 XVII, 239 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 233 - 239 Gebrochene Analysis (DE-588)4722475-7 gnd rswk-swf Gebrochene Analysis (DE-588)4722475-7 s DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016571292&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Das, Shantanu Functional fractional calculus for system identification and controls with ... 11 tables Gebrochene Analysis (DE-588)4722475-7 gnd |
| subject_GND | (DE-588)4722475-7 |
| title | Functional fractional calculus for system identification and controls with ... 11 tables |
| title_auth | Functional fractional calculus for system identification and controls with ... 11 tables |
| title_exact_search | Functional fractional calculus for system identification and controls with ... 11 tables |
| title_exact_search_txtP | Functional fractional calculus for system identification and controls with ... 11 tables |
| title_full | Functional fractional calculus for system identification and controls with ... 11 tables Shantanu Das |
| title_fullStr | Functional fractional calculus for system identification and controls with ... 11 tables Shantanu Das |
| title_full_unstemmed | Functional fractional calculus for system identification and controls with ... 11 tables Shantanu Das |
| title_short | Functional fractional calculus for system identification and controls |
| title_sort | functional fractional calculus for system identification and controls with 11 tables |
| title_sub | with ... 11 tables |
| topic | Gebrochene Analysis (DE-588)4722475-7 gnd |
| topic_facet | Gebrochene Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016571292&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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