Analysis and control of nonlinear systems: a flatness based approach
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2009
|
| Series: | Mathematical engineering
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 307 - 315 |
| Physical Description: | XIII, 319 S. Ill., graph. Darst. |
| ISBN: | 9783642008382 |
Staff View
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| 100 | 1 | |a Lévine, Jean |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Analysis and control of nonlinear systems |b a flatness based approach |c Jean Lévine |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2009 | |
| 300 | |a XIII, 319 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 0 | |a Mathematical engineering | |
| 500 | |a Literaturverz. S. 307 - 315 | ||
| 650 | 4 | |a Nichtlineares dynamisches System - Flachheitsbasierte Folgeregelung | |
| 650 | 4 | |a Nonlinear control theory | |
| 650 | 4 | |a Nonlinear systems | |
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Record in the Search Index
| _version_ | 1804140800260440064 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
1 INTRODUCTION 1
1.1 TRAJECTORY PLANNING AND TRACKING 2
1.2 EQUIVALENCE AND FLATNESS 3
1.3 EQUIVALENCE IN SYSTEM THEORY 5
1.4 EQUIVALENCE AND STABILITY 5
1.5 WHAT IS A NONLINEAR CONTROL SYSTEM? 6
1.5.1 NONLINEARITY VERSUS LINEARITY 6
1.5.2 UNCONTROLLED VERSUS CONTROLLED NONLINEARITY 7
PART I THEORY
2 INTRODUCTION TO DIFFERENTIAL GEOMETRY 13
2.1 MANIFOLD, DIFFEOMORPHISM 14
2.2 VECTOR FIELDS 17
2.2.1 TANGENT SPACE, VECTOR FIELD 17
2.2.2 FLOW, PHASE PORTRAIT 19
2.2.3 LIE DERIVATIVE 21
2.2.4 IMAGE OF A VECTOR FIELD 22
2.2.5 FIRST INTEGRAL, STRAIGHTENING OUT OF A VECTOR FIELD 23 2.2.6 LIE
BRACKET 25
2.2.7 DISTRIBUTION OF VECTOR FIELDS 28
2.2.8 INTEGRAL MANIFOLDS 29
2.2.9 FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS 30
2.3 DIFFERENTIAL FORMS 32
2.3.1 COTANGENT SPACE, DIFFERENTIAL FORM, DUALITY 32
2.3.2 EXTERIOR DIFFERENTIATION 35
2.3.3 IMAGE OF A DIFFERENTIAL FORM 36
2.3.4 PFAFFIAN SYSTEM, COMPLETE INTEGRABILITY 37
2.3.5 LIE DERIVATIVE OF A 1-FORM 39
2.3.6 BACK TO FROBENIUS THEOREM 41
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/992870771
DIGITALISIERT DURCH
IMAGE 2
X CONTENTS
3 INTRODUCTION TO DYNAMICAL SYSTEMS 43
3.1 RECALLS ON FLOWS AND ORBITS 45
3.1.1 EQUILIBRIUM POINT, VARIATIONAL EQUATION 45
3.1.2 PERIODIC ORBIT 47
3.1.3 POINCARE S MAP 50
3.2 STABILITY OF EQUILIBRIUM POINTS AND ORBITS 53
3.2.1 ATTRACTOR 53
3.2.2 LYAPUNOV STABILITY 55
3.2.3 REMARKS ON THE STABILITY OF TIME-VARYING SYSTEMS . .. 58 3.2.4
LYAPUNOV S AND CHETAEV S FUNCTIONS 59
3.2.5 HARTMAN-GROBMAN S AND SHOSHITAISHVILI S THEOREMS, CENTRE MANIFOLD
64
3.3 SINGULARLY PERTURBED SYSTEMS 73
3.3.1 INVARIANT SLOW MANIFOLD 75
3.3.2 PERSISTENCE OF THE INVARIANT SLOW MANIFOLD 76
3.3.3 ROBUSTNESS OF THE STABILITY 78
3.3.4 AN APPLICATION TO MODELLING 79
3.4 APPLICATION TO HIERARCHICAL CONTROL 81
3.4.1 CONTROLLED SLOW DYNAMICS 81
3.4.2 HIERARCHICAL FEEDBACK DESIGN 82
3.4.3 PRACTICAL APPLICATIONS 83
4 CONTROLLED SYSTEMS, CONTROLLABILITY 87
4.1 LINEAR SYSTEM CONTROLLABILITY 87
4.1.1 KALMAN S CRITERION 87
4.1.2 CONTROLLABILITY CANONICAL FORM 90
4.1.3 MOTION PLANNING 93
4.1.4 TRAJECTORY TRACKING, POLE PLACEMENT 95
4.2 NONLINEAR SYSTEM CONTROLLABILITY 96
4.2.1 FIRST ORDER AND LOCAL CONTROLLABILITY 96
4.2.2 LOCAL CONTROLLABILITY AND LIE BRACKETS 97
4.2.3 REACHABILITY 101
4.2.4 LIE BRACKETS AND KALMAN S CRITERION FOR LINEAR SYSTEMS 104
5 JETS OF INFINITE ORDER, LIE-BAECKLUND S EQUIVALENCE 107 5.1 AN
INTRODUCTORY EXAMPLE OF CRANE 107
5.2 DESCRIPTION OF THE SYSTEM TRAJECTORIES 109
5.3 JETS OF INFINITE ORDER, CHANGE OF COORDINATES, EQUIVALENCE . .. 113
5.3.1 JETS OF INFINITE ORDER, GLOBAL COORDINATES 114
5.3.2 PRODUCT MANIFOLDS, PRODUCT TOPOLOGY 114
5.3.3 CARTAN VECTOR FIELDS, FLOWS, CONTROL SYSTEMS 115 5.3.4
LIE-BAECKLUND EQUIVALENCE 121
5.3.5 PROPERTIES OF THE L-B EQUIVALENCE 125
5.3.6 ENDOGENOUS DYNAMIC FEEDBACK 127
IMAGE 3
CONTENTS XI
6 DIFFERENTIALLY FLAT SYSTEMS 131
6.1 FLAT SYSTEM, FLAT OUTPUT 131
6.2 EXAMPLES 133
6.2.1 MASS-SPRING SYSTEM 133
6.2.2 ROBOT CONTROL 134
6.2.3 PENDULUM 135
6.2.4 NON HOLONOMIC VEHICLE 138
6.2.5 VEHICLE WITH TRAILERS 139
6.3 FLATNESS AND CONTROLLABILITY 141
6.4 FLATNESS AND LINEARIZATION 143
6.4.1 MASS-SPRING SYSTEM (FOLLOWED) 144
6.4.2 ROBOT CONTROL (FOLLOWED) 145
6.4.3 PENDULUM (FOLLOWED) 145
6.4.4 NON HOLONOMIC VEHICLE (FOLLOWED) 146
6.5 FLAT OUTPUT CHARACTERIZATION 146
6.5.1 THE RULED MANIFOLD NECESSARY CONDITION 148
6.5.2 VARIATIONAL CHARACTERIZATION 151
6.5.3 THE POLYNOMIAL MATRIX APPROACH 152
6.5.4 PRACTICAL COMPUTATION OF THE SMITH DECOMPOSITION... 155 6.5.5
FLATNESS NECESSARY AND SUFFICIENT CONDITIONS 157 6.5.6 THE OPERATOR 0
160
6.5.7 STRONG CLOSEDNESS NECESSARY AND SUFFICIENT CONDITIONS 163 6.5.8
FLAT OUTPUTS OF LINEAR CONTROLLABLE SYSTEMS 167 6.5.9 EXAMPLES 170
7 FLATNESS AND MOTION PLANNING 181
7.1 MOTION PLANNING WITHOUT CONSTRAINT 182
7.1.1 THE GENERAL CASE 182
7.1.2 REST-TO-REST TRAJECTORIES 184
7.2 MOTION PLANNING WITH CONSTRAINTS 185
7.2.1 GEOMETRIC CONSTRAINTS 186
7.2.2 QUANTITATIVE CONSTRAINTS 189
7.3 APPLICATION TO PREDICTIVE CONTROL 190
8 FLATNESS AND TRACKING 193
8.1 THE TRACKING PROBLEM 193
8.1.1 PENDULUM (CONCLUSION) 194
8.1.2 NON HOLONOMIC VEHICLE (CONCLUSION) 195
8.2 CONTROL OF THE CLOCK 197
PART II APPLICATIONS
9 DC MOTOR STARTING PHASE 203
9.1 TRACKING OF A STEP SPEED REFERENCE 204
9.2 FLATNESS BASED TRACKING 206
IMAGE 4
XII CONTENTS
10 DISPLACEMENTS OF A LINEAR MOTOR WITH OSCILLATING MASSES 211 10.1
SINGLE MASS CASE 212
10.1.1 DISPLACEMENT WITHOUT TAKING ACCOUNT OF THE AUXILIARY MASS 213
10.1.2 DISPLACEMENTS TAKING ACCOUNT OF THE AUXILIARY MASS . 214 10.1.3
COMPARISONS 216
10.2 DISPLACEMENTS WITH TWO AUXILIARY MASSES 220
11 SYNCHRONIZATION OF A PAIR OF INDEPENDENT WINDSHIELD WIPERS 225
11.1 INTRODUCTION 225
11.2 THE MODEL OF A SINGLE WIPER 228
11.3 OPEN LOOP SYNCHRONIZATION OF THE PAIR OF WIPERS BY MOTION PLANNING
229
11.4 TRAJECTORY TRACKING 233
11.5 SYNCHRONIZATION BY CLOCK CONTROL 235
12 CONTROL OF MAGNETIC BEARINGS 243
12.1 ANALYSIS AND CONTROL OF A BALL 245
12.1.1 MODELLING 245
12.1.2 CURRENT CONTROL 246
12.1.3 VOLTAGE CONTROL 253
12.1.4 HIERARCHICAL CONTROL 255
12.2 THE GENERAL SHAFT 265
12.2.1 MODELLING 266
12.2.2 CURRENT CONTROL 267
12.2.3 HIERARCHICAL CONTROL 269
12.3 IMPLEMENTATION 269
12.3.1 OBSERVER DESIGN 270
12.3.2 DIGITAL CONTROL 273
12.4 EXPERIMENTAL RESULTS 273
12.4.1 PLATFORM DESCRIPTION 273
12.4.2 EXPERIMENTS 274
13 CRANE CONTROL 279
13.1 ORIENTATION 279
13.2 STRAIGHT LINE DISPLACEMENT 282
13.2.1 APPROXIMATE TRACKING OF STRAIGHT LINE BY HIERARCHICAL PID CONTROL
282
13.2.2 STRAIGHT LINE TRACKING WITHOUT SMALL ANGLE APPROXIMATION 286
13.3 OBSTACLE AVOIDANCE 290
13.3.1 TRACKING WITH SMALL ANGLE APPROXIMATION 291 13.3.2 TRACKING
WITHOUT SMALL ANGLE APPROXIMATION 293
IMAGE 5
CONTENTS XIII
14 AUTOMATIC FLIGHT CONTROL SYSTEMS 295
14.0.3 GENERIC AIRCRAFT MODEL 296
14.0.4 FLATNESS BASED AUTOPILOT DESIGN 299
REFERENCES 307
INDEX 317
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T22:05:44Z |
| institution | BVB |
| isbn | 9783642008382 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018693799 |
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| physical | XIII, 319 S. Ill., graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
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| publisher | Springer |
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| series2 | Mathematical engineering |
| spelling | Lévine, Jean Verfasser aut Analysis and control of nonlinear systems a flatness based approach Jean Lévine Berlin [u.a.] Springer 2009 XIII, 319 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematical engineering Literaturverz. S. 307 - 315 Nichtlineares dynamisches System - Flachheitsbasierte Folgeregelung Nonlinear control theory Nonlinear systems Flachheitsbasierte Folgeregelung (DE-588)4743050-3 gnd rswk-swf Nichtlineares dynamisches System (DE-588)4126142-2 gnd rswk-swf Nichtlineares dynamisches System (DE-588)4126142-2 s Flachheitsbasierte Folgeregelung (DE-588)4743050-3 s DE-604 Erscheint auch als Online-Ausgabe 978-3-642-00839-9 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018693799&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lévine, Jean Analysis and control of nonlinear systems a flatness based approach Nichtlineares dynamisches System - Flachheitsbasierte Folgeregelung Nonlinear control theory Nonlinear systems Flachheitsbasierte Folgeregelung (DE-588)4743050-3 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd |
| subject_GND | (DE-588)4743050-3 (DE-588)4126142-2 |
| title | Analysis and control of nonlinear systems a flatness based approach |
| title_auth | Analysis and control of nonlinear systems a flatness based approach |
| title_exact_search | Analysis and control of nonlinear systems a flatness based approach |
| title_full | Analysis and control of nonlinear systems a flatness based approach Jean Lévine |
| title_fullStr | Analysis and control of nonlinear systems a flatness based approach Jean Lévine |
| title_full_unstemmed | Analysis and control of nonlinear systems a flatness based approach Jean Lévine |
| title_short | Analysis and control of nonlinear systems |
| title_sort | analysis and control of nonlinear systems a flatness based approach |
| title_sub | a flatness based approach |
| topic | Nichtlineares dynamisches System - Flachheitsbasierte Folgeregelung Nonlinear control theory Nonlinear systems Flachheitsbasierte Folgeregelung (DE-588)4743050-3 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd |
| topic_facet | Nichtlineares dynamisches System - Flachheitsbasierte Folgeregelung Nonlinear control theory Nonlinear systems Flachheitsbasierte Folgeregelung Nichtlineares dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018693799&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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