Stabilisation and motion control of unstable objects:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
De Gruyter
[2015]
|
| Schriftenreihe: | De Gruyter studies in mathematical physics
volume 33 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XVI, 236 Seiten Illustrationen, Diagramme |
| ISBN: | 3110375826 9783110375824 9783110375909 |
Internformat
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| 100 | 1 | |a Formal'skij, Aleksandr M. |e Verfasser |0 (DE-588)1078784000 |4 aut | |
| 245 | 1 | 0 | |a Stabilisation and motion control of unstable objects |c Alexander M. Formalskii |
| 264 | 1 | |a Berlin |b De Gruyter |c [2015] | |
| 264 | 4 | |c © 2015 | |
| 300 | |a XVI, 236 Seiten |b Illustrationen, Diagramme | ||
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| 337 | |b n |2 rdamedia | ||
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| 650 | 0 | 7 | |a Instabilität |0 (DE-588)4139195-0 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1806332825757024256 |
|---|---|
| adam_text |
CONTENTS
PREFACE TO ENGLISH EDITION IX
PREFACE * XI
PART I:
DEVICES CONTAINING A SINGLE-LINK PENDULUM
1 A PENDULUM WITH STATIONARY PIVOT 5
1.1 EQUATIONS OF MOTION 5
1.2 DOMAIN OF CONTROLLABILITY 7
1.3 MAXIMIZING DOMAIN OF ATTRACTION 9
1.4 DELAY IN FEEDBACK LOOP 13
1.5 NONLINEAR CONTROL 16
1.6 CONTROLLABILITY DOMAIN OF THE NONLINEAR MODEL 17
2 A PENDULUM WITH WHEEL-BASED PIVOT * 21
2.1 EQUATIONS OF MOTION 21
2.2 DOMAIN OF CONTROLLABILITY 24
2.3 MAXIMIZING DOMAIN OF ATTRACTION 27
2.4 NONLINEAR CONTROL 29
3 A PENDULUM WITH A FLYWHEEL 31
3.1 THE ARRANGEMENT OF THE PENDULUM WITH A FLYWHEEL * 31
3.2 EQUATIONS OF MOTION 33
3.3 LOCAL STABILIZATION OF THE PENDULUM IN THE TOP EQUILIBRIUM 35
3.4 SUPPRESSING FLYWHEEL ROTATION 41
3.5 SWINGING AND DAMPINGTHE PENDULUM 42
3.6 TRANSLATING THE PENDULUM FROM THE BOTTOM EQUILIBRIUM INTO THE TOP
ONE 45
3.7 NUMERICAL EXPERIMENTS * 46
3.8 PRACTICAL EXPERIMENTS 47
4 WHEEL
ROLLING CONTROL
BY MEANS OF A PENDULUM 50
4.1 MATHEMATICAL MODEL 51
4.2 STEADY MODES OF MOTION 53
4.3 STABILITY OF STEADY-STATE MODES 56
HTTP://D-NB.INFO/1067968199
VI
CONTENTS
5 OPTIMAL SWINGING
AND DAMPING OF A SWING 58
5.1 ON OPTIMAL CONTROL DESIGN IN SECOND-ORDER SYSTEMS 58
5.2 MATHEMATICAL MODEL OF A SWING 62
5.3 MAXIMIZING THE SWING OSCILLATIONS MAGNITUDE 63
5.4 MINIMIZINGSWINGOSCILLATION MAGNITUDE 67
5.5 CONTROLLING A SWING WITH REGARD FOR AERODYNAMIC RESISTANCE AND DRY
FRICTION 69
6 PENDULUM CONTROL THAT MINIMIZES ENERGY
CONSUMPTION 71
6.1 ESTIMATION OF ENERGY CONSUMPTION 71
6.2 TRANSLATING THE PENDULUM TO THE UNSTABLE EQUILIBRIUM 74
6.3 TRANSLATING THE PENDULUM TO THE STABLE EQUILIBRIUM 80
PART II:
DOUBLE PHYSICAL PENDULUM
7 LOCAL STABILIZATION OF AN INVERTED PENDULUM BY MEANS OF A SINGLE
CONTROL
TORQUE 91
7.1 MATHEMATICAL MODEL OF THE PENDULUM * 91
7.2 LINEARIZED MODEL 93
7.3 DOMAINS OF CONTROLLABILITY 94
7.4 FEEDBACK DESIGN. MAXIMIZING DOMAIN OF ATTRACTION 98
7.5 NUMERICAL EXPERIMENTS 104
8 OPTIMAL CONTROL
DESIGN FOR SWINGING AND DAMPING
A DOUBLE
PENDULUM *110
8.1 MATHEMATICAL MODEL 110
8.2 REDUCED ANGLE 112
8.3 OPTIMAL CONTROL THAT SWINGS THE PENDULUM 113
8.4 OPTIMAL CONTROL LAW FOR PENDULUM DAMPING 119
8.5 ON TRANSLATING THE PENDULUM FROM ITS BOTTOM EQUILIBRIUM TO THE TOP
ONE 123
9 GLOBAL STABILIZATION OF AN
INVERTED PENDULUM CONTROLLED BY TORQUE IN THE
INTER-LINK JOINT *126
9.1 MATHEMATICAL MODEL 127
9.2 CASCADE FORM OF DYNAMIC EQUATIONS 128
9.3 CONTROL LAW THAT SWINGS THE PENDULUM 129
9.4 TRACKING THE DESIRED INTER-LINK ANGLE DYNAMICS 130
9.5 LOCAL STABILIZATION OF AN INVERTED PENDULUM 131
9.6 NUMERICAL EXPERIMENTS 131
CONTENTS
VII
10 GLOBAL STABILIZATION OF AN INVERTED PENDULUM
CONTROLLED BY TORQUE IN THE
PIVOT 134
10.1 MATHEMATICAL MODEL 134
10.2 SWINGING THE PENDULUM 135
10.3 STRAIGHTENING THE PENDULUM 135
10.4 LINEAR MODEL, LOCAL STABILIZATION *138
10.5 NUMERICAL EXPERIMENTS 141
11 MULTI-LINK PENDULUM ON A MOVING
BASE 145
11.1 MULTI-LINK PENDULUM ON A WHEEL 145
11.2 SINGLE-LINK PENDULUM ON A WHEEL 149
11.3 GLOBAL STABILIZATION OF THE INVERTED PENDULUM-
11.4 DOMAIN OF CONTROLLABILITY 155
11.5 DESIGNING TIME-OPTIMAL TRAJECTORIES 157
11.6 A PENDULUM ON A CART 159
11.7 FREQUENCY LOWERING AS A RESULT OF CONSTRAINING
PART III:
BALL ON A BEAM
12 STABILIZATION OF A BALL ON A STRAIGHT BEAM 165
12.1 MATHEMATICAL MODEL OF THE SYSTEM 165
12.2 LINEARIZED MODEL 167
12.3 FEEDBACK DESIGN 169
12.4 NUMERICAL EXPERIMENTS 171
13 STABILIZATION OF A BALL ON A CURVILINEAR BEAM 176
13.1 MATHEMATICAL MODEL OF THE SYSTEM *176
13.2 LINEARIZED MODEL 178
13.3 FEEDBACK DESIGN 180
13.4 NUMERICAL EXPERIMENTS 181
PART IV:
GYROSCOPIC STABILIZATION OF A TWO-WHEEL BICYCLE
14 BICYCLE DESIGN 189
14.1 BICYCLE WITH ONE CONTROLLED WHEEL 189
14.2 BICYCLE WITH TWO CONTROLLED WHEELS 192
14.3 GYROSCOPIC STABILIZER 194
14.4 EQUATIONS OF TILT OSCILLATIONS OF THE BICYCLE 195
151
161
VIII *
CONTENTS
15 DESIGNING A CONTROL LAW TO STABILIZE
THE BICYCLE
TILT 198
15.1 BICYCLE TILT MEASUREMENT BY MEANS OF ACCELEROMETERS 198
15.2 BICYCLE MOVEMENT ALONG A STRAIGHT LINE 199
15.3 MOTION ALONG A CIRCLE 201
15.4 NUMERICAL AND PRACTICAL EXPERIMENTS 203
PART V:
AVOIDING UNDESIRED VIBRATIONS
16 BANG-BANG
CONTROL AND FLUENT CONTROL 209
16.1 MATHEMATICAL MODEL 210
16.2 FORMULATION OF THE PROBLEM 212
16.3 BANG-BANG CONTROL VERSUS FLUENT CONTROL 213
17 TRAPEZOIDAL CONTROL
FOR A SYSTEM WITH COMPLIANT ELEMENTS 217
17.1 TRAPEZOIDAL FLUENT CONTROL 217
17.2 TRAPEZOIDAL CONTROL WITH SHORTER TRANSIENTS 220
17.3 RELATIONSHIP BETWEEN TIME
T
AND DISPLACEMENTX^ 223
17.4 NUMERICAL ANALYSIS OF THE OPEN-LOOP SYSTEM * 224
17.5 FEEDBACK CONTROL 227
BIBLIOGRAPHY 229
INDEX 237 |
| any_adam_object | 1 |
| author | Formal'skij, Aleksandr M. |
| author_GND | (DE-588)1078784000 |
| author_facet | Formal'skij, Aleksandr M. |
| author_role | aut |
| author_sort | Formal'skij, Aleksandr M. |
| author_variant | a m f am amf |
| building | Verbundindex |
| bvnumber | BV043019306 |
| classification_rvk | UF 1610 UF 1950 |
| classification_tum | PHY 205f |
| ctrlnum | (OCoLC)904861551 (DE-599)DNB1067968199 |
| dewey-full | 530 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530 |
| dewey-search | 530 |
| dewey-sort | 3530 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-08-03T02:47:01Z |
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| isbn | 3110375826 9783110375824 9783110375909 |
| language | English |
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| physical | XVI, 236 Seiten Illustrationen, Diagramme |
| publishDate | 2015 |
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| publisher | De Gruyter |
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| spelling | Formal'skij, Aleksandr M. Verfasser (DE-588)1078784000 aut Stabilisation and motion control of unstable objects Alexander M. Formalskii Berlin De Gruyter [2015] © 2015 XVI, 236 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier De Gruyter studies in mathematical physics volume 33 Mechanisches System (DE-588)4132811-5 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Instabilität (DE-588)4139195-0 gnd rswk-swf System Dynamics (DE-588)4058802-6 gnd rswk-swf Mechanisches System (DE-588)4132811-5 s System Dynamics (DE-588)4058802-6 s Instabilität (DE-588)4139195-0 s Kontrolltheorie (DE-588)4032317-1 s 1\p DE-604 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-039282-1 Erscheint auch als Online-Ausgabe, PDF 978-3-11-037589-3 De Gruyter studies in mathematical physics volume 33 (DE-604)BV040141722 33 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=5168205&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028444136&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Formal'skij, Aleksandr M. Stabilisation and motion control of unstable objects De Gruyter studies in mathematical physics Mechanisches System (DE-588)4132811-5 gnd Kontrolltheorie (DE-588)4032317-1 gnd Instabilität (DE-588)4139195-0 gnd System Dynamics (DE-588)4058802-6 gnd |
| subject_GND | (DE-588)4132811-5 (DE-588)4032317-1 (DE-588)4139195-0 (DE-588)4058802-6 |
| title | Stabilisation and motion control of unstable objects |
| title_auth | Stabilisation and motion control of unstable objects |
| title_exact_search | Stabilisation and motion control of unstable objects |
| title_full | Stabilisation and motion control of unstable objects Alexander M. Formalskii |
| title_fullStr | Stabilisation and motion control of unstable objects Alexander M. Formalskii |
| title_full_unstemmed | Stabilisation and motion control of unstable objects Alexander M. Formalskii |
| title_short | Stabilisation and motion control of unstable objects |
| title_sort | stabilisation and motion control of unstable objects |
| topic | Mechanisches System (DE-588)4132811-5 gnd Kontrolltheorie (DE-588)4032317-1 gnd Instabilität (DE-588)4139195-0 gnd System Dynamics (DE-588)4058802-6 gnd |
| topic_facet | Mechanisches System Kontrolltheorie Instabilität System Dynamics |
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