Dynamics of controlled mechanical systems with delayed feedback: with 8 tables
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2002
|
| Series: | Engineering online library
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 294 S. graph. Darst. |
| ISBN: | 3540437339 |
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| 245 | 1 | 0 | |a Dynamics of controlled mechanical systems with delayed feedback |b with 8 tables |c H. Y. Hu ; Z. H. Wang |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2002 | |
| 300 | |a XIII, 294 S. |b graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804129229173948416 |
|---|---|
| adam_text | CONTENTS 1 MODELING OF DELAYED DYNAMIC
SYSTEMS............................................................1 1.1
MATHEMATICAL MODELS
..................................................................................1
1.1.1 DYNAMIC SYSTEMS WITH DELAYED FEEDBACK CONTROL
.............................1 1.1.2 DYNAMIC SYSTEMS WITH OPERATOR S
RETARDATION ....................................5 1.2 EXPERIMENTAL
MODELING
...............................................................................9
1.2.1 IDENTIFICATION OF SHORT TIME DELAYS IN LINEAR SYSTEMS
.....................10 1.2.2 IDENTIFICATION OF ARBITRARY TIME DELAYS IN
NONLINEAR SYSTEMS..........14 1.2.3 DISCUSSIONS ON IDENTIFIABILITY OF
TIME DELAYS ...................................21 2 FUNDAMENTALS OF
DELAY DIFFERENTIAL
EQUATIONS..............................................27 2.1 INITIAL
VALUE PROBLEMS
...............................................................................27
2.1.1 EXISTENCE AND UNIQUENESS OF SOLUTION
...............................................28 2.1.2 SOLUTION OF
LINEAR DELAY DIFFERENTIAL EQUATIONS................................33
2.2 STABILITY IN THE SENSE OF LYAPUNOV
............................................................37 2.2.1 THE
LYAPUNOV
METHODS......................................................................38
2.2.2 METHOD OF CHARACTERISTIC
FUNCTION.....................................................42 2.2.3
STABILITY CRITERIA
.................................................................................47
2.3 IMPORTANT FEATURES OF DELAY DIFFERENTIAL
EQUATIONS..................................54 3 STABILITY ANALYSIS OF
LINEAR DELAY SYSTEMS
....................................................59 3.1
DELAY-INDEPENDENT STABILITY OF SINGLE-DEGREE-OF-FREEDOM
SYSTEMS..........60 3.1.1 STABILITY CRITERIA
.................................................................................61
3.1.2 STABILITY CRITERIA IN TERMS OF FEEDBACK GAINS
...................................66 3.2 THE GENERALIZED STURM
CRITERION FOR POLYNOMIALS ....................................70 3.2.1
CLASSICAL STURM CRITERION
...................................................................70
3.2.2 DISCRIMINATION
SEQUENCE....................................................................72
3.2.3 MODIFIED SIGN
TABLE...........................................................................74
3.2.4 GENERALIZED STURM
CRITERION...............................................................75
3.3 DELAY-INDEPENDENT STABILITY OF HIGH DIMENSIONAL
SYSTEMS......................76 3.4 STABILITY OF
SINGLE-DEGREE-OF-FREEDOM SYSTEMS WITH FINITE TIME DELAYS.......86 3.4.1
SYSTEMS WITH EQUAL TIME
DELAYS.......................................................86 3.4.2
SYSTEMS WITH UNEQUAL TIME
DELAYS...................................................90 3.5
STABILITY SWITCHES OF HIGH DIMENSIONAL
SYSTEMS......................................91 3.5.1 SYSTEMS WITH A
SINGLE TIME DELAY.....................................................92
3.5.2 SYSTEMS WITH COMMENSURATE TIME DELAYS
........................................98 CONTENTS XII 3.6 STABILITY
ANALYSIS OF AN ACTIVE
CHASSIS................................................... 102 3.6.1 A
QUARTER CAR MODEL OF SUSPENSION WITH A DELAYED SKY-HOOK DAMPER.... 102
3.6.2 FOUR-WHEEL-STEERING VEHICLE WITH A TIME DELAY IN DRIVE S RESPONSE
..... 109 4 ROBUST STABILITY OF LINEAR DELAY SYSTEMS
.................................................... 115 4.1 ROBUST
STABILITY OF A ONE-PARAMETER FAMILY OF QUASI-POLYNOMIALS........ 116
4.1.1 NON-CONVEXITY OF THE SET OF HURWITZ STABLE QUASI-POLYNOMIALS .....
117 4.1.2 SUFFICIENT AND NECESSARY CONDITIONS FOR INTERVAL STABILITY
.............. 120 4.2 EDGE THEOREM FOR A POLYTOPIC FAMILY OF
QUASI-POLYNOMIALS ................. 124 4.2.1 PROBLEM
FORMULATION........................................................................
125 4.2.2 EDGE THEOREM
..................................................................................
127 4.2.3 SUFFICIENT AND NECESSARY CONDITIONS
............................................... 127 4.3 DIXON S
RESULTANT ELIMINATION
................................................................. 130
4.3.1 DIXON S RESULTANT
ELIMINATION..........................................................
130 4.3.2 ROBUST D -STABILITY OF ONE-PARAMETER FAMILY OF
POLYNOMIALS.......... 136 4.4 ROBUST STABILITY OF SYSTEMS WITH UNCERTAIN
COMMENSURATE DELAYS ....... 140 4.4.1 PROBLEM
FORMULATION........................................................................
141 4.4.2 STABILITY OF VERTEX
QUASI-POLYNOMIALS............................................. 143 4.4.3
STABILITY OF EDGE
QUASI-POLYNOMIALS................................................ 145
4.4.4 A SUFFICIENT AND NECESSARY
CONDITION.............................................. 147 4.4.5 AN
ILLUSTRATIVE EXAMPLE
................................................................... 147
5 EFFECTS OF A SHORT TIME DELAY ON SYSTEM
DYNAMICS.................................... 151 5.1 STABILITY
ESTIMATION OF HIGH DIMENSIONAL SYSTEMS.................................
151 5.1.1 DISTRIBUTION OF EIGENVALUES SUBJECT TO A SHORT TIME
DELAY............. 152 5.1.2 ESTIMATION OF
EIGENVALUES................................................................
155 5.1.3 ILLUSTRATIVE
EXAMPLES........................................................................
158 5.1.4 A RELATION OF ORTHOGONALITY OF MODE
SHAPES.................................. 167 5.2 STABILITY TEST BASED ON
THE PADE APPROXIMATION .................................... 168 5.2.1
TEST OF STABILITY
................................................................................
168 5.2.2 TEST OF INTERVAL
STABILITY...................................................................
176 5.3 DYNAMICS OF SIMPLIFIED SYSTEMS VIA THE TAYLOR
EXPANSION.................... 179 5.3.1 LINEAR SYSTEMS WITH DELAYED
STATE FEEDBACK.................................. 180 5.3.2 NONLINEAR
SYSTEMS WITH DELAYED VELOCITY FEEDBACK ...................... 182 6
DIMENSIONAL REDUCTION OF NONLINEAR DELAY SYSTEMS
.................................. 189 6.1 DECOMPOSITION OF STATE SPACE
OF LINEAR DELAY SYSTEMS......................... 190 6.1.1 SPECTRUM OF A
LINEAR OPERATOR.........................................................
192 6.1.2 DECOMPOSITION OF STATE
SPACE.......................................................... 194 6.2
DIMENSIONAL REDUCTION FOR STIFF-SOFT SYSTEMS
........................................ 198 6.2.1 A QUARTER CAR MODEL
AS A SINGULARLY PERTURBED SYSTEM................... 199 6.2.2 CENTER
MANIFOLD REDUCTION IN CRITICAL CASES...................................
200 6.2.3 REDUCTION FOR SINGULARLY PERTURBED DIFFERENTIAL EQUATIONS
............. 202 CONTENTS XIII 6.3 STABILITY ANALYSIS OF AN ACTIVE
SUSPENSION .............................................205 6.3.1 CENTER
MANIFOLD REDUCTION
..............................................................206 6.3.2
COMPUTATION OF THE APPROXIMATED CENTER
MANIFOLD........................207 6.3.3 STABILITY ANALYSIS
.............................................................................210
7 PERIODIC MOTIONS OF NONLINEAR DELAY SYSTEMS
.............................................213 7.1 THE HOPF
BIFURCATION OF AUTONOMOUS
SYSTEMS.......................................213 7.1.1 THEORY OF THE
HOPF BIFURCATIONS
......................................................214 7.1.2
DECOMPOSITION OF BIFURCATING
SOLUTION............................................217 7.1.3
BIFURCATING SOLUTIONS IN NORMAL
FORM.............................................219 7.2 COMPUTATION OF
BIFURCATING PERIODIC SOLUTIONS.......................................222
7.2.1 METHOD OF THE FREDHOLM
ALTERNATIVE................................................222 7.2.2
STABILITY OF BIFURCATING PERIODIC
SOLUTIONS.......................................227 7.2.3 PERTURBATION
METHOD.........................................................................230
7.3 PERIODIC MOTIONS OF A DUFFING OSCILLATOR WITH DELAYED FEEDBACK
..........234 7.3.1 STABILITY SWITCHES OF EQUILIBRIUM
....................................................235 7.3.2 PERIODIC
MOTION DETERMINED BY METHOD OF FREDHOLM ALTERNATIVE ..237 7.3.3 PERIODIC
MOTION DETERMINED BY METHOD OF MULTIPLE SCALES............243 7.4
PERIODIC MOTIONS OF A FORCED DUFFING OSCILLATOR WITH DELAYED FEEDBACK
...248 7.4.1 PRIMARY
RESONANCE...........................................................................249
7.4.2 1/3 SUBHARMONIC RESONANCE
............................................................254 7.5
SHOOTING SCHEME FOR LOCATING PERIODIC MOTIONS
....................................259 7.5.1 BASIC CONCEPTS AND
COMPUTATION SCHEME .......................................259 7.5.2 CASE
STUDIES
.....................................................................................262
8 DELAYED CONTROL OF DYNAMIC
SYSTEMS...........................................................267
8.1 DELAYED LINEAR FEEDBACK FOR LINEAR SYSTEMS
.........................................267 8.1.1 DELAYED LINEAR
FEEDBACK AND ARTIFICIAL DAMPING...........................267 8.1.2
DELAYED RESONATOR: A TUNABLE VIBRATION ABSORBER
........................269 8.2 STABILIZATION TO CRITICALLY STABLE
NONLINEAR SYSTEMS ...............................272 8.2.1 STATEMENT OF
PROBLEM
.......................................................................274
8.2.2 ANALYSIS ON
STABILIZATION..................................................................275
8.2.3 CASE STUDIES
.....................................................................................278
8.2.4 DISCUSSIONS ON APPROXIMATE INTEGRALS
.............................................280 8.3 CONTROLLING CHAOTIC
MOTION.....................................................................282
8.3.1 BASIC IDEA
.........................................................................................283
8.3.2 CHOICE OF FEEDBACK GAIN
.................................................................284
REFERENCES
..........................................................................................................287
INDEX
...................................................................................................................293
|
| any_adam_object | 1 |
| author | Hu, Haiyan 1956- Wang, Zaihua 1964- |
| author_GND | (DE-588)123801656 (DE-588)123801664 |
| author_facet | Hu, Haiyan 1956- Wang, Zaihua 1964- |
| author_role | aut aut |
| author_sort | Hu, Haiyan 1956- |
| author_variant | h h hh z w zw |
| building | Verbundindex |
| bvnumber | BV014330751 |
| classification_rvk | ZQ 5060 |
| ctrlnum | (OCoLC)248889539 (DE-599)BVBBV014330751 |
| discipline | Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
| format | Book |
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| id | DE-604.BV014330751 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:01:49Z |
| institution | BVB |
| isbn | 3540437339 |
| language | English |
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| owner_facet | DE-703 DE-29T |
| physical | XIII, 294 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Springer |
| record_format | marc |
| series2 | Engineering online library |
| spelling | Hu, Haiyan 1956- Verfasser (DE-588)123801656 aut Dynamics of controlled mechanical systems with delayed feedback with 8 tables H. Y. Hu ; Z. H. Wang Berlin [u.a.] Springer 2002 XIII, 294 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Engineering online library Mechanisches System - Regelung - Differentialgleichung mit nacheilendem Argument - Stabilität Regelung (DE-588)4048971-1 gnd rswk-swf Differentialgleichung mit nacheilendem Argument (DE-588)4199298-2 gnd rswk-swf Mechanisches System (DE-588)4132811-5 gnd rswk-swf Stabilität (DE-588)4056693-6 gnd rswk-swf Mechanisches System (DE-588)4132811-5 s Regelung (DE-588)4048971-1 s Differentialgleichung mit nacheilendem Argument (DE-588)4199298-2 s Stabilität (DE-588)4056693-6 s DE-604 Wang, Zaihua 1964- Verfasser (DE-588)123801664 aut SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009831326&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hu, Haiyan 1956- Wang, Zaihua 1964- Dynamics of controlled mechanical systems with delayed feedback with 8 tables Mechanisches System - Regelung - Differentialgleichung mit nacheilendem Argument - Stabilität Regelung (DE-588)4048971-1 gnd Differentialgleichung mit nacheilendem Argument (DE-588)4199298-2 gnd Mechanisches System (DE-588)4132811-5 gnd Stabilität (DE-588)4056693-6 gnd |
| subject_GND | (DE-588)4048971-1 (DE-588)4199298-2 (DE-588)4132811-5 (DE-588)4056693-6 |
| title | Dynamics of controlled mechanical systems with delayed feedback with 8 tables |
| title_auth | Dynamics of controlled mechanical systems with delayed feedback with 8 tables |
| title_exact_search | Dynamics of controlled mechanical systems with delayed feedback with 8 tables |
| title_full | Dynamics of controlled mechanical systems with delayed feedback with 8 tables H. Y. Hu ; Z. H. Wang |
| title_fullStr | Dynamics of controlled mechanical systems with delayed feedback with 8 tables H. Y. Hu ; Z. H. Wang |
| title_full_unstemmed | Dynamics of controlled mechanical systems with delayed feedback with 8 tables H. Y. Hu ; Z. H. Wang |
| title_short | Dynamics of controlled mechanical systems with delayed feedback |
| title_sort | dynamics of controlled mechanical systems with delayed feedback with 8 tables |
| title_sub | with 8 tables |
| topic | Mechanisches System - Regelung - Differentialgleichung mit nacheilendem Argument - Stabilität Regelung (DE-588)4048971-1 gnd Differentialgleichung mit nacheilendem Argument (DE-588)4199298-2 gnd Mechanisches System (DE-588)4132811-5 gnd Stabilität (DE-588)4056693-6 gnd |
| topic_facet | Mechanisches System - Regelung - Differentialgleichung mit nacheilendem Argument - Stabilität Regelung Differentialgleichung mit nacheilendem Argument Mechanisches System Stabilität |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009831326&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT huhaiyan dynamicsofcontrolledmechanicalsystemswithdelayedfeedbackwith8tables AT wangzaihua dynamicsofcontrolledmechanicalsystemswithdelayedfeedbackwith8tables |