Control of parabolic partial differential equations based on semi-discretizations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Aachen
Shaker
2012
|
| Series: | Modellierung und Regelung komplexer dynamischer Systeme
Bd. 14 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 152 S. graph. Darst. |
| ISBN: | 9783844009323 |
Staff View
MARC
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| 100 | 1 | |a Utz, Tilman |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Control of parabolic partial differential equations based on semi-discretizations |c Tilman Utz |
| 264 | 1 | |a Aachen |b Shaker |c 2012 | |
| 300 | |a X, 152 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Modellierung und Regelung komplexer dynamischer Systeme |v Bd. 14 | |
| 502 | |a Zugl.: Wien, Techn. Univ., Diss., 2012 | ||
| 650 | 0 | 7 | |a Unendlichdimensionales System |0 (DE-588)4207956-1 |2 gnd |9 rswk-swf |
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| 650 | 0 | 7 | |a Vorsteuerung |0 (DE-588)4699634-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Flachheitsbasierte Folgeregelung |0 (DE-588)4743050-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Diskretisierung |0 (DE-588)4012469-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Zustandsschätzung |0 (DE-588)4129826-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Finite-Differenzen-Methode |0 (DE-588)4194626-1 |2 gnd |9 rswk-swf |
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| 830 | 0 | |a Modellierung und Regelung komplexer dynamischer Systeme |v Bd. 14 |w (DE-604)BV035640222 |9 14 | |
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Record in the Search Index
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| adam_text | IMAGE 1
CONTENTS
1 I N T R O D U C T I O N 1
1.1 CONTROL OF INFINITE-DIMENSIONAL SYSTEMS 1
1.2 TRACKING CONTROL AND FLATNESS 2
1.3 INTRODUCTORY EXAMPLE 3
1.4 OUTLINE AND CONTRIBUTIONS 6
1.5 REMARKS ON NOTATION 9
2 F L A T N E S S - B A S E D P A R A M E T R I Z A T I O N O F FINITE
DIFFERENCE S E M I - D I S C R E T I Z E D PARABOLIC P D E S 1 1
2.1 DIFFUSION-CONVECTION-REACTION SYSTEMS 11
2.2 TRANSITIONS BETWEEN STEADY-STATE PROFILES 13
2.3 SEMI-DISCRETIZATION 13
2.3.1 FINITE DIFFERENCES 13
2.3.2 T H E SEMI-DISCRETIZED SYSTEM OF ODES 16
2.4 FLATNESS OF THE SEMI-DISCRETIZED MODEL 17
2.5 ALGORITHM FOR THE PARAMETRIZATION 22
2.6 CONCLUDING REMARKS 25
3 QUASILINEAR P R O B L E M S I N O N E S P A C E D I M E N S I O N A N
D NUMERICAL C O N V E R G E N C E T E S T I N G 2 7
3.1 CONVERGENCE ANALYSIS 28
3.1.1 FROM FINITE DIFFERENCES T O POWER SERIES 29
3.1.2 CONVERGENCE OF THE PARAMETRIZATION 34
3.2 SIMULATION EXAMPLE I 42
3.3 NUMERICAL CONVERGENCE CONSIDERATIONS 43
3.4 SIMULATION EXAMPLE II: HEATING-UP OF A STEEL SLAB 46
3.5 CONCLUDING REMARKS 49
IX
HTTP://D-NB.INFO/1020760168
IMAGE 2
X
CONTENTS
4 QUASILINEAR P R O B L E M S I N T W O S P A C E D I M E N S I O N S A
N D T O O L S FOR T H E G E N E R A T I O N O F ADMISSIBLE PROFILES 5 1
4.1 CONVERGENCE ANALYSIS 52
4.1.1 FROM FINITE DIFFERENCES T O A N INTEGRAL EQUATION 53
4.1.2 CONVERGENCE OF THE PARAMETRIZATION 54
4.2 ANALYTICAL RESULTS FOR ADMISSIBLE PROFILES 63
4.2.1 LINEAR PROBLEM 64
4.2.2 STATE-DEPENDENT PARAMETERS 67
4.2.3 ARBITRARY PROFILES 70
4.3 NUMERICAL RESULTS FOR ADMISSIBLE PROFILES 73
4.3.1 ADMISSIBLE TRAJECTORIES FOR SEMI-DISCRETIZED SYSTEMS . . . . 74
4.3.2 CONSTRUCTION OF ADMISSIBLE PROFILES USING OPTIMIZATION . . . 78
4.3.3 REGULARIZATION OF NUMERICAL DIFFERENTIATION 82
4.4 CONCLUDING REMARKS 89
5 SEMILINEAR S Y S T E M S O F E Q U A T I O N S A N D PARAMETRIZATION O
N A D A P T I V E GRIDS 9 3
5.1 CONVERGENCE ANALYSIS 94
5.1.1 FROM FINITE DIFFERENCES T O POWER SERIES 94
5.1.2 CONVERGENCE OF THE PARAMETRIZATION 96
5.2 SIMULATION EXAMPLE I 99
5.3 PARAMETRIZATION OF SEMI-DISCRETIZATIONS ON NON-EQUIDISTANT GRIDS .
100 5.3.1 GRID NODE PLACEMENT AND ADAPTATION 103
5.3.2 EQUIDISTRIBUTION PRINCIPLE AND RE-GRIDDING ALGORITHM . . . . 104
5.4 SIMULATION EXAMPLE II: FIXED-BED REACTOR 106
5.5 CONCLUDING REMARKS 113
6 R E C E D I N G HORIZON TRACKING C O N T R O L A N D S T A T E E S T I
M A T I O N FOR SEMI-DISCRETIZATIONS O F QUASILINEAR P D E S 1 1 5
6.1 RECEDING HORIZON TRACKING CONTROL 116
6.2 SIMULATION EXAMPLE: STATE FEEDBACK 119
6.3 STATE ESTIMATION FOR THE SEMI-DISCRETIZED SYSTEM 123
6.4 SIMULATION EXAMPLE: STATE ESTIMATION 124
6.5 CONCLUDING REMARKS 127
7 C O N C L U S I O N S A N D O U T L O O K 1 2 9
A L O C A L ERROR ANALYSIS O F FINITE DIFFERENCE S C H E M E S 1 3 1
B R E F E R E N C E TRAJECTORIES FOR FLATNESS-BASED P A R A M E T R I Z
A T I O N 1 3 3
C U S E F U L L E M M A S A N D RELATIONS 1 3 9
B I B L I O G R A P H Y 1 5 2
|
| any_adam_object | 1 |
| author | Utz, Tilman |
| author_facet | Utz, Tilman |
| author_role | aut |
| author_sort | Utz, Tilman |
| author_variant | t u tu |
| building | Verbundindex |
| bvnumber | BV040264590 |
| classification_rvk | SK 920 |
| ctrlnum | (OCoLC)794947541 (DE-599)DNB1020760168 |
| dewey-full | 629.8312 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 629 - Other branches of engineering |
| dewey-raw | 629.8312 |
| dewey-search | 629.8312 |
| dewey-sort | 3629.8312 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Mathematik Elektrotechnik / Elektronik / Nachrichtentechnik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
| format | Thesis Book |
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| genre_facet | Hochschulschrift |
| id | DE-604.BV040264590 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:20:18Z |
| institution | BVB |
| isbn | 9783844009323 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025120297 |
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| owner_facet | DE-703 DE-29T |
| physical | X, 152 S. graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Shaker |
| record_format | marc |
| series | Modellierung und Regelung komplexer dynamischer Systeme |
| series2 | Modellierung und Regelung komplexer dynamischer Systeme |
| spelling | Utz, Tilman Verfasser aut Control of parabolic partial differential equations based on semi-discretizations Tilman Utz Aachen Shaker 2012 X, 152 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Modellierung und Regelung komplexer dynamischer Systeme Bd. 14 Zugl.: Wien, Techn. Univ., Diss., 2012 Unendlichdimensionales System (DE-588)4207956-1 gnd rswk-swf Parabolische Differentialgleichung (DE-588)4173245-5 gnd rswk-swf Vorsteuerung (DE-588)4699634-5 gnd rswk-swf Flachheitsbasierte Folgeregelung (DE-588)4743050-3 gnd rswk-swf Diskretisierung (DE-588)4012469-1 gnd rswk-swf Zustandsschätzung (DE-588)4129826-3 gnd rswk-swf Finite-Differenzen-Methode (DE-588)4194626-1 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Vorsteuerung (DE-588)4699634-5 s Flachheitsbasierte Folgeregelung (DE-588)4743050-3 s Unendlichdimensionales System (DE-588)4207956-1 s Parabolische Differentialgleichung (DE-588)4173245-5 s Diskretisierung (DE-588)4012469-1 s Finite-Differenzen-Methode (DE-588)4194626-1 s Zustandsschätzung (DE-588)4129826-3 s DE-604 Modellierung und Regelung komplexer dynamischer Systeme Bd. 14 (DE-604)BV035640222 14 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025120297&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Utz, Tilman Control of parabolic partial differential equations based on semi-discretizations Modellierung und Regelung komplexer dynamischer Systeme Unendlichdimensionales System (DE-588)4207956-1 gnd Parabolische Differentialgleichung (DE-588)4173245-5 gnd Vorsteuerung (DE-588)4699634-5 gnd Flachheitsbasierte Folgeregelung (DE-588)4743050-3 gnd Diskretisierung (DE-588)4012469-1 gnd Zustandsschätzung (DE-588)4129826-3 gnd Finite-Differenzen-Methode (DE-588)4194626-1 gnd |
| subject_GND | (DE-588)4207956-1 (DE-588)4173245-5 (DE-588)4699634-5 (DE-588)4743050-3 (DE-588)4012469-1 (DE-588)4129826-3 (DE-588)4194626-1 (DE-588)4113937-9 |
| title | Control of parabolic partial differential equations based on semi-discretizations |
| title_auth | Control of parabolic partial differential equations based on semi-discretizations |
| title_exact_search | Control of parabolic partial differential equations based on semi-discretizations |
| title_full | Control of parabolic partial differential equations based on semi-discretizations Tilman Utz |
| title_fullStr | Control of parabolic partial differential equations based on semi-discretizations Tilman Utz |
| title_full_unstemmed | Control of parabolic partial differential equations based on semi-discretizations Tilman Utz |
| title_short | Control of parabolic partial differential equations based on semi-discretizations |
| title_sort | control of parabolic partial differential equations based on semi discretizations |
| topic | Unendlichdimensionales System (DE-588)4207956-1 gnd Parabolische Differentialgleichung (DE-588)4173245-5 gnd Vorsteuerung (DE-588)4699634-5 gnd Flachheitsbasierte Folgeregelung (DE-588)4743050-3 gnd Diskretisierung (DE-588)4012469-1 gnd Zustandsschätzung (DE-588)4129826-3 gnd Finite-Differenzen-Methode (DE-588)4194626-1 gnd |
| topic_facet | Unendlichdimensionales System Parabolische Differentialgleichung Vorsteuerung Flachheitsbasierte Folgeregelung Diskretisierung Zustandsschätzung Finite-Differenzen-Methode Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025120297&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035640222 |
| work_keys_str_mv | AT utztilman controlofparabolicpartialdifferentialequationsbasedonsemidiscretizations |