Optimal control of distributed nuclear reactors:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Plenum Pr.
1990
|
| Series: | Mathematical concepts and methods in science and engineering
41 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XVI, 236 S. graph. Darst. |
| ISBN: | 0306433052 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV004646738 | ||
| 003 | DE-604 | ||
| 005 | 20180524 | ||
| 007 | t | ||
| 008 | 911211s1990 d||| |||| 00||| engod | ||
| 020 | |a 0306433052 |9 0-306-43305-2 | ||
| 035 | |a (OCoLC)20593220 | ||
| 035 | |a (DE-599)BVBBV004646738 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-91 |a DE-703 | ||
| 050 | 0 | |a TK9202 | |
| 082 | 0 | |a 621.48/35/011 |2 20 | |
| 084 | |a UN 5210 |0 (DE-625)146124: |2 rvk | ||
| 084 | |a NUC 635f |2 stub | ||
| 084 | |a NUC 220f |2 stub | ||
| 100 | 1 | |a Christensen, Gustav S. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Optimal control of distributed nuclear reactors |c G. S. Christensen ; S. A. Soliman and R. Nieva |
| 264 | 1 | |a New York u.a. |b Plenum Pr. |c 1990 | |
| 300 | |a XVI, 236 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematical concepts and methods in science and engineering |v 41 | |
| 500 | |a Literaturangaben | ||
| 650 | 4 | |a Réacteurs nucléaires - Contrôle - Modèles mathématiques | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Nuclear reactors |x Control |x Mathematical models | |
| 650 | 0 | 7 | |a Kernreaktorphysik |0 (DE-588)4123503-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kernreaktor |0 (DE-588)4030344-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Regelungstechnik |0 (DE-588)4076594-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Kernreaktor |0 (DE-588)4030344-5 |D s |
| 689 | 0 | 1 | |a Regelungstechnik |0 (DE-588)4076594-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Kernreaktorphysik |0 (DE-588)4123503-4 |D s |
| 689 | 1 | |5 DE-604 | |
| 700 | 1 | |a Soliman, S. A. |e Verfasser |4 aut | |
| 700 | 1 | |a Nieva, R. |e Verfasser |4 aut | |
| 830 | 0 | |a Mathematical concepts and methods in science and engineering |v 41 |w (DE-604)BV000001144 |9 41 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002853580&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-002853580 | ||
Record in the Search Index
| _version_ | 1804118765527367680 |
|---|---|
| adam_text | Contents
1. Introduction
1.1. Nuclear Reactor Operation and Design 1
1.2. Outline of the Book 1
2. Some Mathematical Optimization Techniques
2.1. Introduction 5
2.2. A Review of Matrix Theory 5
2.2.1. Vectors 5
2.2.2. Matrices 6
2.3. Calculus of Variations 10
2.3.1. The Isoperimetric Problem 12
2.3.2. A Distributed System 12
2.4. Dynamic Programming and the Principle of Optimality .... 13
2.4.1. Dynamic Programming for Continuous Processes .... 15
2.5. Pontryagin s Maximum Principle 17
2.6. Minimum Norm Problems of Functional Analysis 18
2.6.1. Some Concepts of Functional Analysis 18
2.6.2. The Minimum Norm Problems 20
References 24
3. Distributed Reactor Modeling
3.1. Introduction 25
3.2. The Multigroup Diffusion Equations 27
3.2.1. Solution of the Diffusion Equation 29
3.2.2. The Method of Degenerate Kernels 30
3.2.3. Practical Example 33
3.3. The Model Expansion 37
3.3.1. The Functional Relation 42
3.3.2. Practical Example 43
xiii
xiv Contents
3.4. Model Decomposition Techniques 47
3.4.1. Symmetry Reduction 48
3.5. An Example: Decoupling of the Optimality Conditions .... 60
3.6. An Example: Reduction of a Cylindrical Reactor Model ... 63
3.7. Time Scale Separation 67
References 68
4. Optimal Control of Distributed Nuclear Reactors
4.1. Introduction 71
4.2. The Reactor Core Model 74
4.3. The Optimal Control Problem 76
4.3.1. A Minimum Norm Approach 76
4.4. Necessary and Sufficient Conditions for Optimality:
A Fredholm Integral Equation 78
4.5. Example: One Neutron Group Diffusion Equation 79
4.6. Discussion 83
4.7. Method for Computing the Optimal Control 85
4.8. Maximum Principle Approach 88
4.8.1. Problem Formulation 90
4.8.2. Regulator Problem 91
4.8.3. Servomechanism Problem 92
4.8.4. Spatial Discretization Scheme 93
4.8.5. Space Time Discretization Scheme 94
4.8.6. Some Examples for Optimal Control Computations 95
4.8.7. Concluding Remarks 99
4.9. Singular Perturbation Theory 100
4.9.1. State Equation 101
4.9.2. Problem Formulation 102
4.9.3. Model Expansion 103
4.9.4. Criticality Conditions and Applicability of Singular
Perturbation Theory 106
4.9.5. Construction of Asymptotic Expansions 107
4.9.6. Practical Numerical Example 112
4.9.7. Concluding Remarks 114
4.10. Systems Tau Method 116
4.10.1. Calculational Method 117
4.10.2. Comparisons of Various Computational Techniques 124
4.10.3. Practical Application of STM for Optimal Control of
Nuclear Reactors 125
4.10.4. Concluding Remarks 130
References 132
Contents xv
5. Control of Distributed Reactors in Load Following
5.1. Introduction 135
5.2. Multistage Mathematical Programming 137
5.2.1. Problem Formulation 137
5.2.2. Objective Function 138
5.2.3. Reactor Core Model 139
5.2.4. Numerical Solution 147
5.2.5. Operational Use 150
5.2.6. Results 153
5.2.7. Concluding Remarks 159
5.3. Xenon Spatial Oscillations in Load Following: Linear Quad¬
ratic Problem 159
5.3.1. The Reactor Feedback Model 160
5.3.2. The Steady State Solution 164
5.3.3. Linearized Equations 164
5.3.4. Performance Index and the Optimal Control Problem 166
5.3.5. Calculation Scheme and Results 170
5.3.6. Concluding Remarks 175
5.4. Multilevel Methods 176
5.4.1. Meanings of Multilevel Control 176
5.4.2. Problem Formulation 184
5.4.3. Solution Algorithm 188
5.4.4. Results 190
5.4.5. Concluding Remarks 193
Appendix A 194
Appendix B 199
References 201
6. Application of the Minimum Norm Formulation to Problems in Control
of Distributed Reactors
6.1. Introduction 203
6.2. The Nuclear Reactor Model 204
6.3. Optimal Control of the State Distribution with Power Level
Adjustment 205
6.3.1. Necessary and Sufficient Conditions of Optimality ... 206
6.4. Optimal Control of the State Distribution during Load
Following 213
6.5. Optimal Control of the State Distribution with Fixed End State 215
6.5.1. Suboptimal Control 217
6.5.2. Minimum Norm Formulation 219
6.5.3. Practical Example 221
References 228
xvi Contents
7. Conclusions
7.1. Summary 231
7.2. Future Work 232
Index 233
|
| any_adam_object | 1 |
| author | Christensen, Gustav S. Soliman, S. A. Nieva, R. |
| author_facet | Christensen, Gustav S. Soliman, S. A. Nieva, R. |
| author_role | aut aut aut |
| author_sort | Christensen, Gustav S. |
| author_variant | g s c gs gsc s a s sa sas r n rn |
| building | Verbundindex |
| bvnumber | BV004646738 |
| callnumber-first | T - Technology |
| callnumber-label | TK9202 |
| callnumber-raw | TK9202 |
| callnumber-search | TK9202 |
| callnumber-sort | TK 49202 |
| callnumber-subject | TK - Electrical and Nuclear Engineering |
| classification_rvk | UN 5210 |
| classification_tum | NUC 635f NUC 220f |
| ctrlnum | (OCoLC)20593220 (DE-599)BVBBV004646738 |
| dewey-full | 621.48/35/011 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 621 - Applied physics |
| dewey-raw | 621.48/35/011 |
| dewey-search | 621.48/35/011 |
| dewey-sort | 3621.48 235 211 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Energietechnik, Energiewirtschaft Physik Energietechnik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02067nam a2200517 cb4500</leader><controlfield tag="001">BV004646738</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20180524 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">911211s1990 d||| |||| 00||| engod</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0306433052</subfield><subfield code="9">0-306-43305-2</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)20593220</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV004646738</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91</subfield><subfield code="a">DE-703</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">TK9202</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">621.48/35/011</subfield><subfield code="2">20</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">UN 5210</subfield><subfield code="0">(DE-625)146124:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">NUC 635f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">NUC 220f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Christensen, Gustav S.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Optimal control of distributed nuclear reactors</subfield><subfield code="c">G. S. Christensen ; S. A. Soliman and R. Nieva</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York u.a.</subfield><subfield code="b">Plenum Pr.</subfield><subfield code="c">1990</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVI, 236 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Mathematical concepts and methods in science and engineering</subfield><subfield code="v">41</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Literaturangaben</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Réacteurs nucléaires - Contrôle - Modèles mathématiques</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematisches Modell</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Nuclear reactors</subfield><subfield code="x">Control</subfield><subfield code="x">Mathematical models</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kernreaktorphysik</subfield><subfield code="0">(DE-588)4123503-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kernreaktor</subfield><subfield code="0">(DE-588)4030344-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Regelungstechnik</subfield><subfield code="0">(DE-588)4076594-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Kernreaktor</subfield><subfield code="0">(DE-588)4030344-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Regelungstechnik</subfield><subfield code="0">(DE-588)4076594-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Kernreaktorphysik</subfield><subfield code="0">(DE-588)4123503-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Soliman, S. A.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Nieva, R.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Mathematical concepts and methods in science and engineering</subfield><subfield code="v">41</subfield><subfield code="w">(DE-604)BV000001144</subfield><subfield code="9">41</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002853580&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-002853580</subfield></datafield></record></collection> |
| id | DE-604.BV004646738 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:15:30Z |
| institution | BVB |
| isbn | 0306433052 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002853580 |
| oclc_num | 20593220 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-703 |
| owner_facet | DE-91 DE-BY-TUM DE-703 |
| physical | XVI, 236 S. graph. Darst. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Plenum Pr. |
| record_format | marc |
| series | Mathematical concepts and methods in science and engineering |
| series2 | Mathematical concepts and methods in science and engineering |
| spelling | Christensen, Gustav S. Verfasser aut Optimal control of distributed nuclear reactors G. S. Christensen ; S. A. Soliman and R. Nieva New York u.a. Plenum Pr. 1990 XVI, 236 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematical concepts and methods in science and engineering 41 Literaturangaben Réacteurs nucléaires - Contrôle - Modèles mathématiques Mathematisches Modell Nuclear reactors Control Mathematical models Kernreaktorphysik (DE-588)4123503-4 gnd rswk-swf Kernreaktor (DE-588)4030344-5 gnd rswk-swf Regelungstechnik (DE-588)4076594-5 gnd rswk-swf Kernreaktor (DE-588)4030344-5 s Regelungstechnik (DE-588)4076594-5 s DE-604 Kernreaktorphysik (DE-588)4123503-4 s Soliman, S. A. Verfasser aut Nieva, R. Verfasser aut Mathematical concepts and methods in science and engineering 41 (DE-604)BV000001144 41 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002853580&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Christensen, Gustav S. Soliman, S. A. Nieva, R. Optimal control of distributed nuclear reactors Mathematical concepts and methods in science and engineering Réacteurs nucléaires - Contrôle - Modèles mathématiques Mathematisches Modell Nuclear reactors Control Mathematical models Kernreaktorphysik (DE-588)4123503-4 gnd Kernreaktor (DE-588)4030344-5 gnd Regelungstechnik (DE-588)4076594-5 gnd |
| subject_GND | (DE-588)4123503-4 (DE-588)4030344-5 (DE-588)4076594-5 |
| title | Optimal control of distributed nuclear reactors |
| title_auth | Optimal control of distributed nuclear reactors |
| title_exact_search | Optimal control of distributed nuclear reactors |
| title_full | Optimal control of distributed nuclear reactors G. S. Christensen ; S. A. Soliman and R. Nieva |
| title_fullStr | Optimal control of distributed nuclear reactors G. S. Christensen ; S. A. Soliman and R. Nieva |
| title_full_unstemmed | Optimal control of distributed nuclear reactors G. S. Christensen ; S. A. Soliman and R. Nieva |
| title_short | Optimal control of distributed nuclear reactors |
| title_sort | optimal control of distributed nuclear reactors |
| topic | Réacteurs nucléaires - Contrôle - Modèles mathématiques Mathematisches Modell Nuclear reactors Control Mathematical models Kernreaktorphysik (DE-588)4123503-4 gnd Kernreaktor (DE-588)4030344-5 gnd Regelungstechnik (DE-588)4076594-5 gnd |
| topic_facet | Réacteurs nucléaires - Contrôle - Modèles mathématiques Mathematisches Modell Nuclear reactors Control Mathematical models Kernreaktorphysik Kernreaktor Regelungstechnik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002853580&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001144 |
| work_keys_str_mv | AT christensengustavs optimalcontrolofdistributednuclearreactors AT solimansa optimalcontrolofdistributednuclearreactors AT nievar optimalcontrolofdistributednuclearreactors |