Numerical operations with polynomial matrices: application to multi-variable dynamic compensator design
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u.a.
Springer
1992
|
| Series: | Lecture notes in control and information sciences
171 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 205 S. graph. Darst. |
| ISBN: | 3540549927 0387549927 |
Staff View
MARC
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| 100 | 1 | |a Stefanidis, Peter |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Numerical operations with polynomial matrices |b application to multi-variable dynamic compensator design |c P. Stefanidis ; A. P. Paplinski ; M. J. Gibbard |
| 264 | 1 | |a Berlin u.a. |b Springer |c 1992 | |
| 300 | |a VII, 205 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Control theory | |
| 650 | 4 | |a Matrices |x Data processing | |
| 650 | 4 | |a Polynomials |x Data processing | |
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Record in the Search Index
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Contents
1 Introduction 1
1.1 Motivation 1
1.2 Pole Assignment 3
1.3 Computational Aspects of the Design 5
1.4 Layout 7
2 Polynomial Matrices and Related Operations 9
2.1 Introduction 9
2.2 Properties of Polynomial Matrices 9
2.2.1 Minimal Polynomial Bases 11
2.2.2 Properties of a Square Polynomial Matrix 14
2.3 Numerical Representation of Polynomial Matrices 15
2.4 Operations on the Numerical Representation of a Polynomial Matrix . 16
2.4.1 Introduction 16
2.4.2 Addition or Subtraction of Row Block Matrices 17
2.4.3 Block Transpose of a Block Matrix 18
2.4.4 Resultant of a Polynomial Matrix 19
2.4.5 Multiplication of Polynomial Matrices 21
2.4.6 Synthesis of a Polynomial Block Matrix Description of a Square
Polynomial Matrix with Specified Properties 23
V
2.4.6.1 The Skeleton Block Matrix of a Polynomial Matrix . 26
2.4.6.2 A 'Standard' Structure Matrix and its Skeleton Block
Matrix 33
2.4.7 Construction of a Non Singular Polynomial Matrix with a Specified
Set of Eigenvalues 36
2.4.7.1 Summary 42
2.4.8 The Determinant of a Polynomial Matrix 42
2.4.8.1 Summary 48
2.4.9 Transforming a Full Row Rank Polynomial Matrix to its Row
Proper Form 48
2.4.9.1 Summary 52
3 Model Descriptions and Transformations Between Models 53
3.1 Introduction 53
3.1.1 Mathematical Notation 54
3.2 Properties of the MFD 55
3.2.1 Introduction 55
3.2.2 Properties of the RMFD 56
3.2.3 Properties of the LMFD 60
3.3 Numerical Algorithms for the Transformation from SSD to MFD 63
3.3.1 Introduction 63
3.3.2 An Algorithm to Transform a SSD to RMFD 65
3.3.3 Summary 80
3.4 The Inverse of a Polynomial Matrix 80
3.4.1 Introduction 80
3.4.2 Computing the Adjoint of a Polynomial Matrix 81
3.4.3 Summary 85
3.5 Transforming a MFD to TFMD 86
3.5.1 Introduction 86
VI
3.5.2 An Algorithm to transform a MFD to TFMD 86
3.5.3 Summary 88
3.6 The AutoRegressive Moving Average Model 88
3.6.1 Introduction 88
3.6.2 Canonical Monic Form of ARMA Model 89
4 The Design of the Closed—Loop System Compensator 91
4.1 Introduction 91
4.2 The Closed Loop System 93
4.2.1 The System Configuration 93
4.2.2 The Closed Loop Transfer Function 95
4.3 The Output Feedback Compensator 98
4.3.1 The Modified Left Compensator Equation 98
4.3.2 Solving the Modified Left Compensator Equation 101
4.3.2.1 Summary .116
4.4 The Pre compensator 116
4.4.1 Introduction 116
4.4.2 The Alignment Error 117
4.4.3 The Following Error 120
4.4.4 The Following Error for a Continuous Time System 120
4.4.5 The Following Error for a Discrete Time System 123
4.4.6 Summary 125
4.5 Example of the Design Calculations 125
5 Design Examples 138
5.1 Introduction 138
5.2 The Chemical Reactor 139
5.3 The Pressurised Flow Box 147
5.4 The L 1011 Aircraft 154
5.5 The Flight Control System 165
VII
6 Conclusions and Suggestions for Future Work 172
A Proof: The Numerical Block Matrix Multiplication of
Two Conformable Polynomial Matrices 176
B The Lower Triangular Toeplitz Block Matrix and its Inverse 178
B.I Introduction 178
B.2 The Inverse of a Lower Triangular Toeplitz Block Matrix 180
C Algorithm to Transform a Polynomial Matrix into a Regular Form 182
C.I Introduction 182
C.2 Transformation of a Polynomial Matrix into a Regular Form by Post
Multiplication 185
C.3 Transformation of a Polynomial Matrix into a Regular Form by Pre
Multiplication 187
D Pseudo Inverse of a Resultant 189
E Calculation of the Controllability Indices of a State Space System 191
F Symbols 193
Bibliography 196
Index 204 |
| any_adam_object | 1 |
| author | Stefanidis, Peter Paplinski, Andrzej P. Gibbard, Michael J. |
| author_facet | Stefanidis, Peter Paplinski, Andrzej P. Gibbard, Michael J. |
| author_role | aut aut aut |
| author_sort | Stefanidis, Peter |
| author_variant | p s ps a p p ap app m j g mj mjg |
| building | Verbundindex |
| bvnumber | BV004687458 |
| callnumber-first | Q - Science |
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| callnumber-raw | QA188 |
| callnumber-search | QA188 |
| callnumber-sort | QA 3188 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 845 SK 920 |
| classification_tum | MAT 496f MAT 657f |
| ctrlnum | (OCoLC)231269459 (DE-599)BVBBV004687458 |
| dewey-full | 512.9/434 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.9/434 |
| dewey-search | 512.9/434 |
| dewey-sort | 3512.9 3434 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV004687458 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T07:37:08Z |
| institution | BVB |
| isbn | 3540549927 0387549927 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002879090 |
| oclc_num | 231269459 |
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| owner_facet | DE-384 DE-12 DE-91G DE-BY-TUM DE-706 DE-634 DE-11 DE-188 |
| physical | VII, 205 S. graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in control and information sciences |
| series2 | Lecture notes in control and information sciences |
| spelling | Stefanidis, Peter Verfasser aut Numerical operations with polynomial matrices application to multi-variable dynamic compensator design P. Stefanidis ; A. P. Paplinski ; M. J. Gibbard Berlin u.a. Springer 1992 VII, 205 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in control and information sciences 171 Commande, théorie de la ram Matrices - Informatique ram Polynômes - Informatique ram Datenverarbeitung Control theory Matrices Data processing Polynomials Data processing Kompensator (DE-588)4164866-3 gnd rswk-swf Polynommatrix (DE-588)4121492-4 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Mehrgrößenregelungssystem (DE-588)4135771-1 gnd rswk-swf Entwurf (DE-588)4121208-3 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf Polynommatrix (DE-588)4121492-4 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Mehrgrößenregelungssystem (DE-588)4135771-1 s Kompensator (DE-588)4164866-3 s Entwurf (DE-588)4121208-3 s Numerische Mathematik (DE-588)4042805-9 s Algorithmus (DE-588)4001183-5 s Paplinski, Andrzej P. Verfasser aut Gibbard, Michael J. Verfasser aut Lecture notes in control and information sciences 171 (DE-604)BV005848579 171 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002879090&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stefanidis, Peter Paplinski, Andrzej P. Gibbard, Michael J. Numerical operations with polynomial matrices application to multi-variable dynamic compensator design Lecture notes in control and information sciences Commande, théorie de la ram Matrices - Informatique ram Polynômes - Informatique ram Datenverarbeitung Control theory Matrices Data processing Polynomials Data processing Kompensator (DE-588)4164866-3 gnd Polynommatrix (DE-588)4121492-4 gnd Numerische Mathematik (DE-588)4042805-9 gnd Mehrgrößenregelungssystem (DE-588)4135771-1 gnd Entwurf (DE-588)4121208-3 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Algorithmus (DE-588)4001183-5 gnd |
| subject_GND | (DE-588)4164866-3 (DE-588)4121492-4 (DE-588)4042805-9 (DE-588)4135771-1 (DE-588)4121208-3 (DE-588)4128130-5 (DE-588)4001183-5 |
| title | Numerical operations with polynomial matrices application to multi-variable dynamic compensator design |
| title_auth | Numerical operations with polynomial matrices application to multi-variable dynamic compensator design |
| title_exact_search | Numerical operations with polynomial matrices application to multi-variable dynamic compensator design |
| title_full | Numerical operations with polynomial matrices application to multi-variable dynamic compensator design P. Stefanidis ; A. P. Paplinski ; M. J. Gibbard |
| title_fullStr | Numerical operations with polynomial matrices application to multi-variable dynamic compensator design P. Stefanidis ; A. P. Paplinski ; M. J. Gibbard |
| title_full_unstemmed | Numerical operations with polynomial matrices application to multi-variable dynamic compensator design P. Stefanidis ; A. P. Paplinski ; M. J. Gibbard |
| title_short | Numerical operations with polynomial matrices |
| title_sort | numerical operations with polynomial matrices application to multi variable dynamic compensator design |
| title_sub | application to multi-variable dynamic compensator design |
| topic | Commande, théorie de la ram Matrices - Informatique ram Polynômes - Informatique ram Datenverarbeitung Control theory Matrices Data processing Polynomials Data processing Kompensator (DE-588)4164866-3 gnd Polynommatrix (DE-588)4121492-4 gnd Numerische Mathematik (DE-588)4042805-9 gnd Mehrgrößenregelungssystem (DE-588)4135771-1 gnd Entwurf (DE-588)4121208-3 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Algorithmus (DE-588)4001183-5 gnd |
| topic_facet | Commande, théorie de la Matrices - Informatique Polynômes - Informatique Datenverarbeitung Control theory Matrices Data processing Polynomials Data processing Kompensator Polynommatrix Numerische Mathematik Mehrgrößenregelungssystem Entwurf Numerisches Verfahren Algorithmus |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002879090&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005848579 |
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