Subspace identification for linear systems

✍ Scribed by van Overschee P., Moor B.L.

• Publisher: Kluwer
• Year: 1996
• Tongue: English
• Leaves: 268
• Category: Library

✦ Synopsis

Subspace Identification for Linear Systems focuses on the theory, implementation and applications of subspace identification algorithms for linear time-invariant finite- dimensional dynamical systems. These algorithms allow for a fast, straightforward and accurate determination of linear multivariable models from measured input-output data. The theory of subspace identification algorithms is presented in detail. Several chapters are devoted to deterministic, stochastic and combined deterministic-stochastic subspace identification algorithms. For each case, the geometric properties are stated in a main 'subspace' Theorem. Relations to existing algorithms and literature are explored, as are the interconnections between different subspace algorithms. The subspace identification theory is linked to the theory of frequency weighted model reduction, which leads to new interpretations and insights. The implementation of subspace identification algorithms is discussed in terms of the robust and computationally efficient RQ and singular value decompositions, which are well-established algorithms from numerical linear algebra. The algorithms are implemented in combination with a whole set of classical identification algorithms, processing and validation tools in Xmath's ISID, a commercially available graphical user interface toolbox. The basic subspace algorithms in the book are also implemented in a set of Matlab files accompanying the book. An application of ISID to an industrial glass tube manufacturing process is presented in detail, illustrating the power and user-friendliness of the subspace identification algorithms and of their implementation in ISID. The identified model allows for an optimal control of the process, leading to a significant enhancement of the production quality. The applicability of subspace identification algorithms in industry is further illustrated with the application of the Matlab files to ten practical problems. Since all necessary data and Matlab files are included, the reader can easily step through these applications, and thus get more insight in the algorithms. Subspace Identification for Linear Systems is an important reference for all researchers in system theory, control theory, signal processing, automization, mechatronics, chemical, electrical, mechanical and aeronautical engineering.

✦ Table of Contents

Contents......Page 5
Preface......Page 11
1.1 Models Of Systems And System Identification......Page 15
1.2.1 State Space Models Are Good Engineering Models......Page 20
1.2.2 How Do Subspace Identification Algorithms Work?......Page 23
1.2.3 What’s New In Subspace Identification?......Page 25
1.2.4 Some Historical Elements......Page 26
1.3 Overview......Page 29
1.4.1 Orthogonal Projections......Page 33
1.4.2 Oblique Projections......Page 35
1.4.3 Principal Angles And Directions......Page 37
1.4.4 Statistical Tools......Page 39
1.4.5 Geometric Tools In A Statistical Framework......Page 41
1.5 Conclusions......Page 43
Deterministic Identification......Page 45
2.1.1 Problem description......Page 46
2.1.2 Notation......Page 47
2.2.2 Main Theorem......Page 51
2.3 Relation To Other Algorithms......Page 58
2.3.1 Intersection Algorithms......Page 59
2.3.2 Projection Algorithms......Page 60
2.3.3 Notes On Noisy Measurements......Page 61
2.4.1 Algorithm 1 Using The States......Page 64
2.4.2 Algorithm 2 Using The Extended Observability Matrix......Page 65
2.5 Conclusions......Page 69
3.1.1 Problem description......Page 71
3.1.2 Properties Of Stochastic Systems......Page 74
3.1.3 Notation......Page 81
3.1.4 Kalman Filte States......Page 83
3.1.5 About Positive Real Sequences......Page 87
3.2.1 Main Theorem......Page 88
3.3 Relation To Other Algorithms......Page 91
3.3.1 The principal component algorithm (PC)......Page 92
3.3.2 The unweighted principal component algorithm (UPC)......Page 93
3.3.3 The canonical variate algorithm (CVA)......Page 94
3.3.4 A Simulation Example......Page 95
3.4.1 Algorithm 1 Using The States......Page 96
3.4.3 Algorithm 3 Leading To A Positive Real Sequence......Page 99
3.4.4 A Simulation Example......Page 103
3.5 Conclusions......Page 105
Combined Deterministic-stochastic Identification......Page 109
4.1.1 Problem description......Page 110
4.1.2 Notation......Page 112
4.1.3 Kalman Filte States......Page 114
4.2.2 A Projection Theorem......Page 118
4.2.3 Main Theorem......Page 120
4.2.4 Intuition Behind The Theorems......Page 123
4.3 Relation To Other Algorithms......Page 125
4.3.1 N4SID......Page 126
4.3.2 MOESP......Page 127
4.3.3 CVA......Page 128
4.3.4 A Simulation Example......Page 129
4.4.1 Algorithm 1: Unbiased, Using The States......Page 131
4.4.2 Algorithm 2: Biased, Using The States......Page 134
4.4.3 Variations and optimizations of Algorithm 1......Page 137
4.4.4 Algorithm 3: A Robust Identificatio Algorithm......Page 142
4.5 Connections To The Previous Chapters......Page 144
4.6 Conclusions......Page 148
State Space Bases And Model Reduction......Page 149
5.1 Introduction......Page 150
5.2 Notation......Page 151
5.3 Frequency Weighted Balancing......Page 155
5.4 Subspace Identification And Frequency Weighted Balancing......Page 158
5.4.1 Main Theorem 1......Page 159
5.4.2 Special Cases Of The Firs Main Theorem......Page 160
5.4.3 Main Theorem 2......Page 161
5.4.5 Connections Between The Main Theorems......Page 162
5.5.1 Error Bounds For Truncated Models......Page 163
5.5.2 Reduced Order Identificatio......Page 167
5.6 Example......Page 169
5.7 Conclusions......Page 173
Implementation And Applications......Page 175
6.1.1 An Rq Decomposition......Page 176
6.1.2 Expressions For The Geometric Operations......Page 178
6.1.3 An Implementation Of The Robust Identificatio Algorithm......Page 182
6.2.1 Why A Graphical User Interface?......Page 184
6.2.2 ISID: Where system identification and GUI meet......Page 186
6.2.3 Using ISID......Page 192
6.2.4 An Overview Of ISID Algorithms
......Page 193
6.3 An Application Of ISID......Page 195
6.3.2 Chain Description And Results......Page 196
6.3.3 PIID Control Of The Process......Page 200
6.4 Practical Examples In Matlab......Page 203
6.5 Conclusions......Page 207
7.1 Conclusions......Page 211
7.2 Open Problems......Page 212
Proofs......Page 215
Matlab Functions......Page 237
Notation......Page 243
References......Page 249
Index......Page 263