Linear system fundamentals: continuus and discrete, classic and modern
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | Undetermined |
| Veröffentlicht: |
New York [u.a.]
McGraw-Hill
1983
|
| Ausgabe: | 1. print. |
| Schriftenreihe: | McGraw-Hill series in electrical engineering
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 484 S. |
| ISBN: | 0070518084 |
Internformat
MARC
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| 300 | |a 484 S. | ||
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Datensatz im Suchindex
| _version_ | 1804135827272368128 |
|---|---|
| adam_text | CONTENTS
Preface xv
Part 1 Classic Analysis
1 Input Output Characteristics of a Linear
Dynamic System: Time Domain 3
1 1 Basic Properties of a Linear Dynamic System Time Response 4
1 2 The Principle of Linear Superposition 14
1 3 The Convolution Integral of a Linear Time Invariant System 26
1 4 Relation between the Discrete Pulse Response Sequence and the
Continuous Impulse Response 33
1 5 The System Step Response 35
1 6 Performance Characteristics of the Step Response 39
1 7 Stability 43
*l 8 Time Delay and Distributed Parameter Systems 45
1 9 Linear Time Varying Systems 48
1 10 Summary 49
Notes and References 50
Problems 50
2 Classic Solution to the Linear Time Invariant
Ordinary Differential Equation Model 54
2 1 Deriving the Differential Equation Model 55
2 2 The Form of the Complete Solution 58
2 3 The Homogeneous Solution 62
2 4 System Stability 65
* An asterisk indicates an advanced topic area that may be omitted from the course of study with no
loss in continuity to later material.
ix
X CONTENTS
2 5 The Particular Solution for Exponential Inputs 66
2 6 The Complete Solution 76
2 7 Elementary Row Operations and the Linear Equation Problem 79
2 8 A Very Subtle Point: The Difference between t0 and t0+ 84
2 9 The System Step Response 88
2 10 The Impulse Response Function 91
2 11 Summary 95
Notes and References 96
Problems 100
3 Input Output Characteristics of a Dynamic Linear
System: Frequency Domain 101
3 1 Steady State Response to Sinusoid Inputs 101
3 2 The Bode Magnitude Plot 104
3 3 The Bode Phase Angle Plot 107
3 4 The Fourier Transform 117
3 5 Properties of the Fourier Transform 121
*3 6 Time Delay Systems 130
*3 7 Correlation between the System Input and the
Steady State Output 131
*3 8 The Discrete and Fast Fourier Transforms 133
*3 9 Digitally Sampled Signals, Aliasing, and Shannon s
Sampling Theorem 134
3 10 Summary 138
Notes and References 138
Problems 139
4 Laplace Transform Analysis 142
4 1 Definition and Relation to Fourier Transform 142
4 2 Properties of the Laplace Transform 145
4 3 Using the Laplace Transform to Solve the Differential Equation 150
4 4 Unit Step Response Revisited I54
4 5 Interconnection of Linear Systems 158
*4 6 Unity Feedback and the System Poles and Zeros 165
4 7 Summary 166
Problems 167
Notes and References 170
5 The Finite Difference Equation in Modeling
Continuous Systems 171
5 1 Derivation of the Finite Difference Equation 172
5 2 The Homogeneous Response 81
5 3 Stability 182
5 4 Relation between the Continuous Poles, pt, and the
Discrete Poles, pTi 183
5 5 The Particular Solution 188
5 6 Particular Solution to Discrete Sinusoidal Input 193
5 7 The Complete Solution 194
CONTENTS XI
5 8 The z Transform 196
5 9 Properties of the z Transform 198
*5 10 The z Transform Used to Solve the Finite Difference Equation 201
5 11 Summary 202
Notes and References 202
Problems 203
Part 2 State Variable Analysis
6 Deriving the State Variable Model 209
6 1 Phase Variable Canonical Form 210
6 2 States Derived via the Simulation Diagram 218
6 3 Diagonal Form, Distinct Roots 223
6 4 Physical Variable States 226
6 5 Introduction to MIMO State Equations 234
6 6 Summary 237
Notes and References 238
Problems 238
7 State Space Analysis: Continuous Time 241
7 1 Simplest Case: First Order State Model 241
7 2 General State Space Model 246
7 3 The Resolvent Matrix and eAI 247
7 4 Properties of the Matrix Exponential Function 250
7 5 The General State Solution 255
7 6 Further Consideration of the Fundamental Concept of State 256
7 7 State Space Solution to Unit Singularity Inputs 258
7 8 Further Consideration of H (s) 261
7 9 Summary 264
Notes and References 264
Problems 264
8 State Space Analysis: Discrete Time 268
8 1 Discrete Time Simulation: First Order System 268
8 2 Discrete Time Simulation: General MIMO System 273
8 3 Calculation of AT and BT 214
8 4 Stability and the Poles of AT 279
8 5 Relation between the Discrete State Model and the Finite
Difference Equation for the SISO System 280
8 6 Calculation of the Discrete Pulse Response from the Discrete
State Model 284
8 7 Introduction to Discrete State Controllability 286
8 8 Introduction to Discrete Observability 290
8 9 The System Hankel Matrix Revisited 292
8 10 Summary 293
Notes and References 294
Problems 294
Xli CONTENTS
9 Fundamentals of Linear Vector Spaces and
Transformation of State Coordinates 300
9 1 The Definition of a Vector Space 300
9 2 Vector Norms and Inner Products 302
9 3 Linear Combinations of Vectors and Vector Subspaces 305
9 4 Linear Dependence, Independence, and Basis 307
9 5 Transformation of Basis 310
9 6 Transformation of State Coordinates 314
9 7 Use of Controllability and Observability Matrices to Transform
State Coordinates 319
9 8 Summary 321
Notes and References 322
Problems 322
10 Eigenvalues, Eigenvectors, and eAt 325
10 1 The Eigenvalue and Eigenvector Linear Equation Problem 325
10 2 The General Linear Equation Problem 328
10 3 Elementary Row Operations and the Complete Solution 334
10 4 The Eigenvector Solution 337
10 5 Transforming to the Diagonal and Block Diagonal
Canonical Forms 341
*10 6 The Jordan Canonical Form 345
* 10 7 Eigenvalues and Eigenvectors of Real Symmetric Matrices 347
10 8 eAt and the Eigenvalues and Eigenvectors 349
10 9 Finding eAt Using the Block Diagonal Form 354
* 10 10 Computing eAt with the Jordan Canonical Form 356
10 11 eAt and the Cayley Hamilton Theorem 357
10 12 Summary 360
Notes and References 360
Problems 361
11 Controllability and Observability 367
11 1 Controllability Analyzed via Applying the Cayley Hamilton
Theorem 367
11 2 Observability Analyzed via the Cayley Hamilton Theorem 372
11 3 Controllability, Observability, and the Transfer Function for the
SISO System 375
11 4 Kalman s Canonical Decomposition of State Space 378
11 5 Controllability and Observability Analyzed in Diagonal
State Coordinates 380
* 11 6 The Hankel Matrix and Determination of System Model Order 383
* 11 7 Alternative Methods for Calculation of Controllability
(Observability) 386
* 11 8 Minimum Effort Control and Controllability 387
11 9 Summary 392
Notes and References 392
Problems 393
CONTENTS xiii
12 Linear Time Varying State Models 397
12 1 The General Linear Time Varying State Model Solution 397
12 2 Properties of the State Transition Matrix 403
* 12 3 Controllability of the Linear Time Varying System 405
*12 4 Observability of the Linear Time Varying System 406
12 5 Discrete Time Simulation of the Linear Time Varying System 407
12 6 Linearizing a Nonlinear State Differential Equation 412
12 7 Summary 421
Problems 422
Notes and References 424
Appendixes 425
A Finding the Transfer Function for a Linear Circuit via
Linear Graphs 425
B Introduction to Matrices 438
C Partial Fraction Expansions 444
D Recursive Calculation of the Resolvent Matrix 449
E Introduction to the Singular Value Decomposition 451
F Applicable Software 458
G List of Symbols 461
H Problem Solutions 464
Index 477
|
| adam_txt |
CONTENTS
Preface xv
Part 1 Classic Analysis
1 Input Output Characteristics of a Linear
Dynamic System: Time Domain 3
1 1 Basic Properties of a Linear Dynamic System Time Response 4
1 2 The Principle of Linear Superposition 14
1 3 The Convolution Integral of a Linear Time Invariant System 26
1 4 Relation between the Discrete Pulse Response Sequence and the
Continuous Impulse Response 33
1 5 The System Step Response 35
1 6 Performance Characteristics of the Step Response 39
1 7 Stability 43
*l 8 Time Delay and Distributed Parameter Systems 45
1 9 Linear Time Varying Systems 48
1 10 Summary 49
Notes and References 50
Problems 50
2 Classic Solution to the Linear Time Invariant
Ordinary Differential Equation Model 54
2 1 Deriving the Differential Equation Model 55
2 2 The Form of the Complete Solution 58
2 3 The Homogeneous Solution 62
2 4 System Stability 65
* An asterisk indicates an advanced topic area that may be omitted from the course of study with no
loss in continuity to later material.
ix
X CONTENTS
2 5 The Particular Solution for Exponential Inputs 66
2 6 The Complete Solution 76
2 7 Elementary Row Operations and the Linear Equation Problem 79
2 8 A Very Subtle Point: The Difference between t0" and t0+ 84
2 9 The System Step Response 88
2 10 The Impulse Response Function 91
2 11 Summary 95
Notes and References 96
Problems 100
3 Input Output Characteristics of a Dynamic Linear
System: Frequency Domain 101
3 1 Steady State Response to Sinusoid Inputs 101
3 2 The Bode Magnitude Plot 104
3 3 The Bode Phase Angle Plot 107
3 4 The Fourier Transform 117
3 5 Properties of the Fourier Transform 121
*3 6 Time Delay Systems 130
*3 7 Correlation between the System Input and the
Steady State Output 131
*3 8 The Discrete and Fast Fourier Transforms 133
*3 9 Digitally Sampled Signals, Aliasing, and Shannon's
Sampling Theorem 134
3 10 Summary 138
Notes and References 138
Problems 139
4 Laplace Transform Analysis 142
4 1 Definition and Relation to Fourier Transform 142
4 2 Properties of the Laplace Transform 145
4 3 Using the Laplace Transform to Solve the Differential Equation 150
4 4 Unit Step Response Revisited I54
4 5 Interconnection of Linear Systems 158
*4 6 Unity Feedback and the System Poles and Zeros 165
4 7 Summary 166
Problems 167
Notes and References 170
5 The Finite Difference Equation in Modeling
Continuous Systems 171
5 1 Derivation of the Finite Difference Equation 172
5 2 The Homogeneous Response '81
5 3 Stability 182
5 4 Relation between the Continuous Poles, pt, and the
Discrete Poles, pTi 183
5 5 The Particular Solution 188
5 6 Particular Solution to Discrete Sinusoidal Input 193
5 7 The Complete Solution 194
CONTENTS XI
5 8 The z Transform 196
5 9 Properties of the z Transform 198
*5 10 The z Transform Used to Solve the Finite Difference Equation 201
5 11 Summary 202
Notes and References 202
Problems 203
Part 2 State Variable Analysis
6 Deriving the State Variable Model 209
6 1 Phase Variable Canonical Form 210
6 2 States Derived via the Simulation Diagram 218
6 3 Diagonal Form, Distinct Roots 223
6 4 Physical Variable States 226
6 5 Introduction to MIMO State Equations 234
6 6 Summary 237
Notes and References 238
Problems 238
7 State Space Analysis: Continuous Time 241
7 1 Simplest Case: First Order State Model 241
7 2 General State Space Model 246
7 3 The Resolvent Matrix and eAI 247
7 4 Properties of the Matrix Exponential Function 250
7 5 The General State Solution 255
7 6 Further Consideration of the Fundamental Concept of State 256
7 7 State Space Solution to Unit Singularity Inputs 258
7 8 Further Consideration of H (s) 261
7 9 Summary 264
Notes and References 264
Problems 264
8 State Space Analysis: Discrete Time 268
8 1 Discrete Time Simulation: First Order System 268
8 2 Discrete Time Simulation: General MIMO System 273
8 3 Calculation of AT and BT 214
8 4 Stability and the Poles of AT 279
8 5 Relation between the Discrete State Model and the Finite
Difference Equation for the SISO System 280
8 6 Calculation of the Discrete Pulse Response from the Discrete
State Model 284
8 7 Introduction to Discrete State Controllability 286
8 8 Introduction to Discrete Observability 290
8 9 The System Hankel Matrix Revisited 292
8 10 Summary 293
Notes and References 294
Problems 294
Xli CONTENTS
9 Fundamentals of Linear Vector Spaces and
Transformation of State Coordinates 300
9 1 The Definition of a Vector Space 300
9 2 Vector Norms and Inner Products 302
9 3 Linear Combinations of Vectors and Vector Subspaces 305
9 4 Linear Dependence, Independence, and Basis 307
9 5 Transformation of Basis 310
9 6 Transformation of State Coordinates 314
9 7 Use of Controllability and Observability Matrices to Transform
State Coordinates 319
9 8 Summary 321
Notes and References 322
Problems 322
10 Eigenvalues, Eigenvectors, and eAt 325
10 1 The Eigenvalue and Eigenvector Linear Equation Problem 325
10 2 The General Linear Equation Problem 328
10 3 Elementary Row Operations and the Complete Solution 334
10 4 The Eigenvector Solution 337
10 5 Transforming to the Diagonal and Block Diagonal
Canonical Forms 341
*10 6 The Jordan Canonical Form 345
* 10 7 Eigenvalues and Eigenvectors of Real Symmetric Matrices 347
10 8 eAt and the Eigenvalues and Eigenvectors 349
10 9 Finding eAt Using the Block Diagonal Form 354
* 10 10 Computing eAt with the Jordan Canonical Form 356
10 11 eAt and the Cayley Hamilton Theorem 357
10 12 Summary 360
Notes and References 360
Problems 361
11 Controllability and Observability 367
11 1 Controllability Analyzed via Applying the Cayley Hamilton
Theorem 367
11 2 Observability Analyzed via the Cayley Hamilton Theorem 372
11 3 Controllability, Observability, and the Transfer Function for the
SISO System 375
11 4 Kalman's Canonical Decomposition of State Space 378
11 5 Controllability and Observability Analyzed in Diagonal
State Coordinates 380
* 11 6 The Hankel Matrix and Determination of System Model Order 383
* 11 7 Alternative Methods for Calculation of Controllability
(Observability) 386
* 11 8 Minimum Effort Control and Controllability 387
11 9 Summary 392
Notes and References 392
Problems 393
CONTENTS xiii
12 Linear Time Varying State Models 397
12 1 The General Linear Time Varying State Model Solution 397
12 2 Properties of the State Transition Matrix 403
* 12 3 Controllability of the Linear Time Varying System 405
*12 4 Observability of the Linear Time Varying System 406
12 5 Discrete Time Simulation of the Linear Time Varying System 407
12 6 Linearizing a Nonlinear State Differential Equation 412
12 7 Summary 421
Problems 422
Notes and References 424
Appendixes 425
A Finding the Transfer Function for a Linear Circuit via
Linear Graphs 425
B Introduction to Matrices 438
C Partial Fraction Expansions 444
D Recursive Calculation of the Resolvent Matrix 449
E Introduction to the Singular Value Decomposition 451
F Applicable Software 458
G List of Symbols 461
H Problem Solutions 464
Index 477 |
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| spelling | Reid, Graham Verfasser aut Linear system fundamentals continuus and discrete, classic and modern 1. print. New York [u.a.] McGraw-Hill 1983 484 S. txt rdacontent n rdamedia nc rdacarrier McGraw-Hill series in electrical engineering Lineares System (DE-588)4125617-7 gnd rswk-swf Systemanalyse (DE-588)4116673-5 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Systemanalyse (DE-588)4116673-5 s DE-604 Lineares System (DE-588)4125617-7 s 2\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015101049&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Reid, Graham Linear system fundamentals continuus and discrete, classic and modern Lineares System (DE-588)4125617-7 gnd Systemanalyse (DE-588)4116673-5 gnd |
| subject_GND | (DE-588)4125617-7 (DE-588)4116673-5 (DE-588)4151278-9 |
| title | Linear system fundamentals continuus and discrete, classic and modern |
| title_auth | Linear system fundamentals continuus and discrete, classic and modern |
| title_exact_search | Linear system fundamentals continuus and discrete, classic and modern |
| title_exact_search_txtP | Linear system fundamentals continuus and discrete, classic and modern |
| title_full | Linear system fundamentals continuus and discrete, classic and modern |
| title_fullStr | Linear system fundamentals continuus and discrete, classic and modern |
| title_full_unstemmed | Linear system fundamentals continuus and discrete, classic and modern |
| title_short | Linear system fundamentals |
| title_sort | linear system fundamentals continuus and discrete classic and modern |
| title_sub | continuus and discrete, classic and modern |
| topic | Lineares System (DE-588)4125617-7 gnd Systemanalyse (DE-588)4116673-5 gnd |
| topic_facet | Lineares System Systemanalyse Einführung |
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