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Control Theory: Multivariable and Nonlinear Methods

Torkel Glad and Lennart Ljung
Format
Book
Published
London ; New York : Taylor & Francis, 2000.
Language
English
Swedish (translated from)
Uniform Title
Reglerteori English
ISBN
0748408770 (hb : alk. paper), 0748408789 (pb : alk. paper)
Contents
  • 1.1 Multivariable Systems 2
  • 1.2 Nonlinear Systems 5
  • 1.3 Discrete and Continuous Time Models and Controllers 6
  • 1.4 Some Basic Concepts in Control 8
  • 1.5 Gain and Signal Size 15
  • 1.6 Stability and the Small Gain Theorem 18
  • Part I Linear Systems 25
  • 2 Representation of Linear Systems 27
  • 2.1 Impulse Response and Weighting Function 27
  • 2.2 Transfer Function Matrices 28
  • 2.3 Transfer Operator 30
  • 2.4 Input--Output Equations 30
  • 2.5 State Space Form 31
  • 2.6 Discrete Time Systems 37
  • 3 Properties of Linear Systems 43
  • 3.1 Solving the System Equations 43
  • 3.2 Controllability and Observability 44
  • 3.3 Poles and Zeros 48
  • 3.4 Stability 53
  • 3.5 Frequency Response and Frequency Functions 58
  • 3.6 Model Reduction 63
  • 3.7 Discrete Time Systems 68
  • 3A Proofs 79
  • 4 Sampled Data Systems 83
  • 4.1 Approximating Continuous Time Systems 83
  • 4.2 System Sampling 85
  • 4.3 Poles and Zeros 90
  • 4.4 Controllability and Observability 93
  • 4.5 Frequency Functions 96
  • 5 Disturbance Models 101
  • 5.1 Disturbances 101
  • 5.2 Signal Size and Scaling 103
  • 5.3 Spectral Description of Disturbances 106
  • 5.4 Description of Disturbances in the Time Domain 112
  • 5.5 Estimation of One Signal from Another 114
  • 5.6 Measurement and System Disturbances 116
  • 5.7 Observers and Kalman Filters 124
  • 5.8 Discrete Time Systems 131
  • 5.9 Practical Aspects of Signal Sampling 139
  • 5A Proofs 141
  • Part II Linear Control Theory 145
  • 6 Closed Loop System 147
  • 6.1 Transfer Functions of the Closed Loop System 147
  • 6.2 Stability of the Closed System 150
  • 6.3 Sensitivity and Robustness 152
  • 6.4 Specifications 155
  • 6.5 Specifications in the Time Domain 156
  • 6.6 Specifications in the Frequency Domain 159
  • 6.7 Sampled Data Controllers 164
  • 7 Basic Limitations in Control Design 171
  • 7.1 Scaling of Variables 171
  • 7.2 Intuitive Analysis 172
  • 7.3 Loop Gain Limitations 176
  • 7.4 S and T: Individual Limitations 179
  • 7.5 Consequences for the System Performance 186
  • 7.6 Effects of Control Signal Bounds 192
  • 7.7 Multivariable Case 195
  • 7.8 Some Examples 201
  • 7A Proofs 209
  • 8 Controller Structures and Control Design 215
  • 8.1 Main Ideas 216
  • 8.2 Configuration of Multivariable Controllers 219
  • 8.3 Internal Model Control 228
  • 8.4 Feedback from Reconstructed States 233
  • 9 Minimization of Quadratic Criteria: LQG 239
  • 9.1 Criterion and the Main Ideas 239
  • 9.2 Optimal Controller: Main Results 242
  • 9.3 Some Practical Aspects 247
  • 9.4 Robustness for LQG Controllers 257
  • 9.5 Discrete Time Systems 264
  • 9A Proofs 273
  • 10 Loop Shaping 277
  • 10.1 Direct Methods 277
  • 10.2 Formalization of the Requirements 278
  • 10.3 Optimal H[subscript 2] Control 284
  • 10.4 Optimal H[subscript infinity] Control 285
  • 10.5 Robust Loop Shaping 293
  • 10.6 Discrete Time Systems 300
  • 10A To Decrease the Spread of the Singular Values 303
  • Part III Nonlinear Control Theory 305
  • 11 Describing Nonlinear Systems 307
  • 11.1 Linear Versus Nonlinear 308
  • 11.2 Examples of Nonlinear Systems 312
  • 11.3 Mathematical Description 314
  • 11.4 Equilibria and Linearization 317
  • 12 Stability of Nonlinear Systems 321
  • 12.1 Stability of Equilibria 321
  • 12.2 Stability and Lyapunov Functions 323
  • 12.3 Circle Criterion 329
  • 12A Proofs 337
  • 13 Phase Plane Analysis 339
  • 13.1 Phase Planes for Linear Systems 339
  • 13.2 Phase Planes for Nonlinear Systems 346
  • 14 Oscillations and Describing Functions 355
  • 14.1 Describing Function Method 356
  • 14.2 Computing Amplitude and Frequency of Oscillations 360
  • 14A Some Describing Functions 366
  • 15 Controller Synthesis for Nonlinear Systems 371
  • 15.1 Linearg Design and Nonlinear Verification 371
  • 15.2 Nonlinear Internal Model Control 372
  • 15.3 Parametric Optimization 374
  • 15.4 Other Approaches 377
  • 15.5 State Feedback and Observer 378
  • 16 Model Predictive Control 383
  • 16.1 Basic Idea: Predict the Output 383
  • 16.2 [kappa]-step Prediction for Linear Systems 384
  • 16.3 Criterion and the Controller 385
  • 17 To Compensate Exactly for Nonlinearities 393
  • 17.1 Examples of Exact Linearization 393
  • 17.2 Relative Degree 395
  • 17.3 Input-Output Linearization 397
  • 17.4 Exact State Linearization 401
  • 18 Optimal Control 407
  • 18.1 Goddard Rocket Problem 407
  • 18.2 Maximum Principle 410
  • 18.3 Solution of the Goddard Rocket Problem 424
  • 18.4 Minimum Time Problems 428
  • 18.5 Optimal Feedback 436
  • 18.6 Numerical Methods 442
  • 18A Proof of the Maximum Principle 445.
Description
xiv, 467 p. : ill. ; 25 cm.
Notes
Includes bibliographical references and index.
Technical Details
  • Access in Virgo Classic
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    g| 1.1 t| Multivariable Systems g| 2 -- g| 1.2 t| Nonlinear Systems g| 5 -- g| 1.3 t| Discrete and Continuous Time Models and Controllers g| 6 -- g| 1.4 t| Some Basic Concepts in Control g| 8 -- g| 1.5 t| Gain and Signal Size g| 15 -- g| 1.6 t| Stability and the Small Gain Theorem g| 18 -- g| Part I t| Linear Systems g| 25 -- g| 2 t| Representation of Linear Systems g| 27 -- g| 2.1 t| Impulse Response and Weighting Function g| 27 -- g| 2.2 t| Transfer Function Matrices g| 28 -- g| 2.3 t| Transfer Operator g| 30 -- g| 2.4 t| Input--Output Equations g| 30 -- g| 2.5 t| State Space Form g| 31 -- g| 2.6 t| Discrete Time Systems g| 37 -- g| 3 t| Properties of Linear Systems g| 43 -- g| 3.1 t| Solving the System Equations g| 43 -- g| 3.2 t| Controllability and Observability g| 44 -- g| 3.3 t| Poles and Zeros g| 48 -- g| 3.4 t| Stability g| 53 -- g| 3.5 t| Frequency Response and Frequency Functions g| 58 -- g| 3.6 t| Model Reduction g| 63 -- g| 3.7 t| Discrete Time Systems g| 68 -- g| 3A t| Proofs g| 79 -- g| 4 t| Sampled Data Systems g| 83 -- g| 4.1 t| Approximating Continuous Time Systems g| 83 -- g| 4.2 t| System Sampling g| 85 -- g| 4.3 t| Poles and Zeros g| 90 -- g| 4.4 t| Controllability and Observability g| 93 -- g| 4.5 t| Frequency Functions g| 96 -- g| 5 t| Disturbance Models g| 101 -- g| 5.1 t| Disturbances g| 101 -- g| 5.2 t| Signal Size and Scaling g| 103 -- g| 5.3 t| Spectral Description of Disturbances g| 106 -- g| 5.4 t| Description of Disturbances in the Time Domain g| 112 -- g| 5.5 t| Estimation of One Signal from Another g| 114 -- g| 5.6 t| Measurement and System Disturbances g| 116 -- g| 5.7 t| Observers and Kalman Filters g| 124 -- g| 5.8 t| Discrete Time Systems g| 131 -- g| 5.9 t| Practical Aspects of Signal Sampling g| 139 -- g| 5A t| Proofs g| 141 -- g| Part II t| Linear Control Theory g| 145 -- g| 6 t| Closed Loop System g| 147 -- g| 6.1 t| Transfer Functions of the Closed Loop System g| 147 -- g| 6.2 t| Stability of the Closed System g| 150 -- g| 6.3 t| Sensitivity and Robustness g| 152 -- g| 6.4 t| Specifications g| 155 -- g| 6.5 t| Specifications in the Time Domain g| 156 -- g| 6.6 t| Specifications in the Frequency Domain g| 159 -- g| 6.7 t| Sampled Data Controllers g| 164 -- g| 7 t| Basic Limitations in Control Design g| 171 -- g| 7.1 t| Scaling of Variables g| 171 -- g| 7.2 t| Intuitive Analysis g| 172 -- g| 7.3 t| Loop Gain Limitations g| 176 -- g| 7.4 t| S and T: Individual Limitations g| 179 -- g| 7.5 t| Consequences for the System Performance g| 186 -- g| 7.6 t| Effects of Control Signal Bounds g| 192 -- g| 7.7 t| Multivariable Case g| 195 -- g| 7.8 t| Some Examples g| 201 -- g| 7A t| Proofs g| 209 -- g| 8 t| Controller Structures and Control Design g| 215 -- g| 8.1 t| Main Ideas g| 216 -- g| 8.2 t| Configuration of Multivariable Controllers g| 219 -- g| 8.3 t| Internal Model Control g| 228 -- g| 8.4 t| Feedback from Reconstructed States g| 233 -- g| 9 t| Minimization of Quadratic Criteria: LQG g| 239 -- g| 9.1 t| Criterion and the Main Ideas g| 239 -- g| 9.2 t| Optimal Controller: Main Results g| 242 -- g| 9.3 t| Some Practical Aspects g| 247 -- g| 9.4 t| Robustness for LQG Controllers g| 257 -- g| 9.5 t| Discrete Time Systems g| 264 -- g| 9A t| Proofs g| 273 -- g| 10 t| Loop Shaping g| 277 -- g| 10.1 t| Direct Methods g| 277 -- g| 10.2 t| Formalization of the Requirements g| 278 -- g| 10.3 t| Optimal H[subscript 2] Control g| 284 -- g| 10.4 t| Optimal H[subscript infinity] Control g| 285 -- g| 10.5 t| Robust Loop Shaping g| 293 -- g| 10.6 t| Discrete Time Systems g| 300 -- g| 10A t| To Decrease the Spread of the Singular Values g| 303 -- g| Part III t| Nonlinear Control Theory g| 305 -- g| 11 t| Describing Nonlinear Systems g| 307 -- g| 11.1 t| Linear Versus Nonlinear g| 308 -- g| 11.2 t| Examples of Nonlinear Systems g| 312 -- g| 11.3 t| Mathematical Description g| 314 -- g| 11.4 t| Equilibria and Linearization g| 317 -- g| 12 t| Stability of Nonlinear Systems g| 321 -- g| 12.1 t| Stability of Equilibria g| 321 -- g| 12.2 t| Stability and Lyapunov Functions g| 323 -- g| 12.3 t| Circle Criterion g| 329 -- g| 12A t| Proofs g| 337 -- g| 13 t| Phase Plane Analysis g| 339 -- g| 13.1 t| Phase Planes for Linear Systems g| 339 -- g| 13.2 t| Phase Planes for Nonlinear Systems g| 346 -- g| 14 t| Oscillations and Describing Functions g| 355 -- g| 14.1 t| Describing Function Method g| 356 -- g| 14.2 t| Computing Amplitude and Frequency of Oscillations g| 360 -- g| 14A t| Some Describing Functions g| 366 -- g| 15 t| Controller Synthesis for Nonlinear Systems g| 371 -- g| 15.1 t| Linearg Design and Nonlinear Verification g| 371 -- g| 15.2 t| Nonlinear Internal Model Control g| 372 -- g| 15.3 t| Parametric Optimization g| 374 -- g| 15.4 t| Other Approaches g| 377 -- g| 15.5 t| State Feedback and Observer g| 378 -- g| 16 t| Model Predictive Control g| 383 -- g| 16.1 t| Basic Idea: Predict the Output g| 383 -- g| 16.2 t| [kappa]-step Prediction for Linear Systems g| 384 -- g| 16.3 t| Criterion and the Controller g| 385 -- g| 17 t| To Compensate Exactly for Nonlinearities g| 393 -- g| 17.1 t| Examples of Exact Linearization g| 393 -- g| 17.2 t| Relative Degree g| 395 -- g| 17.3 t| Input-Output Linearization g| 397 -- g| 17.4 t| Exact State Linearization g| 401 -- g| 18 t| Optimal Control g| 407 -- g| 18.1 t| Goddard Rocket Problem g| 407 -- g| 18.2 t| Maximum Principle g| 410 -- g| 18.3 t| Solution of the Goddard Rocket Problem g| 424 -- g| 18.4 t| Minimum Time Problems g| 428 -- g| 18.5 t| Optimal Feedback g| 436 -- g| 18.6 t| Numerical Methods g| 442 -- g| 18A t| Proof of the Maximum Principle g| 445.
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    0
    a| Control theory.
    700
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    a| Ljung, Lennart.
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