Linear Systems Control

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Format: Hardcover
Pub. Date: 2009-02-28
Publisher(s): Springer Verlag
List Price: $219.99

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Summary

"Modern control theory and in particular state space or state variable methods can be adapted to the description of many systems because they depend strongly on physical modelling and physical intuition. The laws of physics are in the form of continuous differential equations and for this reason, this book concentrates on system descriptions in this form: coupled sets of linear or nonlinear differential equations. The physical approach is emphasized in this book because it is most natural for complex systems. It also makes it easier to immediately apply the theory to the understanding and control of many different types of systems." "In line with the approach set forth above, the book first deals with system modelling in state space as well as transfer function form. The modelling methods are described with many examples. Linearization is treated in detail. Because computer control is so fundamental to modern applications, discrete time modelling of systems as difference equations is introduced immediately after the more intuitive differential and transfer function models. Many control schemes, based on linearized state space models, are treated in the deterministic as well as in the stochastic case."--BOOK JACKET.

Table of Contents

Introductionp. 1
The Invisible Threadp. 1
Classical Control Systems and their Backgroundp. 2
Primitive Period Developmentsp. 2
Pre-Classical Period Developmentsp. 4
Classical Control Periodp. 6
Modern Control Theoryp. 7
State Space Modelling of Physical Systemsp. 9
Modelling of Physical Systemsp. 9
Linear System Modelsp. 10
State Space Models from Transfer Functionsp. 21
Companion Form 1p. 21
Companion Form 2p. 25
Linearizationp. 27
Discrete Time Modelsp. 49
Summaryp. 51
Problemsp. 52
Analysis of State Space Modelsp. 59
Solution of the Linear State Equationp. 59
The Time Varying Systemp. 59
The Time Invariant Systemp. 64
Transfer Functions from State Space Modelsp. 72
Natural Modesp. 74
Discrete Time Models of Continuous Systemsp. 76
Solution of the Discrete Time State Equationp. 82
The Time Invariant Discrete Time Systemp. 83
Discrete Time Transfer Functionsp. 87
Similarity Transformationsp. 92
Stabilityp. 101
Stability Criteria for Linear Systemsp. 104
Time Invariant Systemsp. 106
BIBO Stabilityp. 114
Internal and External Stabilityp. 115
Lyapunov's Methodp. 117
Controllability and Observabilityp. 121
Controllability (Continuous Time Systems)p. 124
Controllability and Similarity Transformationsp. 132
Reachability (Continuous Time Systems)p. 132
Controllability (Discrete Time Systems)p. 137
Reachability (Discrete Time Systems)p. 138
Observability (Continuous Time Systems)p. 142
Observability and Similarity Transformationsp. 146
Observability (Discrete Time Systems)p. 148
Dualityp. 150
Modal Decompositionp. 150
Controllable/Reachable Subspace Decompositionp. 154
Observable Subspace Decompositionp. 157
Canonical Formsp. 159
Controller Canonical Formp. 159
Observer Canonical Formp. 164
Duality for Canonical Formsp. 167
Pole-zero Cancellation in SISO Systemsp. 168
Realizabilityp. 169
Minimalityp. 173
Summaryp. 182
Notesp. 183
Linear Systems Theoryp. 183
Problemsp. 186
Linear Control System Designp. 193
Control System Designp. 193
Controller Operating Modesp. 196
Full State Feedback for Linear Systemsp. 199
State Feedback for SISO Systemsp. 208
Controller Design Based on the Controller Canonical Formp. 208
Ackermann's Formulap. 210
Conditions for Eigenvalue Assignmentp. 212
State Feedback for MIMO Systemsp. 226
Eigenstructure Assignment for MIMO Systemsp. 227
Dead Beat Regulatorsp. 232
Integral Controllersp. 234
Deterministic Observers and State Estimationp. 251
Continuous Time Full Order Observersp. 252
Discrete Time Full Order Observersp. 255
Observer Design for SISO Systemsp. 256
Observer Design Based on the Observer Canonical Formp. 256
Ackermann's Formula for the Observerp. 259
Conditions for Eigenvalue Assignmentp. 264
Observer Design for MIMO Systemsp. 265
Eigenstructure Assignment for MIMO Observersp. 266
Dead Beat Observersp. 266
Reduced Order Observersp. 267
State Feedback with Observersp. 272
Combining Observers and State Feedbackp. 273
State Feedback with Integral Controller and Observerp. 277
State Feedback with Reduced Order Observerp. 284
Summaryp. 286
Notesp. 287
Background for Observersp. 287
Problemsp. 287
Optimal Controlp. 293
Introduction to Optimal Controlp. 293
The General Optimal Control Problemp. 294
The Basis of Optimal Control - Calculus of Variationsp. 296
The Linear Quadratic Regulatorp. 304
The Quadratic Cost Functionp. 305
Linear Quadratic Controlp. 307
Steady State Linear Quadratic Regulatorp. 316
Robustness of LQR Controlp. 324
LQR Design: Eigenstructure Assignment Approachp. 325
Discrete Time Optimal Controlp. 328
Discretization of the Performance Indexp. 329
Discrete Time State Feedbackp. 330
Steady State Discrete Optimal Controlp. 332
Summaryp. 339
Notesp. 340
The Calculus of Variationsp. 340
Problemsp. 342
Noise in Dynamic Systemsp. 351
Introductionp. 351
Random Variablesp. 353
Expectation (Average) Values of a Random Variablep. 357
Average Value of Discrete Random Variablesp. 361
Characteristic Functionsp. 362
Joint Probability Distribution and Density Functionsp. 366
Random Processesp. 371
Random Processesp. 371
Moments of a Stochastic Processp. 375
Stationary Processesp. 378
Ergodic Processesp. 380
Independent Increment Stochastic Processesp. 382
Noise Propagation: Frequency and Time Domainsp. 392
Continuous Random Processes: Time Domainp. 394
Continuous Random Processes: Frequency Domainp. 397
Continuous Random Processes: Time Domainp. 402
Inserting Noise into Simulation Systemsp. 408
Discrete Time Stochastic Processesp. 412
Translating Continuous Noise into Discrete Time Systemsp. 414
Discrete Random Processes: Frequency Domainp. 416
Discrete Random Processes: Running in Timep. 420
Summaryp. 422
Notesp. 423
The Normal Distributionp. 423
The Wiener Processp. 423
Stochastic Differential Equationsp. 424
Problemsp. 425
Optimal Observers: Kalman Filtersp. 431
Introductionp. 431
Continuous Kalman Filterp. 432
Block Diagram of a CKFp. 436
Innovation Processp. 446
Discrete Kalman Filterp. 449
A Real Time Discrete Kalman Filter (Open Form)p. 449
Block Diagram of an Open Form DKFp. 453
Closed Form of a DKFp. 456
Discrete and Continuous Kalman Filter Equivalencep. 461
Stochastic Integral Quadratic Formsp. 464
Separation Theoremp. 466
Evaluation of the Continuous LQG Indexp. 469
Evaluation of the Discrete LQG Indexp. 475
Summaryp. 476
Notesp. 478
Background for Kalman Filteringp. 478
Problemsp. 479
Static Optimizationp. 493
Optimization Basicsp. 493
Constrained Static Optimizationp. 496
Problemsp. 498
Linear Algebrap. 501
Matrix Basicsp. 501
Eigenvalues and Eigenvectorsp. 503
Partitioned Matricesp. 506
Quadratic Formsp. 507
Matrix Calculusp. 509
Continuous Riccati Equationp. 511
Estimator Riccati Equationp. 511
Time Axis Reversalp. 511
Using the LQR Solutionp. 512
Discrete Time SISO Systemsp. 515
Introductionp. 515
The Sampling Processp. 516
The Z-Transformp. 521
Inverse Z-Transformp. 524
Discrete Transfer Functionsp. 526
Discrete Systems and Difference Equationsp. 528
Discrete Time Systems with Zero-Order-Holdp. 528
Transient Response, Poles and Stabilityp. 529
Frequency Responsep. 532
Discrete Approximations to Continuous Transfer Functionsp. 534
Tustin Approximationp. 535
Matched-Pole-Zero Approximation (MPZ)p. 536
Discrete Equivalents to Continuous Controllersp. 539
Choice of Sampling Periodp. 545
Referencesp. 547
Indexp. 549
Table of Contents provided by Ingram. All Rights Reserved.

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