
Linear Systems Control
by Hendricks, Elbert; Jannerup, Ole; Sorensen, Paul HaaseRent Textbook
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Summary
Table of Contents
Introduction | p. 1 |
The Invisible Thread | p. 1 |
Classical Control Systems and their Background | p. 2 |
Primitive Period Developments | p. 2 |
Pre-Classical Period Developments | p. 4 |
Classical Control Period | p. 6 |
Modern Control Theory | p. 7 |
State Space Modelling of Physical Systems | p. 9 |
Modelling of Physical Systems | p. 9 |
Linear System Models | p. 10 |
State Space Models from Transfer Functions | p. 21 |
Companion Form 1 | p. 21 |
Companion Form 2 | p. 25 |
Linearization | p. 27 |
Discrete Time Models | p. 49 |
Summary | p. 51 |
Problems | p. 52 |
Analysis of State Space Models | p. 59 |
Solution of the Linear State Equation | p. 59 |
The Time Varying System | p. 59 |
The Time Invariant System | p. 64 |
Transfer Functions from State Space Models | p. 72 |
Natural Modes | p. 74 |
Discrete Time Models of Continuous Systems | p. 76 |
Solution of the Discrete Time State Equation | p. 82 |
The Time Invariant Discrete Time System | p. 83 |
Discrete Time Transfer Functions | p. 87 |
Similarity Transformations | p. 92 |
Stability | p. 101 |
Stability Criteria for Linear Systems | p. 104 |
Time Invariant Systems | p. 106 |
BIBO Stability | p. 114 |
Internal and External Stability | p. 115 |
Lyapunov's Method | p. 117 |
Controllability and Observability | p. 121 |
Controllability (Continuous Time Systems) | p. 124 |
Controllability and Similarity Transformations | p. 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 Transformations | p. 146 |
Observability (Discrete Time Systems) | p. 148 |
Duality | p. 150 |
Modal Decomposition | p. 150 |
Controllable/Reachable Subspace Decomposition | p. 154 |
Observable Subspace Decomposition | p. 157 |
Canonical Forms | p. 159 |
Controller Canonical Form | p. 159 |
Observer Canonical Form | p. 164 |
Duality for Canonical Forms | p. 167 |
Pole-zero Cancellation in SISO Systems | p. 168 |
Realizability | p. 169 |
Minimality | p. 173 |
Summary | p. 182 |
Notes | p. 183 |
Linear Systems Theory | p. 183 |
Problems | p. 186 |
Linear Control System Design | p. 193 |
Control System Design | p. 193 |
Controller Operating Modes | p. 196 |
Full State Feedback for Linear Systems | p. 199 |
State Feedback for SISO Systems | p. 208 |
Controller Design Based on the Controller Canonical Form | p. 208 |
Ackermann's Formula | p. 210 |
Conditions for Eigenvalue Assignment | p. 212 |
State Feedback for MIMO Systems | p. 226 |
Eigenstructure Assignment for MIMO Systems | p. 227 |
Dead Beat Regulators | p. 232 |
Integral Controllers | p. 234 |
Deterministic Observers and State Estimation | p. 251 |
Continuous Time Full Order Observers | p. 252 |
Discrete Time Full Order Observers | p. 255 |
Observer Design for SISO Systems | p. 256 |
Observer Design Based on the Observer Canonical Form | p. 256 |
Ackermann's Formula for the Observer | p. 259 |
Conditions for Eigenvalue Assignment | p. 264 |
Observer Design for MIMO Systems | p. 265 |
Eigenstructure Assignment for MIMO Observers | p. 266 |
Dead Beat Observers | p. 266 |
Reduced Order Observers | p. 267 |
State Feedback with Observers | p. 272 |
Combining Observers and State Feedback | p. 273 |
State Feedback with Integral Controller and Observer | p. 277 |
State Feedback with Reduced Order Observer | p. 284 |
Summary | p. 286 |
Notes | p. 287 |
Background for Observers | p. 287 |
Problems | p. 287 |
Optimal Control | p. 293 |
Introduction to Optimal Control | p. 293 |
The General Optimal Control Problem | p. 294 |
The Basis of Optimal Control - Calculus of Variations | p. 296 |
The Linear Quadratic Regulator | p. 304 |
The Quadratic Cost Function | p. 305 |
Linear Quadratic Control | p. 307 |
Steady State Linear Quadratic Regulator | p. 316 |
Robustness of LQR Control | p. 324 |
LQR Design: Eigenstructure Assignment Approach | p. 325 |
Discrete Time Optimal Control | p. 328 |
Discretization of the Performance Index | p. 329 |
Discrete Time State Feedback | p. 330 |
Steady State Discrete Optimal Control | p. 332 |
Summary | p. 339 |
Notes | p. 340 |
The Calculus of Variations | p. 340 |
Problems | p. 342 |
Noise in Dynamic Systems | p. 351 |
Introduction | p. 351 |
Random Variables | p. 353 |
Expectation (Average) Values of a Random Variable | p. 357 |
Average Value of Discrete Random Variables | p. 361 |
Characteristic Functions | p. 362 |
Joint Probability Distribution and Density Functions | p. 366 |
Random Processes | p. 371 |
Random Processes | p. 371 |
Moments of a Stochastic Process | p. 375 |
Stationary Processes | p. 378 |
Ergodic Processes | p. 380 |
Independent Increment Stochastic Processes | p. 382 |
Noise Propagation: Frequency and Time Domains | p. 392 |
Continuous Random Processes: Time Domain | p. 394 |
Continuous Random Processes: Frequency Domain | p. 397 |
Continuous Random Processes: Time Domain | p. 402 |
Inserting Noise into Simulation Systems | p. 408 |
Discrete Time Stochastic Processes | p. 412 |
Translating Continuous Noise into Discrete Time Systems | p. 414 |
Discrete Random Processes: Frequency Domain | p. 416 |
Discrete Random Processes: Running in Time | p. 420 |
Summary | p. 422 |
Notes | p. 423 |
The Normal Distribution | p. 423 |
The Wiener Process | p. 423 |
Stochastic Differential Equations | p. 424 |
Problems | p. 425 |
Optimal Observers: Kalman Filters | p. 431 |
Introduction | p. 431 |
Continuous Kalman Filter | p. 432 |
Block Diagram of a CKF | p. 436 |
Innovation Process | p. 446 |
Discrete Kalman Filter | p. 449 |
A Real Time Discrete Kalman Filter (Open Form) | p. 449 |
Block Diagram of an Open Form DKF | p. 453 |
Closed Form of a DKF | p. 456 |
Discrete and Continuous Kalman Filter Equivalence | p. 461 |
Stochastic Integral Quadratic Forms | p. 464 |
Separation Theorem | p. 466 |
Evaluation of the Continuous LQG Index | p. 469 |
Evaluation of the Discrete LQG Index | p. 475 |
Summary | p. 476 |
Notes | p. 478 |
Background for Kalman Filtering | p. 478 |
Problems | p. 479 |
Static Optimization | p. 493 |
Optimization Basics | p. 493 |
Constrained Static Optimization | p. 496 |
Problems | p. 498 |
Linear Algebra | p. 501 |
Matrix Basics | p. 501 |
Eigenvalues and Eigenvectors | p. 503 |
Partitioned Matrices | p. 506 |
Quadratic Forms | p. 507 |
Matrix Calculus | p. 509 |
Continuous Riccati Equation | p. 511 |
Estimator Riccati Equation | p. 511 |
Time Axis Reversal | p. 511 |
Using the LQR Solution | p. 512 |
Discrete Time SISO Systems | p. 515 |
Introduction | p. 515 |
The Sampling Process | p. 516 |
The Z-Transform | p. 521 |
Inverse Z-Transform | p. 524 |
Discrete Transfer Functions | p. 526 |
Discrete Systems and Difference Equations | p. 528 |
Discrete Time Systems with Zero-Order-Hold | p. 528 |
Transient Response, Poles and Stability | p. 529 |
Frequency Response | p. 532 |
Discrete Approximations to Continuous Transfer Functions | p. 534 |
Tustin Approximation | p. 535 |
Matched-Pole-Zero Approximation (MPZ) | p. 536 |
Discrete Equivalents to Continuous Controllers | p. 539 |
Choice of Sampling Period | p. 545 |
References | p. 547 |
Index | p. 549 |
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