Preface p. xi Chapter 1 Feedback Control p. 1 The Mechanism of Feedback p. 1 Feedback Control Engineering p. 6 Control Theory Background p. 8 Scope and Organization of This Book p. 10 Notes p. 12 References p. 13 Chapter 2 State-Space Representation of Dynamic Systems p. 14 Mathematical Models p. 14 Physical Notion of System State p. 16 Block-Diagram Representations p. 25 Lagrange's Equations p. 29 Rigid Body Dynamics p. 33 Aerodynamics p. 40 Chemical and Energy Processes p. 45 Problems p. 52 Notes p. 55 References p. 56 Chapter 3 Dynamics of Linear Systems p. 58 Differential Equations Revisited p. 58 Solution of Linear Differential Equations in State-Space Form p. 59 Interpretation and Properties of the State-Transition Matrix p. 65 Solution by the Laplace Transform: The Resolvent p. 68 Input-Output Relations: Transfer Functions p. 75 Transformation of State Variables p. 84 State-Space Representation of Transfer Functions: Canonical Forms p. 88 Problems p. 107 Notes p. 109 References p. 111 Chapter 4 Frequency-Domain Analysis p. 112 Status of Frequency-Domain Methods p. 112 Frequency-Domain Characterization of Dynamic Behavior p. 113 Block-Diagram Algebra p. 116 Stability p. 124 Routh-Hurwitz Stability Algorithms p. 128 Graphical Methods p. 133 Steady State Responses: System Type p. 156 Dynamic Response: Bandwidth p. 161 Robustness and Stability (Gain and Phase) Margins p. 169 Multivariable Systems: Nyquist Diagram and Singular Values p. 174 Problems p. 184 Notes p. 187 References p. 189 Chapter 5 Controllability and Observability p. 190 Introduction p. 190 Where Do Uncontrollable or Unobservable Systems Arise? p. 194 Definitions and Conditions for Controllability and Observability p. 203 Algebraic Conditions for Controllability and Observability p. 209 Disturbances and Tracking Systems: Exogenous Variables p. 216 Problems p. 218 Notes p. 219 References p. 221 Chapter 6 Shaping the Dynamic Response p. 222 Introduction p. 222 Design of Regulators for Single-Input, Single-Output Systems p. 224 Multiple-Input Systems p. 234 Disturbances and Tracking Systems: Exogenous Variables p. 236 Where Should the Closed-Loop Poles Be Placed? p. 243 Problems p. 254 Notes p. 257 References p. 258 Chapter 7 Linear Observers p. 259 The Need for Observers p. 259 Structure and Properties of Observers p. 260 Pole-Placement for Single-Output Systems p. 263 Disturbances and Tracking Systems: Exogenous Variables p. 267 Reduced-Order Observers p. 276 Problems p. 287 Notes p. 288 References p. 289 Chapter 8 Compensator Design by the Separation Principle p. 290 The Separation Principle p. 290 Compensators Designed Using Full-Order Observers p. 291 Reduced-Order Observers p. 298 Robustness: Effects of Modeling Errors p. 301 Disturbances and Tracking Systems: Exogenous Variables p. 310 Selecting Observer Dynamics: Robust Observers p. 314 Summary of Design Process p. 326 Problems p. 332 Notes p. 335 References p. 336 Chapter 9 Linear, Quadratic Optimum Control p. 337 Why Optimum Control? p. 337 Formulation of the Optimum Control Problem p. 338 Quadratic Integrals and Matrix Differential Equations p. 341 The Optimum Gain Matrix p. 343 The Steady State Solution p. 345 Disturbances and Reference Inputs: Exogenous Variables p. 350 General Performance Integral p. 364 Weighting of Performance at Terminal Time p. 365 Problems p. 369 Notes p. 375 Chapter 10 References p. 377 Random Processes p. 378 Introduction p. 378 Conceptual Models for Random Processes p. 379 Statistical Characteristics of Random Processes p. 381 Power Spectral Density Function p. 384 White Noise and Linear System Response p. 386 Spectral Factorization p. 393 Systems with State-Space Representation p. 396 The Wiener Process and Other Integrals of Stationary Processes p. 404 Problems p. 407 Notes p. 408 References p. 409 Chapter 11 Kalman Filters: Optimum Observers p. 411 Background p. 411 The Kalman Filter is an Observer p. 412 Kalman Filter Gain and Variance Equations p. 414 Steady State Kalman Filter p. 417 The "Innovations" Process p. 425 Reduced-Order Filters and Correlated Noise p. 427 Stochastic Control: The Separation Theorem p. 442 Choosing Noise for Robust Control p. 455 Problems p. 461 Notes p. 468 References p. 469 Appendix Matrix Algebra and Analysis p. 471 Bibliography p. 498 Index of Applications p. 503 Index p. 506