Control Theory: Multivariable and Nonlinear Methods

 Content: 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.