Algebraic Identification and Estimation Methods in FeedbackControl Systems presents a model-based algebraic approach toonline parameter and state estimation in uncertain dynamic feedbackcontrol systems. This approach evades the mathematical intricaciesof the traditional stochastic approach, proposing a directmodel-based scheme with several easy-to-implement computationaladvantages. The approach can be used with continuous and discrete,linear and nonlinear, mono-variable and multi-variable systems. Theestimators based on this approach are not of asymptotic nature, anddo not require any statistical knowledge of the corrupting noisesto achieve good performance in a noisy environment. Theseestimators are fast, robust to structured perturbations, and easyto combine with classical or sophisticated control laws. This book uses module theory, differential algebra, andoperational calculus in an easy-to-understand manner and alsodetails how to apply these in the context of feedback controlsystems. A wide variety of examples, including mechanical systems,power converters, electric motors, and chaotic systems, are alsoincluded to illustrate the algebraic methodology. Key features: * Presents a radically new approach to online parameter and stateestimation. * Enables the reader to master the use and understand theconsequences of the highly theoretical differential algebraicviewpoint in control systems theory. * Includes examples in a variety of physical applications withexperimental results. * Covers the latest developments and applications. Algebraic Identification and Estimation Methods in FeedbackControl Systems is a comprehensive reference for researchersand practitioners working in the area of automatic control, and isalso a useful source of information for graduate and undergraduatestudents.
Series Preface xiii
Preface xv
1 Introduction 1 (14)
1.1 Feedback Control of Dynamic Systems 2 (1)
1.1.1 Feedback 2 (1)
1.1.2 Why Do We Need Feedback? 3 (1)
1.2 The Parameter Identification Problem 3 (1)
1.2.1 Identifying a System 4 (1)
1.3 A Brief Survey on Parameter 4 (1)
Identification
1.4 The State Estimation Problem 5 (3)
1.4.1 Observers 6 (1)
1.4.2 Reconstructing the State via Time 7 (1)
Derivative Estimation
1.5 Algebraic Methods in Control Theory: 8 (1)
Differences from Existing Methodologies
1.6 Outline of the Book 9 (6)
References 12 (3)
2 Algebraic Parameter Identification in 15 (56)
Linear Systems
2.1 Introduction 15 (2)
2.1.1 The Parameter-Estimation Problem 16 (1)
in Linear Systems
2.2 Introductory Examples 17 (36)
2.2.1 Dragging an Unknown Mass in Open 17 (7)
Loop
2.2.2 A Perturbed First-Order System 24 (6)
2.2.3 The Visual Servoing Problem 30 (5)
2.2.4 Balancing of the Plane Rotor 35 (3)
2.2.5 On the Control of the Linear Motor 38 (4)
2.2.6 Double-Bridge Buck Converter 42 (1)
2.2.7 Closed-Loop Behavior 43 (4)
2.2.8 Control of an unknown variable 47 (3)
gain motor
2.2.9 Identifying Classical Controller 50 (3)
Parameters
2.3 A Case Study Introducing a "Sentinel" 53 (14)
Criterion
2.3.1 A Suspension System Model 54 (13)
2.4 Remarks 67 (4)
References 68 (3)
3 Algebraic Parameter Identification in 71 (74)
Nonlinear Systems
3.1 Introduction 71 (1)
3.2 Algebraic Parameter Identification 72 (33)
for Nonlinear Systems
3.2.1 Controlling an Uncertain Pendulum 74 (6)
3.2.2 A Block-Driving Problem 80 (4)
3.2.3 The Fully Actuated Rigid Body 84 (6)
3.2.4 Parameter Identification Under 90 (2)
Sliding Motions
3.2.5 Control of an Uncertain Inverted 92 (4)
Pendulum Driven by a DC Motor
3.2.6 Identification and Control of a 96 (7)
Convey Crane
3.2.7 Identification of a Magnetic 103 (2)
Levitation System
3.3 An Alternative Construction of the 105 (36)
System of Linear Equations
3.3.1 Genesio--Tesi Chaotic System 107 (1)
3.3.2 The Ueda Oscillator 108 (4)
3.3.3 Identification and Control of an 112 (7)
Uncertain Brushless DC Motor
3.3.4 Parameter Identification and 119 (9)
Self-tuned Control for the Inertia
Wheel Pendulum
3.3.5 Algebraic Parameter 128 (8)
Identification for Induction Motors
3.3.6 A Criterion to Determine the 136 (5)
Estimator Convergence: The Error Index
3.4 Remarks 141 (4)
References 141 (4)
4 Algebraic Parameter Identification in 145 (46)
Discrete-Time Systems
4.1 Introduction 145 (1)
4.2 Algebraic Parameter Identification in 145 (15)
Discrete-Time Systems
4.2.1 Main Purpose of the Chapter 146 (1)
4.2.2 Problem Formulation and 147 (1)
Assumptions
4.2.3 An Introductory Example 148 (2)
4.2.4 Samuelson's Model of the National 150 (5)
Economy
4.2.5 Heating of a Slab from Two 155 (2)
Boundary Points
4.2.6 An Exact Backward Shift 157 (3)
Reconstructor
4.3 A Nonlinear Filtering Scheme 160 (18)
4.3.1 Henon System 161 (3)
4.3.2 A Hard Disk Drive 164 (2)
4.3.3 The Visual Servo Tracking Problem 166 (4)
4.3.4 A Shape Control Problem in a 170 (5)
Rolling Mill
4.3.5 Algebraic Frequency 175 (3)
Identification of a Sinusoidal Signal
by Means of Exact Discretization
4.4 Algebraic Identification in 178 (10)
Fast-Sampled Linear Systems
4.4.1 The Delta-Operator Approach: A 179 (2)
Theoretical Framework
4.4.2 Delta-Transform Properties 181 (1)
4.4.3 A DC Motor Example 181 (7)
4.5 Remarks 188 (3)
References 188 (3)
5 State and Parameter Estimation in Linear 191 (54)
Systems
5.1 Introduction 191 (2)
5.1.1 Signal Time Derivation Through 192 (1)
the "Algebraic Derivative Method"
5.1.2 Observability of Nonlinear Systems 192 (1)
5.2 Fast State Estimation 193 (29)
5.2.1 An Elementary Second-Order Example 193 (1)
5.2.2 An Elementary Third-Order Example 194 (4)
5.2.3 A Control System Example 198 (3)
5.2.4 Control of a Perturbed 201 (2)
Third-Order System
5.2.5 A Sinusoid Estimation Problem 203 (2)
5.2.6 Identification of Gravitational 205 (5)
Wave Parameters
5.2.7 A Power Electronics Example 210 (3)
5.2.8 A Hydraulic Press 213 (5)
5.2.9 Identification and Control of a 218 (4)
Plotter
5.3 Recovering Chaotically Encrypted 222 (19)
Signals
5.3.1 State Estimation for a Lorenz 227 (2)
System
5.3.2 State Estimation for Chen's System 229 (2)
5.3.3 State Estimation for Chua's 231 (1)
Circuit
5.3.4 State Estimation for Rossler's 232 (2)
System
5.3.5 State Estimation for the 234 (5)
Hysteretic Circuit
5.3.6 Simultaneous Chaotic 239 (1)
Encoding---Decoding with Singularity
Avoidance
5.3.7 Discussion 240 (1)
5.4 Remarks 241 (4)
References 242 (3)
6 Control of Nonlinear Systems via Output 245 (36)
Feedback
6.1 Introduction 245 (1)
6.2 Time-Derivative Calculations 246 (9)
6.2.1 An Introductory Example 247 (6)
6.2.2 Identifying a Switching Input 253 (2)
6.3 The Nonlinear Systems Case 255 (23)
6.3.1 Control of a Synchronous Generator 256 (5)
6.3.2 Control of a Multi-variable 261 (6)
Nonlinear System
6.3.3 Experimental Results on a 267 (11)
Mechanical System
6.4 Remarks 278 (3)
References 279 (2)
7 Miscellaneous Applications 281 (48)
7.1 Introduction 281 (17)
7.1.1 The Separately Excited DC Motor 282 (3)
7.1.2 Justification of the ETEDPOF 285 (2)
Controller
7.1.3 A Sensorless Scheme Based on Fast 287 (5)
Adaptive Observation
7.1.4 Control of the Boost Converter 292 (6)
7.2 Alternative Elimination of Initial 298 (6)
Conditions
7.2.1 A Bounded Exponential Function 299 (1)
7.2.2 Correspondence in the Frequency 300 (1)
Domain
7.2.3 A System of Second Order 301 (3)
7.3 Other Functions of Time for Parameter 304 (14)
Estimation
7.3.1 A Mechanical System Example 304 (6)
7.3.2 A Derivative Approach to 310 (2)
Demodulation
7.3.3 Time Derivatives via Parameter 312 (2)
Identification
7.3.4 Example 314 (4)
7.4 An Algebraic Denoising Scheme 318 (7)
7.4.1 Example 321 (1)
7.4.2 Numerical Results 322 (3)
7.5 Remarks 325 (4)
References 326 (3)
Appendix A Parameter Identification in Linear 329 (10)
Continuous Systems: A Module Approach
A.1 Generalities on Linear Systems 329 (10)
Identification
A.1.1 Example 330 (1)
A.1.2 Some Definitions and Results 330 (1)
A.1.3 Linear Identifiability 331 (2)
A.1.4 Structured Perturbations 333 (4)
A.1.5 The Frequency Domain Alternative 337 (1)
References 338 (1)
Appendix B Parameter Identification in Linear 339 (10)
Discrete Systems: A Module Approach
B.1 A Short Review of Module Theory over 339 (10)
Principal Ideal Rings
B.1.1 Systems 340 (1)
B.1.2 Perturbations 340 (1)
B.1.3 Dynamics and Input---Output 341 (1)
Systems
B.1.4 Transfer Matrices 341 (1)
B.1.5 Identifiability 342 (1)
B.1.6 An Algebraic Setting for 342 (2)
Identifiability
B.1.7 Linear identifiability of 344 (1)
transfer functions
B.1.8 Linear Identification of 345 (2)
Perturbed Systems
B.1.9 Persistent Trajectories 347 (1)
References 348 (1)
Appendix C Simultaneous State and Parameter 349 (8)
Estimation: An Algebraic Approach
C.1 Rings, Fields and Extensions 349 (1)
C.2 Nonlinear Systems 350 (3)
C.2.1 Differential Flatness 351 (1)
C.2.2 Observability and Identifiability 352 (1)
C.2.3 Observability 352 (1)
C.2.4 Identifiable Parameters 352 (1)
C.2.5 Determinable Variables 352 (1)
C.3 Numerical Differentiation 353 (4)
C.3.1 Polynomial Time Signals 353 (1)
C.3.2 Analytic Time Signals 353 (1)
C.3.3 Noisy Signals 354 (1)
References 354 (3)
Appendix D Generalized Proportional Integral 357 (12)
Control
D.1 Generalities on GPI Control 357 (8)
D.2 Generalization to MIMO Linear Systems 365 (4)
References 368 (1)
Index 369
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