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E-raamat: Algebraic Identification and Estimation Methods in Feedback Control Systems

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Algebraic Identification and Estimation Methods in Feedback Control SystemsSuurem pilt
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"Algebraic Identification and Estimation Methods in Feedback Control Systems presents the model-based algebraic approach to on-line parameter and state estimation in uncertain dynamic feedback control systems"--

"Presents a model-based algebraic approach to on-line parameter and state estimation in uncertain dynamic feedback control systemsAlgebraic Identification and Estimation Methods in Feedback Control Systems presents the model-based algebraic approach to on-line parameter and state estimation in uncertain dynamic feedback control systems. This approach evades the mathematical intricacies of the traditional stochastic approach, proposing a direct model-based scheme with several, easy to implement, computational advantages. This book contains many illustrative, tutorial style, developed examples of the recently introduced algebraic approach for parameter and state estimation in a variety of physical systems of continuous, and discrete, nature. The developments include some laboratory experimental results in several areas related to mechatronics systems. The reader, with an engineering level mathematical background and through the many expository examples, will be able to master the use and understand the consequences of the highly theoretical differential algebraic viewpoint in control systems theory"--

Algebraic Identification and Estimation Methods in Feedback Control Systems presents a model-based algebraic approach to online parameter and state estimation in uncertain dynamic feedback control systems. This approach evades the mathematical intricacies of the traditional stochastic approach, proposing a direct model-based scheme with several easy-to-implement computational advantages. The approach can be used with continuous and discrete, linear and nonlinear, mono-variable and multi-variable systems. The estimators based on this approach are not of asymptotic nature, and do not require any statistical knowledge of the corrupting noises to achieve good performance in a noisy environment. These estimators are fast, robust to structured perturbations, and easy to combine with classical or sophisticated control laws.

This book uses module theory, differential algebra, and operational calculus in an easy-to-understand manner and also details how to apply these in the context of feedback control systems. A wide variety of examples, including mechanical systems, power converters, electric motors, and chaotic systems, are also included to illustrate the algebraic methodology.

Key features:

  • Presents a radically new approach to online parameter and state estimation.
  • Enables the reader to master the use and understand the consequences of the highly theoretical differential algebraic viewpoint in control systems theory.
  • Includes examples in a variety of physical applications with experimental results.
  • Covers the latest developments and applications.

Algebraic Identification and Estimation Methods in Feedback Control Systems is a comprehensive reference for researchers and practitioners working in the area of automatic control, and is also a useful source of information for graduate and undergraduate students.

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 Identification
4(1)
1.4 The State Estimation Problem
5(3)
1.4.1 Observers
6(1)
1.4.2 Reconstructing the State via Time Derivative Estimation
7(1)
1.5 Algebraic Methods in Control Theory: Differences from Existing Methodologies
8(1)
1.6 Outline of the Book
9(6)
References
12(3)
2 Algebraic Parameter Identification in Linear Systems
15(56)
2.1 Introduction
15(2)
2.1.1 The Parameter-Estimation Problem in Linear Systems
16(1)
2.2 Introductory Examples
17(36)
2.2.1 Dragging an Unknown Mass in Open Loop
17(7)
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 gain motor
47(3)
2.2.9 Identifying Classical Controller Parameters
50(3)
2.3 A Case Study Introducing a "Sentinel" Criterion
53(14)
2.3.1 A Suspension System Model
54(13)
2.4 Remarks
67(4)
References
68(3)
3 Algebraic Parameter Identification in Nonlinear Systems
71(74)
3.1 Introduction
71(1)
3.2 Algebraic Parameter Identification for Nonlinear Systems
72(33)
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 Sliding Motions
90(2)
3.2.5 Control of an Uncertain Inverted Pendulum Driven by a DC Motor
92(4)
3.2.6 Identification and Control of a Convey Crane
96(7)
3.2.7 Identification of a Magnetic Levitation System
103(2)
3.3 An Alternative Construction of the System of Linear Equations
105(36)
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 Uncertain Brushless DC Motor
112(7)
3.3.4 Parameter Identification and Self-tuned Control for the Inertia Wheel Pendulum
119(9)
3.3.5 Algebraic Parameter Identification for Induction Motors
128(8)
3.3.6 A Criterion to Determine the Estimator Convergence: The Error Index
136(5)
3.4 Remarks
141(4)
References
141(4)
4 Algebraic Parameter Identification in Discrete-Time Systems
145(46)
4.1 Introduction
145(1)
4.2 Algebraic Parameter Identification in Discrete-Time Systems
145(15)
4.2.1 Main Purpose of the
Chapter
146(1)
4.2.2 Problem Formulation and Assumptions
147(1)
4.2.3 An Introductory Example
148(2)
4.2.4 Samuelson's Model of the National Economy
150(5)
4.2.5 Heating of a Slab from Two Boundary Points
155(2)
4.2.6 An Exact Backward Shift Reconstructor
157(3)
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 Rolling Mill
170(5)
4.3.5 Algebraic Frequency Identification of a Sinusoidal Signal by Means of Exact Discretization
175(3)
4.4 Algebraic Identification in Fast-Sampled Linear Systems
178(10)
4.4.1 The Delta-Operator Approach: A Theoretical Framework
179(2)
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 Systems
191(54)
5.1 Introduction
191(2)
5.1.1 Signal Time Derivation Through the "Algebraic Derivative Method"
192(1)
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 Third-Order System
201(2)
5.2.5 A Sinusoid Estimation Problem
203(2)
5.2.6 Identification of Gravitational Wave Parameters
205(5)
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 Plotter
218(4)
5.3 Recovering Chaotically Encrypted Signals
222(19)
5.3.1 State Estimation for a Lorenz System
227(2)
5.3.2 State Estimation for Chen's System
229(2)
5.3.3 State Estimation for Chua's Circuit
231(1)
5.3.4 State Estimation for Rossler's System
232(2)
5.3.5 State Estimation for the Hysteretic Circuit
234(5)
5.3.6 Simultaneous Chaotic Encoding---Decoding with Singularity Avoidance
239(1)
5.3.7 Discussion
240(1)
5.4 Remarks
241(4)
References
242(3)
6 Control of Nonlinear Systems via Output Feedback
245(36)
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 Nonlinear System
261(6)
6.3.3 Experimental Results on a Mechanical System
267(11)
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 Controller
285(2)
7.1.3 A Sensorless Scheme Based on Fast Adaptive Observation
287(5)
7.1.4 Control of the Boost Converter
292(6)
7.2 Alternative Elimination of Initial Conditions
298(6)
7.2.1 A Bounded Exponential Function
299(1)
7.2.2 Correspondence in the Frequency Domain
300(1)
7.2.3 A System of Second Order
301(3)
7.3 Other Functions of Time for Parameter Estimation
304(14)
7.3.1 A Mechanical System Example
304(6)
7.3.2 A Derivative Approach to Demodulation
310(2)
7.3.3 Time Derivatives via Parameter Identification
312(2)
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 Continuous Systems: A Module Approach
329(10)
A.1 Generalities on Linear Systems Identification
329(10)
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 Discrete Systems: A Module Approach
339(10)
B.1 A Short Review of Module Theory over Principal Ideal Rings
339(10)
B.1.1 Systems
340(1)
B.1.2 Perturbations
340(1)
B.1.3 Dynamics and Input---Output Systems
341(1)
B.1.4 Transfer Matrices
341(1)
B.1.5 Identifiability
342(1)
B.1.6 An Algebraic Setting for Identifiability
342(2)
B.1.7 Linear identifiability of transfer functions
344(1)
B.1.8 Linear Identification of Perturbed Systems
345(2)
B.1.9 Persistent Trajectories
347(1)
References
348(1)
Appendix C Simultaneous State and Parameter Estimation: An Algebraic Approach
349(8)
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 Control
357(12)
D.1 Generalities on GPI Control
357(8)
D.2 Generalization to MIMO Linear Systems
365(4)
References
368(1)
Index 369
H. Sira-Ramírez obtained an Electrical Engineers degree from the Universidad de Los Andes in Mérida (Venezuela) in 1970; an MSc in Electrical Engineering and an Electrical Engineers degree in 1974, and a PhD in Electrical Engineering in 1977, all from the Massachusetts Institute of Technology (Cambridge, MA). Dr. Sira-Ramírez worked for 28 years at the Universidad de Los Andes, becoming an Emeritus Professor. Currently, he is a Titular Researcher in the Centro de Investigación y Estudios Avanzados del Instituto Politécnico Nacional (Cinvestav-IPN) in Mexico City, Mexico. He is a co-author of five books on automatic control, and the author of over 460 technical articles in book chapters, credited journals, and international conferences. Dr. Sira-Ramírez is interested in the theoretical and practical aspects of feedback regulation of nonlinear systems, with special emphasis on variable structure feedback control, algebraic methods in automatic control, power electronics, and active disturbance rejection control.

C. García-Rodríguez received a B.Eng. degree from the Technological Institute of Veracruz, Veracruz, Mexico in 2002, and Masters and Doctor of Science degrees from the Center for Research and Advanced Studies of the National Polytechnic Institute, Cinvestav-IPN, Mexico in 2005 and 2011, respectively, all in Electrical Engineering. He was with the Technological Institute for Higher Studies of Ecatepec, Edo. de México, in 2005. Since 2010, he has been a Professor at the Electronic and Mechatronic Institute, Technological University of Mixteca, Oaxaca, Mexico. He is currently also Coordinator of the Masters Program in Electronics with Option in Applied Intelligent Systems of this university. Dr. García-Rodríguez is a candidate member of the National System of Researchers and a member of the CONACYT Registry of Accredited Evaluators. His current research and teaching interests include control of electrical machines, power converters for variable-speed systems, power electronics, robust control, and algebraic identification.

A. Luviano Juárez received a BS degree in Mechatronics Engineering from the National Polytechnic Institute (Mexico), an MSc in Automatic Control from the Department of Automatic Control at the Center of Research and Advanced Studies of the National Polytechnic Institute (Cinvestav-IPN), and a PhD in Electrical Engineering from the Electrical Engineering Department at Cinvestav -IPN. Currently, he is a Professor at the National Polytechnic Institute UPIITA in the Research and Postgraduate Section. His teaching and research interests include control of mechatronic systems, algebraic methods in estimation, identification and control, robotics, and related subjects.

John Cortés-Romero, PhD is a Research Associate Professor in the Department of Electrical and Electronic Engineering at the National University of Colombia. During his tenure at the NationalUniversity, Professor Cortés-Romero served as the coordinator of the Industrial Automation Masters program. Professor Cortés-Romero received his BS in Electrical Engineering, MSc in Industrial Automation, and MSc in Mathematics from the National University of Colombia in 1995, 1999, and 2007, respectively. In 2007, he was selected for the prestigious OAS fellowship program and earned his PhD in Electrical Engineering from the Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional (CINVESTAV-IPN), Mexico City, Mexico in 2011. He is the author of over 40 technical papers in journals and international conference proceedings. His main research areas include nonlinear control applications, active disturbance rejection control, algebraic identification and estimation methods in feedback control systems, and supervisory control of industrial processes.
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