Robust Systems Theory and Applications

by ;
Edition: 1st
Format: Hardcover
Pub. Date: 1998-08-17
Publisher(s): Wiley-Interscience
List Price: $247.45

Buy New

Usually Ships in 8 - 10 Business Days.
$235.67

Rent Textbook

Select for Price
There was a problem. Please try again later.

Used Textbook

We're Sorry
Sold Out

eTextbook

We're Sorry
Not Available

How Marketplace Works:

  • This item is offered by an independent seller and not shipped from our warehouse
  • Item details like edition and cover design may differ from our description; see seller's comments before ordering.
  • Sellers much confirm and ship within two business days; otherwise, the order will be cancelled and refunded.
  • Marketplace purchases cannot be returned to eCampus.com. Contact the seller directly for inquiries; if no response within two days, contact customer service.
  • Additional shipping costs apply to Marketplace purchases. Review shipping costs at checkout.

Summary

A complete, up-to-date textbook on an increasingly important subjectRobust Systems Theory and Applications covers both the techniques used in linear robust control analysis/synthesis and in robust (control-oriented) identification. The main analysis and design methods are complemented by elaborated examples and a group of worked-out applications that stress specific practical issues: nonlinearities, robustness against changes in operating conditions, uncertain infinite dimensional plants, and actuator and sensor limitations. Designed expressly as a textbook for master's and first-year PhD students, this volume: Introduces basic robustness concepts in the context of SISO systems described by Laplace transforms, establishing connections with well-known classical control techniques Presents the internal stabilization problem from two different points of view: algebraic and state -space Introduces the four basic problems in robust control and the Loop shaping design method Presents the optimal *2 control problem from a different viewpoint, including an analysis of the robustness properties of *2 controllers and a treatment of the generalized *2 problem Presents the *2 control problem using both the state-space approach developed in the late 1980s and a Linear Matrix Inequality approach (developed in the mid 1990s) that encompasses more general problems Discusses more general types of uncertainties (parametric and mixed type) and A?A?-synthesis as a design tool Presents an overview of optimal ,1 control theory and covers the fundamentals of its star-norm approximation Presents the basic tools of model order reduction Provides a tutorial on robust identification Offers numerous end-of-chapter problems and worked-out examples of robust control

Author Biography

RICARDO S. S-NCHEZ-PE-A, MSEE, PhD, is a researcher at the National Commission of Space Activities (CONAE) and Professor of Control Systems at the School of Engineering at the University of Buenos Aires, Argentina. MARIO SZNAIER, MSEE, PhD, is an Associate Professor in the Department of Electrical Engineering at Pennsylvania State University, University Park, USA.

Table of Contents

1 Introduction
1(22)
1.1 General Control Problem
1(10)
1.1.1 Experimental Phase
2(1)
1.1.2 Simulation Phase
3(2)
1.1.3 Theoretical Phase
5(6)
1.2 Why Feedback?
11(3)
1.3 Feedback Loop Trade-off
14(3)
1.4 Objectives of an Applied Theory
17(2)
1.5 Objectives of This Book
19(4)
1.5.1 General Remarks
19(1)
1.5.2 Scope
19(2)
1.5.3 How to Use This Book
21(2)
2 SISO Systems
23(38)
2.1 Introduction
23(1)
2.2 Well Posedness
24(2)
2.3 Nominal Internal Stability
26(3)
2.4 Robust Stability
29(13)
2.4.1 Phase and Gain Margins
29(3)
2.4.2 Global Dynamic Uncertainty
32(10)
2.5 Nominal Performance
42(8)
2.5.1 Known Disturbance/Noise/Reference
42(2)
2.5.2 Bounded Disturbances at the Output
44(3)
2.5.3 Other Performance Criteria
47(3)
2.6 Robust Performance
50(5)
2.7 Extension to MIMO Systems
55(2)
2.8 Problems
57(4)
3 Stabilization
61(32)
3.1 Introduction
61(2)
3.2 Well Posedness and Internal Stability
63(2)
3.2.1 Well Posedness
63(1)
3.2.2 Internal Stability
64(1)
3.3 Open-Loop Stable Plants
65(3)
3.4 The General Case
68(10)
3.4.1 Special Problems
69(6)
3.4.2 The Output Feedback Case
75(3)
3.5 Controller Structure and Separation Principle
78(1)
3.6 Closed-Loop Mappings
79(1)
3.7 A Coprime Factorization Approach
80(8)
3.7.1 Coprime Factorizations
80(8)
3.8 LFTs and Stability
88(2)
3.9 Problems
90(3)
4 Loop Shaping
93(34)
4.1 Introduction
93(4)
4.2 Nominal Performance
97(1)
4.3 Robust Stability
98(1)
4.4 Nominal Performance and Robust Stability
99(1)
4.5 Robust Performance
100(5)
4.5.1 Sensor Uncertainty
101(1)
4.5.2 Actuator Uncertainty
102(3)
4.6 Design Procedure
105(4)
4.7 Examples
109(14)
4.7.1 Permanent Magnet Stepper Motor
109(10)
4.7.2 Loop Shaping Q(s)
119(4)
4.8 Related Design Procedures
123(2)
4.9 Problems
125(2)
5 H(2) Optimal Control
127(30)
5.1 Introduction
127(1)
5.2 The Classical Linear Quadratic Regulator Problem
128(5)
5.3 The Standard H(2) Problem
133(8)
5.4 Relaxing Some of the Assumptions
141(1)
5.5 Closed-Loop Properties
142(7)
5.5.1 The LQR Case: Kalman's Inequality
143(2)
5.5.2 Some Consequences of Kalman's Inequality
145(1)
5.5.3 Stability Margins of Optimal H(2) Controllers
146(3)
5.6 Related Problems
149(3)
5.7 Problems
152(5)
6 H(XXX) Control
157(50)
6.1 Introduction
157(1)
6.2 The Standard H(XXX) Problem
158(21)
6.2.1 Background: Hankel and Mixed Hankel-Toeplitz Operators
161(15)
6.2.2 Proof of Theorem 6.1
176(3)
6.3 Relaxing Some of the Assumptions
179(1)
6.4 LMI Approach to H(XXX) Control
180(12)
6.4.1 Characterization of All Output Feedback H(XXX) Controllers
183(5)
6.4.2 Connections with the DGKF Results
188(4)
6.5 Limiting Behavior
192(1)
6.6 The Youla Parametrization Approach
193(10)
6.7 Problems
203(4)
7 Structured Uncertainty
207(38)
7.1 Introduction
207(8)
7.1.1 Stability Margin
210(5)
7.2 Structured Dynamic Uncertainty
215(8)
7.2.1 Computation
215(4)
7.2.2 Analysis and Design
219(4)
7.3 Parametric Uncertainty
223(14)
7.3.1 Introduction
223(2)
7.3.2 Research Directions
225(5)
7.3.3 Kharitonov's Theorem
230(3)
7.3.4 Mapping Theorem
233(4)
7.4 Mixed Type Uncertainty
237(5)
7.4.1 Introduction
237(2)
7.4.2 Mixed Mu
239(3)
7.5 Problems
242(3)
8 L(1) Control
245(48)
8.1 Introduction
245(2)
8.2 Robust Stability Revisited
247(7)
8.2.1 Robust Stability Under LTV Perturbations
250(3)
8.2.2 Stability Under Time Invariant Perturbations
253(1)
8.3 A Solution to the SISO l(1) Control Problem
254(13)
8.3.1 Properties of the Solution
262(4)
8.3.2 The MIMO Case
266(1)
8.4 Approximate Solutions
267(15)
8.4.1 An Upper Bound of the l(1) Norm
268(1)
8.4.2 The * Norm
269(4)
8.4.3 Full State Feedback
273(3)
8.4.4 All Output Feedback Controllers for Optimal *-Norm Problems
276(6)
8.5 The Continuous Time Case
282(6)
8.5.1 Solution Via Duality
282(3)
8.5.2 Rational Approximations to the Optimal l(1) Controller
285(3)
8.6 Problems
288(5)
9 Model Order Reduction
293(30)
9.1 Introduction
293(2)
9.2 Geometry of State-Space Realizations
295(9)
9.2.1 Controllable/ Unobservable Spaces
295(2)
9.2.2 Principal Components
297(7)
9.3 Hankel Singular Values
304(6)
9.3.1 Continuous Systems
304(2)
9.3.2 Discrete Systems
306(4)
9.4 Model Reduction
310(8)
9.4.1 Introduction
310(1)
9.4.2 Hankel Operator Reduction
310(2)
9.4.3 Balanced Realizations
312(2)
9.4.4 Balanced Truncation
314(4)
9.5 Algorithms
318(3)
9.5.1 Approximation Error
319(2)
9.6 Problems
321(2)
10 Robust Identification
323(54)
10.1 Introduction
323(1)
10.2 General Setup
324(15)
10.2.1 Input Data
325(1)
10.2.2 Consistency
326(2)
10.2.3 Identification Error
328(6)
10.2.4 Convergence
334(4)
10.2.5 Validation
338(1)
10.3 Frequency-Domain Identification
339(22)
10.3.1 Preliminaries
340(2)
10.3.2 Sampling Procedure
342(2)
10.3.3 Consistency
344(2)
10.3.4 Identification Procedures
346(15)
10.4 Time-Domain Identification
361(11)
10.4.1 Preliminaries
362(4)
10.4.2 Identification Procedures
366(6)
10.5 Further Research Topics
372(5)
10.5.1 Unstable Systems
372(1)
10.5.2 Nonuniformly Spaced Experimental Points
372(1)
10.5.3 Model Reduction
373(1)
10.5.4 Continuous Time Plants
373(1)
10.5.5 Sample Complexity
373(1)
10.5.6 Mixed Time/ Frequency Experiments
374(1)
10.5.7 Mixed Parametric/Nonparametric Models
374(3)
11 Application Examples
377(50)
11.1 SAC-C Attitude Control Analysis
377(12)
11.1.1 Introduction
377(1)
11.1.2 Linear Model
378(3)
11.1.3 Design Constraints
381(2)
11.1.4 Robustness Analysis
383(2)
11.1.5 Simulations
385(4)
11.2 Controller Design for a D(2)O Plant
389(11)
11.2.1 Model of the Plant
389(2)
11.2.2 Robustness Analysis
391(6)
11.2.3 Controller Design
397(3)
11.3 X-29 Parametric Analysis
400(7)
11.3.1 Linear Model
400(5)
11.3.2 Results
405(2)
11.4 Control of a DC-to-DC Resonant Converter
407(20)
11.4.1 Introduction
407(1)
11.4.2 The Conventional Parallel Resonant Converter
407(2)
11.4.3 Small Signal Model
409(1)
11.4.4 Control Objectives
410(1)
11.4.5 Analysis of the Plant
411(3)
11.4.6 Control Design
414(6)
11.4.7 Controller Synthesis
420(1)
11.4.8 Simulation Results
421(6)
Bibliography
427(18)
A Mathematical Background
445(20)
A.1 Algebraic Structures
445(4)
A.1.1 Field
445(1)
A.1.2 Linear Vector Space
446(1)
A.1.3 Metric, Norm, and Inner Products
447(2)
A.2 Function Spaces
449(8)
A.2.1 Introduction
449(1)
A.2.2 Banach and Hilbert Spaces
449(1)
A.2.3 Operator and Signal Spaces
450(2)
A.2.4 Isomorphism
452(1)
A.2.5 Induced Norms
453(2)
A.2.6 Some Important Induced System Norms
455(2)
A.3 Duality and Dual Spaces
457(3)
A.3.1 The Dual Space
457(1)
A.3.2 Minimum Norm Problems
458(2)
A.4 Singular Values
460(5)
A.4.1 Definition
460(1)
A.4.2 Properties and Applications
461(4)
B System Computations
465(16)
B.1 Series
465(1)
B.2 Change of Variables
466(1)
B.3 State Feedback
467(1)
B.4 State Estimation
467(1)
B.5 Transpose System
467(1)
B.6 Conjugate System
467(1)
B.7 Addition
468(1)
B.8 Output Feedback
468(1)
B.9 Inverse
469(1)
B.10 Linear Fractional Transformations
470(5)
B.11 Norm Computations
475(4)
B.11.1 H(2) Norm Computation
475(1)
B.11.2 H(x) Norm Computation
476(1)
B.11.3 l(1) Norm Computation
476(3)
B.12 Problems
479(2)
C Riccati Equations
481(6)
Index 487

An electronic version of this book is available through VitalSource.

This book is viewable on PC, Mac, iPhone, iPad, iPod Touch, and most smartphones.

By purchasing, you will be able to view this book online, as well as download it, for the chosen number of days.

Digital License

You are licensing a digital product for a set duration. Durations are set forth in the product description, with "Lifetime" typically meaning five (5) years of online access and permanent download to a supported device. All licenses are non-transferable.

More details can be found here.

A downloadable version of this book is available through the eCampus Reader or compatible Adobe readers.

Applications are available on iOS, Android, PC, Mac, and Windows Mobile platforms.

Please view the compatibility matrix prior to purchase.