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E-raamat: Delay Systems: From Theory to Numerics and Applications

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  • Sari: Advances in Delays and Dynamics 1
  • Ilmumisaeg: 07-Sep-2013
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319016955
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  • Formaat: PDF+DRM
  • Sari: Advances in Delays and Dynamics 1
  • Ilmumisaeg: 07-Sep-2013
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319016955

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This volume is the first of the new series Advances in Dynamics and Delays. It offers the latest advances in the research of analyzing and controlling dynamical systems with delays, which arise in many real-world problems. The contributions in this series are a collection across various disciplines, encompassing engineering, physics, biology, and economics, and some are extensions of those presented at the IFAC (International Federation of Automatic Control) conferences since 2011. The series is categorized in five parts covering the main themes of the contributions:

· Stability Analysis and Control Design

· Networks and Graphs

· Time Delay and Sampled-Data Systems

· Computational and Software Tools

· Applications

This volume will become a good reference point for researchers and PhD students in the field of delay systems, and for those willing to learn more about the field, and it will also be a resource for control engineers, who will find innovative control methodologies for relevant applications, from both theory and numerical analysis perspectives.



Launching the series Advances in Dynamics and Delays, this book covers new ways of analyzing and controlling dynamical systems with delays, which arise in many real-world problems. Spans disciplines, encompassing engineering, physics, biology and economics.
Part I Stability Analysis and Control Design
Necessary Stability Conditions for One Delay Systems: A Lyapunov Matrix Approach
3(14)
Carlos Cuvas
Adrian Ramirez
Alexey Egorov
Sabine Mondie
1 Introduction
3(2)
2 Preliminaries
5(4)
2.1 Theoretical Framework
5(2)
2.2 Auxiliary Results
7(2)
3 Necessary Conditions
9(3)
4 Illustrative Example and Additional Considerations
12(3)
5 Concluding Remarks
15(2)
References
16(1)
Control of Linear Delay Systems: An Approach without Explicit Predictions
17(14)
Nicole Gehring
Joachim Rudolph
Frank Woittennek
1 Introduction
17(2)
2 Controllability Properties
19(2)
3 Remarks on Modules over the Ring K[ δ]
21(1)
4 Prediction-Free Control
22(2)
4.1 Conditions in the Commensurate Case
22(1)
4.2 Conditions in the Incommensurate Case
23(1)
4.3 Control Design
23(1)
5 Example: A Heat Accumulator
24(7)
5.1 Control via the Jacket Temperature T0
25(2)
5.2 Control via the Inlet Temperature Tin
27(1)
5.3 Two Control Inputs
28(1)
References
29(2)
New Integral Inequality and Its Application to Time-Delay Systems
31(14)
Alexandre Seuret
Frederic Gouaisbaut
1 Introduction
31(2)
2 Preliminaries
33(1)
2.1 Jensen's Inequality
33(1)
2.2 Different Wirtinger Inequalities
33(1)
3 Application of the Wirtinger's Inequalities
34(3)
4 Appropriate Inequalities for Robust Stability Analysis
37(1)
5 Application to the Stability Analysis of Time-Delay Systems
38(5)
5.1 Systems with Constant and Known Delay
39(1)
5.2 Systems with Constant and Unknown Delay: Delay Range Stability
40(1)
5.3 Examples
41(2)
6 Conclusions
43(2)
References
43(2)
A Matrix Technique for Robust Controller Design for Discrete-Time Time-Delayed Systems
45(12)
Ali Fuat Ergenc
1 Introduction
45(2)
2 The Problem Statement
47(1)
3 Robust Stability Analysis
48(4)
4 Dominant Pole Assignment
52(1)
5 Example Case Studies
52(2)
6 Conclusion and Discussion
54(3)
References
55(2)
Dominant Trio of Poles Assignment in Delayed PID Control Loop
57(14)
Pavel Zitek
Jaromir Fiser
Tomas Vyhlidal
1 Introduction
57(2)
2 Selecting the Candidate Group of Dominant Poles
59(1)
3 Three Pole Dominant Placement in Delayed PID Feedback Loop
60(3)
3.1 Ultimate Frequency Assessment
62(1)
4 Argument Increment Based Check to Prove the Dominance
63(1)
5 Relative Damping Optimization in the PID Parameter Setting
64(4)
5.1 Damping Optimization
65(1)
5.2 Example 1 - Controlling Second Order System
65(2)
5.3 Example 2 - Controlling Third Order System
67(1)
6 Concluding Remarks
68(3)
References
69(2)
Stability of Systems with State Delay Subjected to Digital Control
71(16)
David Lehotzky
Tamas Insperger
1 Introduction
71(2)
2 Semi-discretization
73(6)
2.1 One-Point Methods
73(4)
2.2 Two-Point Methods
77(2)
3 Example: The Delayed Oscillator
79(2)
4 Example: Application to Turning Processes
81(1)
5 Conclusions
82(5)
References
83(4)
Part II Networks and Graphs
Control Design for Teleoperation over Unreliable Networks: A Predictor-Based Approach
87(14)
Alexandre Kruszewski
Bo Zhang
Jean-Pierre Richard
1 Introduction
87(2)
2 A Delay Formulation for Teleoperation Problems
89(1)
3 Force-Reflecting Emulator Control Scheme
90(9)
3.1 System Description and Problem Formulation
90(2)
3.2 Problem 1: Local Controller Design
92(1)
3.3 Problem 2: Master-Emulator Synchronization
93(1)
3.4 Problem 3: Slave-Emulator Synchronization
94(1)
3.5 Global Stability and Performance Analysis
95(3)
3.6 Tracking in Abrupt Changing Motion
98(1)
3.7 Tracking in Wall Contact Motion
98(1)
4 Conclusions
99(2)
References
99(2)
Graph Laplacian Design of a LTI Consensus System for the Largest Delay Margin: Case Studies
101(12)
Wei Qiao
Rifat Sipahi
1 Introduction
101(1)
2 Preliminaries
102(4)
2.1 Consensus Dynamics
102(1)
2.2 Stability, Responsible Eigenvalue (RE), Graph Synthesis
103(2)
2.3 Design Rules
105(1)
3 Case Studies
106(4)
3.1 Tailoring Stable 2(Ga) with Stable 2(Gb)
106(2)
3.2 Tailoring an Unstable System with a Stable System
108(2)
4 Conclusion
110(3)
References
111(2)
Second-Order Leaderless Consensus Protocols with Multiple Communication and Input Delays from Stability Perspective
113(14)
Rudy Cepeda-Gomez
Nejat Olgac
1 Introduction
113(1)
2 Problem Statement
114(4)
3 Stability Analysis Using CTCR Paradigm and SDS Domain
118(4)
4 Deployment on a Case Study
122(2)
5 Conclusions
124(3)
References
125(2)
Analysis of Gene Regulatory Networks under Positive Feedback
127(14)
Mehmet Eren Ahsen
Hitay Ozbay
Silviu-Iulian Niculescu
1 Introduction
127(2)
2 Notation, Preliminaries and Problem Formulation
129(2)
3 Analysis of the Cyclic Network under Positive Feedback
131(5)
3.1 General Conditions for Global Stability
131(1)
3.2 Analysis of Homogenous Gene Regulatory Networks
131(5)
4 Examples
136(3)
5 Conclusions
139(2)
References
139(2)
Analysis and Design of Pattern Formation in Networks of Nonlinear Systems with Delayed Couplings
141(14)
Toshiki Oguchi
Eiichi Uchida
1 Introduction
141(1)
2 Analysis of Oscillatory Patterns in Networks of Nonlinear Systems with Delayed Couplings
142(6)
2.1 Nonlinear Network Systems with Delayed Couplings
142(1)
2.2 Analysis of Periodic Solutions
143(3)
2.3 Numerical Examples
146(2)
3 Synthesis of Networks with Delays
148(5)
3.1 Design Method
148(2)
3.2 Examples
150(3)
4 Conclusions
153(2)
Appendix
153(1)
References
154(1)
Consensus in Networks of Discrete-Time Multi-agent Systems: Dynamical Topologies and Delays
155(16)
Wenlian Lu
Fatihcan M. Atay
Jurgen Jost
1 Introduction
155(3)
2 Stability Analysis
158(3)
3 Linear Model
161(3)
4 Multi-agent Model with Nonlinear Coupling
164(1)
5 Numerical Examples: Dynamical Networks for Random Waypoint Model
165(2)
6 Conclusion
167(4)
References
167(4)
Part III Time-Delay and Sampled-Data Systems
Sampled-Data Stabilization under Round-Robin Scheduling
171(14)
Kun Liu
Emilia Fridman
Laurentiu Hetel
Jean-Pierre Richard
1 Introduction
171(2)
2 Problem Formulation
173(2)
3 Main Results
175(7)
3.1 Stability Conditions for NCSs: Variable Sampling and Constant Input/Output Delay
175(3)
3.2 Stability Conditions for Sample-Data Systems: Constant vs Variable Sampling
178(4)
4 Example
182(1)
5 Conclusions
183(2)
References
183(2)
Structure of Discrete Systems with Variable Nonlocal Behavior
185(14)
Erik I. Verriest
1 Introduction: Behavioral Approach
185(2)
2 Discrete Delay System
187(1)
3 Time-Variant Delay
188(2)
3.1 Causal Models
188(1)
3.2 State Space and Trajectories
189(1)
4 Periodic Time Delay System
190(3)
5 Reflecto-difference Equation
193(4)
6 Conclusions
197(2)
References
197(2)
Decentralized Robustification of Interconnected Time-Delay Systems Based on Integral Input-to-State Stability
199(16)
Hiroshi Ito
Pierdomenico Pepe
Zhong-Ping Jiang
1 Introduction
199(2)
2 Idea and Issues to Be Solved
201(3)
3 Invariantly Differentiable Functionals
204(1)
4 Interconnected Time-Delay Systems with Discontinuous Right-Hand Side
205(2)
5 Decentralized iISS and ISS Feedback Redesign
207(3)
6 An Example
210(2)
7 Conclusions
212(3)
References
212(3)
Global Stability Analysis of Nonlinear Sampled-Data Systems Using Convex Methods
215(14)
Matthew M. Peet
Alexandre Seuret
1 Introduction to the Problem of Stability of Sampled-Data Systems
215(2)
2 Background
217(3)
2.1 Sampled-Data Systems
217(1)
2.2 A Lyapunov Theorem
218(1)
2.3 Sum-of-Squares Optimization
219(1)
3 Main Results
220(3)
3.1 The Synchronous Case
221(1)
3.2 The Asynchronous Case
222(1)
4 Numerical Examples
223(3)
4.1 Example 1: 1-D Nonlinear Dynamical System
224(1)
4.2 Example 2: Controlled Model of a Jet Engine
224(2)
4.3 Example 3: 1-D System, Unknown Sampling Period
226(1)
5 Conclusion
226(3)
References
226(3)
DDE Model-Based Control of Glycemia via Sub-cutaneous Insulin Administration
229(14)
Pasquale Palumbo
Pierdomenico Pepe
Simona Panunzi
Andrea De Gaetano
1 Introduction
229(2)
2 The Glucose-Insulin Model
231(2)
3 The Feedback Control Law
233(3)
4 Simulation Results
236(2)
5 Conclusions
238(5)
References
239(4)
Part IV Computational and Software Tools
Eigenvalue Based Algorithms and Software for the Design of Fixed-Order Stabilizing Controllers for Interconnected Systems with Time-Delays
243(14)
Wim Michiels
Suat Gumussoy
1 Introduction
243(2)
2 Preliminaries and Assumptions
245(1)
3 Spectral Properties and Stability
246(3)
3.1 Exponential Stability
246(1)
3.2 Continuity of the Spectral Abscissa and Strong Stability
246(3)
4 Robust Stabilization by Eigenvalue Optimization
249(1)
5 Illustration of the Software
250(5)
6 Duality with the H∞ Problem
255(2)
References
255(2)
Computer Aided Control System Design for Time Delay Systems Using MATLAB®
257(14)
Suat Gumussoy
Pascal Gahinet
1 Introduction
257(1)
2 Motivation Examples
258(1)
3 System Representation
259(2)
4 Interconnections
261(2)
5 Time / Frequency Domain Analyses and Visualizations
263(2)
6 Controller Design
265(2)
7 Possible Enhancements in CACSD
267(1)
8 Concluding Remarks
268(3)
References
268(3)
Analysis and Control of Time Delay Systems Using the LambertWDDE Toolbox
271(14)
Sun Yi
Shiming Duan
Patrick W. Nelson
A. Galip Ulsoy
1 Introduction
272(1)
1.1 Motivation and Background
272(1)
1.2 Purpose and Scope
273(1)
2 Theory, Examples and Numerical Simulation
273(9)
2.1 Lambert W Function
273(1)
2.2 Scalar Case
273(1)
2.3 Example 1 - Spectrum and Series Expansion in the Scalar Case
274(1)
2.4 Example 2 - Scalar Case Approximation Response
275(1)
2.5 General Case
276(1)
2.6 Example 3 - General Case Approximation
277(1)
2.7 Observability and Controllability
278(1)
2.8 Example 4 - Piecewise Observability and Controllability
279(1)
2.9 Placement of Dominant Poles
279(1)
2.10 Example 5 - Rightmost Eigenvalue Assignment
280(1)
2.11 Robust Control and Time Domain Specifications
281(1)
2.12 Decay Function for TDS
281(1)
2.13 Example 6 - Factor and Decay Rate
281(1)
3 Concluding Remarks
282(3)
References
282(3)
H∞-Stability Analysis of (Fractional) Delay Systems of Retarded and Neutral Type with the Matlab Toolbox YALTA
285(14)
David Avanessoff
Andre R. Fioravanti
Catherine Bonnet
Le Ha Vy Nguyen
1 Introduction
285(2)
2 Functionalities of YALTA
287(2)
2.1 Asymptotic Axes and Poles of High Modulus
288(1)
2.2 Stability Windows and Root Locus
288(1)
2.3 Approximation of Poles of Small Modulus
288(1)
2.4 H∞-stability Analysis
289(1)
3 Practical Aspects
289(2)
3.1 Continuation Algorithm
289(1)
3.2 Pade Approximation
290(1)
4 Examples of YALTA Application
291(5)
4.1 Example 1- Bifurcation Analysis of a Small Degree System
291(2)
4.2 Example 2- Stability of a Fractional System
293(1)
4.3 Example 3- Computational Aspects
294(1)
4.4 Example 4- Pade-2 Approximation
295(1)
5 Conclusion
296(3)
References
296(3)
QPmR - Quasi-Polynomial Root-Finder: Algorithm Update and Examples
299(16)
Tomas Vyhlidal
Pavel Zitek
1 Introduction
299(2)
1.1 Problem Formulation
300(1)
2 Algorithm for Spectrum Computation
301(2)
2.1 Mapping the Zero Level Curves
302(1)
3 Spectrum Analysis
303(3)
3.1 Spectral Features of Neutral Quasi-Polynomial
304(2)
4 Working with QPmR v.2 in Matlab
306(4)
4.1 Examples
307(3)
5 Conclusions
310(5)
References
311(4)
Part V Applications
Analysis of a New Model of Cell Population Dynamics in Acute Myeloid Leukemia
315(14)
Jose Louis Avila
Catherine Bonnet
Jean Clairambault
Hitay Ozbay
Silviu-Iulian Niculescu
Faten Merhi
Annabelle Ballesta
Ruoping Tang
Jean-Pierre Marie
1 Introduction
316(1)
2 Mathematical Model of AML
317(2)
3 Model Transformation
319(2)
4 Analysis of the i-th Compartmental Model
321(3)
4.1 Equilibrium Points
321(2)
4.2 Model Linearization and Stability
323(1)
5 Numerical Example and Simulation Results
324(3)
6 Conclusions
327(2)
References
328(1)
The Influence of Time Delay on Crane Operator Performance
329(14)
Joshua Vaughan
William Singhose
1 Introduction
329(3)
2 The Influence of Communication Delay on Bridge Crane Operators
332(4)
2.1 Experimental Protocol
332(2)
2.2 Experimental Results
334(2)
3 Remote Operation of a Tower Crane
336(3)
4 Conclusions
339(4)
References
340(3)
Decomposing the Dynamics of Delayed Hodgkin-Huxley Neurons
343(16)
Gabor Orosz
1 Introduction
343(2)
2 Decomposition of Delayed Networks around Synchronous States
345(4)
2.1 Stability of Synchronous Equilibria and Periodic Orbits
348(1)
3 Synchrony of Delay Coupled Hodgkin-Huxley Neurons
349(7)
3.1 Stability of Synchronous Equilibria
350(3)
3.2 Stability of Synchronous Periodic Orbits
353(3)
4 Conclusion and Discussion
356(3)
References
356(3)
Practical Delay Modeling of Externally Recirculated Burned Gas Fraction for Spark-Ignited Engines
359(14)
Delphine Bresch-Pietri
Thomas Leroy
Jonathan Chauvin
Nicolas Petit
1 Introduction
359(3)
1.1 Why Exhaust Gas Recirculation?
360(1)
1.2 Necessity of a Virtual Composition Sensor
361(1)
1.3 Comparison with Diesel EGR
361(1)
2 Modeling
362(4)
2.1 Dilution Dynamics and Transport Delay
362(2)
2.2 Transport Delay Description
364(1)
2.3 Estimation Strategy with Practical Identification Procedure
365(1)
3 Experimental Results
366(3)
3.1 Experimental Setup and Indirect Validation Methodology from FAR Measurements
366(1)
3.2 First Validation: Variation of the Amount of Reintroduced EGR (Constant Delay)
367(2)
3.3 Second Validation: Torque Transients (Varying Delay)
369(1)
4 Conclusion and Perspectives
369(4)
References
371(2)
Design and Control of Force Feedback Haptic Systems with Time Delay
373(16)
Quoc Viet Dang
Antoine Dequidt
Laurent Vermeiren
Michel Dambrine
1 Introduction
373(2)
2 Optimal Design Method for Haptic Device
375(6)
2.1 Dynamic Constraint
375(1)
2.2 Mechanical Model of the Haptic Device
376(1)
2.3 Necessary and Sufficient Stability Condition
377(1)
2.4 Optimal Design Method for Haptic Device
378(3)
3 Proposed Force Feedback Architecture
381(4)
3.1 Design of the Virtual Wall and the State Observer
381(2)
3.2 Numerical Simulation Results
383(2)
4 Conclusions
385(4)
References
386(3)
Engineering a Genetic Oscillator Using Delayed Feedback
389(14)
Edward Lambert
Edward J. Hancock
Antonis Papachristodoulou
1 Introduction
389(1)
2 Background
390(1)
3 Oscillations Using Delayed Negative Feedback
391(4)
3.1 Period
392(1)
3.2 Amplitude
393(2)
4 Coupled Delay Oscillators
395(4)
4.1 Genetic Coupling
396(1)
4.2 Coupled Delay Oscillators
396(3)
5 Conclusion
399(4)
References
402(1)
Index 403