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Fractional-order Systems and Controls: Fundamentals and Applications 2010 ed. [Hardback]

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  • Formāts: Hardback, 415 pages, height x width: 235x155 mm, weight: 910 g, XVI, 415 p. With online files/update., 1 Hardback
  • Sērija : Advances in Industrial Control
  • Izdošanas datums: 10-Sep-2010
  • Izdevniecība: Springer London Ltd
  • ISBN-10: 1849963347
  • ISBN-13: 9781849963343
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Fractional-order Systems and Controls: Fundamentals and Applications 2010 ed.Palielināt
  • Formāts: Hardback, 415 pages, height x width: 235x155 mm, weight: 910 g, XVI, 415 p. With online files/update., 1 Hardback
  • Sērija : Advances in Industrial Control
  • Izdošanas datums: 10-Sep-2010
  • Izdevniecība: Springer London Ltd
  • ISBN-10: 1849963347
  • ISBN-13: 9781849963343
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781849963343.html
Keywords:
Fractional-order Systems and Controls details the use of fractional calculus in the description and modeling of systems, and in a range of control design and practical applications. It is largely self-contained, covering the fundamentals of fractional calculus together with some analytical and numerical techniques and providing MATLAB® codes for the simulation of fractional-order control (FOC) systems.Many different FOC schemes are presented for control and dynamic systems problems. Practical material relating to a wide variety of applications is also provided. All the control schemes and applications are presented in the monograph with either system simulation results or real experimental results, or both.Fractional-order Systems and Controls provides readers with a basic understanding of FOC concepts and methods, so they can extend their use of FOC in other industrial system applications, thereby expanding their range of disciplines by exploiting this versatile new set of control techniques.

Fractional-order Systems and Controls provides a basic understanding of FOC concepts and methods. Readers will learn the broad range of uses of FOC in control systems through a variety of real-world problems in fields like mechatronics, civil engineering and biological systems.
Part I Fundamentals of Fractinal-order Systems an Controls
1 Introduction
3(6)
1.1 Why Fractional Order?
3(4)
1.2 Brief Historical Overview
7(1)
1.3 Summary
8(1)
2 Fundamentals of Fractional-order Systems
9(26)
2.1 Fractional-order Operators: Definitions and Properties
9(3)
2.1.1 Introduction
9(1)
2.1.2 Fractional-order Integrals
10(1)
2.1.3 Fractional-order Derivatives
10(2)
2.1.4 Laplace and Fourier Transforms
12(1)
2.2 Fractional-order Differential Equations
12(5)
2.2.1 Relaxation and Oscillation Equations
13(2)
2.2.2 Numerical Solutions
15(2)
2.3 Fractional-order Systems
17(17)
2.3.1 Models and Representations
17(2)
2.3.2 Stability
19(7)
2.3.3 Analysis of Time and Frequency Domain Responses
26(5)
2.3.4 Bode's Ideal Loop Transfer Function as References System
31(3)
2.4 Summary
34(1)
3 State-space Representation and Analysis
35(40)
3.1 Continuous-time LTI State-space Models
35(8)
3.1.1 Stability Analysis
36(1)
3.1.2 State-space Realizations
37(6)
3.2 Solution of the State Equation of Continous LTI Commensurate-order Systems
43(11)
3.2.1 Inverse Laplace Transform Method
45(1)
3.2.2 Jordan Matrix Decomposition Method
46(1)
3.2.3 Cayley-Hamilton Method
46(8)
3.3 Controllability of Continuous LTI Commensurate-order Systems
54(3)
3.4 Observability of Continuous LTI Commensurate-orde Systems
57(2)
3.5 Discrete-time LTI State-space Models
59(3)
3.5.1 Discrete-time State-space Equivalent Model of a Continous LTI System
59(1)
3.5.2 Discrete-time State-space Model Based on Finite Differences
60(1)
3.5.3 Discrete-time State-space Model Based on the Expanded State
61(1)
3.6 Solution of the Discrete-time LTI Commensurate-order State Equation
62(4)
3.6.1 Solution of the Homogeneous Discrete-time State Equation
62(2)
3.6.2 Solution of the Complete Discrete-time State Equation
64(2)
3.7 Stability of Discrete-time LTI Commensurate-order Systems
66(2)
3.8 Controllability of Discrete-time LTI Commensurate-order Systems
68(3)
3.8.1 Reachability Conditions
69(1)
3.8.2 Controllability Conditions
70(1)
3.9 Observability of Discrete-time LTI Commensurate-order Systems
71(3)
3.10 Summary
74(1)
4 Fundamentals of Fractional-order Control
75(12)
4.1 Why Fractional-order Control: Historical Review
75(2)
4.2 Generalized Fractional-order Control Actions
77(4)
4.2.1 Integral Action
77(2)
4.2.2 Derivative Action
79(2)
4.3 Generalized PID Controller
81(3)
4.3.1 Classical PID Controller
81(1)
4.3.2 Fractional-order PID Controller
82(2)
4.4 Summary
84(3)
Part II Fractional-order PID-Type Controllers
5 Fractional-order Proportional Integral Controller Tuning for First-order Plus Delay Time Plants
87(20)
5.1 Introduction
88(1)
5.2 F-MIGO: Fractional Ms Contrained Integral Gain Optimization Method
89(7)
5.2.1 Geometric Interpretation of Optimization Problems
92(1)
5.2.2 Numerical Solution of Optimization Problems
93(3)
5.3 Development of the Tuning Rules
96(4)
5.3.1 Introduction to the Method Used
96(1)
5.3.2 Test Batch
96(1)
5.3.3 F-MIGO Applied to the Test Batch
97(1)
5.3.4 Tuning Tables
98(2)
5.3.5 Summary of Tuning Rules
100(1)
5.4 Simulation Results
100(5)
5.4.1 Validity of the F-MIGO Method
100(1)
5.4.2 Three Types of FOPDT Systems
101(2)
5.4.3 Special Systems
103(2)
5.5 Summary
105(2)
6 Fractional-order Proportional Derivative Controller Tuning for Motion Systems
107(14)
6.1 Introduction
107(1)
6.2 Fractional-order PD Controller Design for a Class of Second-order Plants
108(3)
6.2.1 Conventional PD Controllers (μ = 1)
109(1)
6.2.2 Fractional-order PDμ Controllers
110(1)
6.3 Design Procedure
111(1)
6.4 Simulation Example
111(4)
6.4.1 Step Response Comparison with Varying Kp
112(1)
6.4.2 Ramp Response Comparison with Varying Kp
113(2)
6.5 Experiments
115(4)
6.5.1 Introduction to the Experimental Platform
115(1)
6.5.2 Experimental Model Simulation
116(2)
6.5.3 Experiments on the Dynamometer
118(1)
6.6 Summary
119(2)
7 Fractional-order Proportional Integral Derivative Controllers
121(12)
7.1 Introduction
121(1)
7.2 Design Specifications and Tuning Problem
122(3)
7.3 Experimental Results
125(4)
7.4 Summary
129(4)
Part III Fractional-order Lead-lag Compensators
8 Tuning of Fractional-order Lead-lag Compensators
133(8)
8.1 Introduction
133(2)
8.2 The Design Method
135(3)
8.3 Simulation Results
138(2)
8.4 Summary
140(1)
9 Auto-tuning of Fractional-order Lead-lag Compensators
141(10)
9.1 Introduction
141(1)
9.2 Relay Test for Auto-tuning
142(2)
9.3 Design of the Fractional-order Lag Part
144(1)
9.4 Design of the Fractional-order Lead Part
145(2)
9.5 Formulation of the Resulting Controller
147(1)
9.6 Summary
147(4)
Part IV Other Fractional-order Control Strategies
10 Other Robust Control Techniques
151(14)
10.1 CRONE: Commande Robuste d'Ordre Non Entier
151(7)
10.1.1 First Generation CRONE Controller
152(1)
10.1.2 Second Generation CRONE Controller
153(2)
10.1.3 Third Generation CRONE Controller
155(3)
10.2 QFT: Quantitative Feedback Theory
158(5)
10.2.1 Some Preliminaries About QFT
159(1)
10.2.2 Case Study with a Fractional-order Lead-lag Compensator
160(2)
10.2.3 Simulation Results
162(1)
10.3 Summary
163(2)
11 Some Nonlinear Fractional-order Control Strategies
165(26)
11.1 Sliding Mode Control
165(8)
11.1.1 Introduction
165(1)
11.1.2 SMC of the Double Integrator
166(4)
11.1.3 Fractional Sliding
170(3)
11.2 Model Reference Adaptive Control
173(8)
11.2.1 Introduction
173(1)
11.2.2 MRAC: A Brief Review
174(1)
11.2.3 Using Fractional Calculus in MRAC Scheme
175(6)
11.2.4 Concluding Remarks
181(1)
11.3 Reset Control
181(7)
11.3.1 Introduction
181(1)
11.3.2 Reset Integrator
182(1)
11.3.3 Generalized Reset Integrator
183(1)
11.3.4 Fractional Reset Integrator
184(2)
11.3.5 Simulation Results
186(2)
11.4 Summary
188(3)
Part V Implementations of Fractional-order Controllers: Methods and Tools
12 Implementations of Fractional-order Controllers
191(22)
12.1 Continuous-time Implementations of Fractional-order Operators
192(4)
12.1.1 Continued Fraction Approximations
192(1)
12.1.2 Oustaloup Recursive Approximations
193(2)
12.1.3 Modified Oustaloup Filter
195(1)
12.2 Discrete-time Implementation of Fractional-order Operators
196(5)
12.2.1 FIR Filter Approximation
198(1)
12.2.2 Discretization Using the Tustin Method with Prewarping
198(2)
12.2.3 Discrete-time Implementation with Step or Impulse Response Invariants
200(1)
12.3 Frequency Response Fitting of Fractional-order Controllers
201(4)
12.3.1 Continuous-time Approximation
201(1)
12.3.2 Discrete-time Approximation
202(1)
12.3.3 Transfer Function Approximations to Complicated Fractional-order Controllers
203(2)
12.4 Sub-optimal Approximation of FOTFs
205(7)
12.5 Summary
212(1)
13 Numerical Issues and Matlab Implementations for Fractional-order Control Systems
213(46)
13.1 Computations in Fractional Calculus
214(17)
13.1.1 Evaluation of Mittag-Leffler functions
214(3)
13.1.2 Evaluations of Fractional-order Derivatives
217(4)
13.1.3 Closed-form Solutions to Linear Fractional-order Differential Equations
221(3)
13.1.4 Analytical Solutions to Linear Fractional-order Differential Equations
224(7)
13.2 Fractional-order Transfer Functions
231(12)
13.2.1 Design of an FOTF Object
232(1)
13.2.2 Modeling Using FOTFs
233(4)
13.2.3 Stability Assessment of FOTFs
237(2)
13.2.4 Numerical Time Domain Analysis
239(2)
13.2.5 Frequency Domain Analysis
241(2)
13.3 Simulation Studies of Fractional-order Nonlinear Systems with Block Diagrams
243(5)
13.3.1 Design of a Fractional-order Operator Block in Simulink
244(1)
13.3.2 Simulation Studies by Examples
245(2)
13.3.3 Validations of Simulation Results
247(1)
13.4 Optimum Controller Design for Fractional-order Systems
248(8)
13.4.1 Optimum Criterion Selection
249(2)
13.4.2 Optimal Controller Design via Optimizations
251(2)
13.4.3 Optimum PIλDμ Controller Design
253(3)
13.5 Summary
256(3)
Part VI Real Applications
14 Systems Identification
259(14)
14.1 Introduction
259(1)
14.2 Frequency Domain Identification of Commensurate-order Systems
260(1)
14.3 Electrochemical Process
261(5)
14.4 Flexible Structure
266(5)
14.5 Summary
271(2)
15 Position Control of a Single-link Flexible Robot
273(28)
15.1 Introduction
274(2)
15.2 Problem Statement
276(3)
15.3 Dynamic Model of the Single-link Flexible Manipulator
279(3)
15.4 General Control Scheme
282(4)
15.4.1 Inner-loop
283(1)
15.4.2 Simplifying-loop
284(1)
15.4.3 Outer-loop
285(1)
15.5 Design of the Outer-loop Controller Re (s)
286(5)
15.5.1 Condition for Constant Phase Margin
287(1)
15.5.2 Condition for Removing the Effects of Disturbance
288(1)
15.5.3 Ideal Response to a Step Command
288(1)
15.5.4 Controller Design
289(2)
15.6 Some Practical Issues
291(6)
15.6.1 Robustness to Higher Vibration Modes (Spillover)
292(3)
15.6.2 Effect of the Non-negligible Inner-loop Dynamics
295(1)
15.6.3 Fractional-order Controller Implementation
296(1)
15.7 Experimental Results
297(3)
15.8 Summary
300(1)
16 Automatic Control of a Hydraulic Canal
301(52)
16.1 Background and Motivations
301(3)
16.2 Description of the Laboratory Hydraulic Canal
304(3)
16.3 Control-oriented Hydraulic Canal Dynamic Model
307(5)
16.4 Design and Experimental Studies of Fractional-order PI Controllers
312(15)
16.4.1 Fractional-order PI Controller Design
312(6)
16.4.2 Time Response of the Fractional-order PI Controller
318(4)
16.4.3 Experiments with the Fractional-order PI Controller
322(5)
16.5 Design and Experimental Studies of PID Controllers
327(7)
16.5.1 Design of a PID Controller
327(3)
16.5.2 Experimental Comparison of the PID Controller and the Fractional-order Controllers
330(3)
16.5.3 Conclusions on the Robust Control of the Laboratory Hydraulic Canal
333(1)
16.6 Control of Hydraulic Canals with Significant Delays
334(5)
16.6.1 Standard Control Scheme
335(1)
16.6.2 Smith Predictor Based Control Scheme
336(3)
16.7 Fractional-order Control of Hydraulic Canals with Significant Delays
339(1)
16.7.1 Design Method for Smith Predictor Based Iλ Controllers (SP-FI)
339(1)
16.7.2 Design Method for Smith Predictor Based PIλ Controllers (SP-FPI)
339(1)
16.8 Control-oriented Dynamic Model of an IMCP
340(3)
16.9 Comparison of Controllers from Simulation Results
343(8)
16.9.1 Controller Design Specifications for the Nominal Plant
343(1)
16.9.2 Standard PI Controller
344(1)
16.9.3 Smith Predictor Based PI Controller
344(1)
16.9.4 Smith Predictor Based PID Controller
345(1)
16.9.5 Fractional-order I Controller with Smith Predictor
346(2)
16.9.6 Fractional-order PI Controller with Smith Predictor
348(2)
16.9.7 Conclusions on the Robust Control of the IMCP with LTVD
350(1)
16.10 Summary
351(2)
17 Mechatronics
353(12)
17.1 The Experimental Platform
353(2)
17.2 Experimental Tuning of the Control Platform
355(4)
17.2.1 Position Servo
355(2)
17.2.2 Velocity Servo
357(2)
17.3 Experimental Auto-tuning on the Mechatronic Platform
359(4)
17.4 Summary
363(2)
18 Fractional-order Control Strategies for Power Electronic Buck Converters
365(26)
18.1 Introduction
365(2)
18.2 Model of the Buck Converter
367(4)
18.2.1 Discrete Plant Model
368(1)
18.2.2 Linearized Plant Model
369(1)
18.2.3 Real System Model for Design
370(1)
18.3 Linear Fractional-order Control
371(4)
18.3.1 Controller Design Based on the Smith Predictor Structure
371(2)
18.3.2 Controller Design Using Phase-lag Compensation
373(1)
18.3.3 Controller Design Based on the Discrete Linearized Model
374(1)
18.4 Fractional Sliding Mode Control (FrSMC)
375(6)
18.4.1 Sliding Surfaces Through PID and PI Structures
376(2)
18.4.2 Fractional Sliding Surfaces
378(3)
18.5 Simulation and Experimental Results
381(6)
18.5.1 Simulation Results
381(3)
18.5.2 Experimental Results
384(2)
18.5.3 Robustness Comments on Simulation Results
386(1)
18.6 Summary
387(4)
Appendix Laplace Transforms Involving Fractional and Irrational Operations
391(4)
A.1 Laplace Transforms
391(1)
A.2 Special Functions for Laplace Transform
391(1)
A.3 Laplace Transform Tables
391(4)
References 395(14)
Index 409
Doctor Concepción A. Monje has been working on fractional derivatives and their applications for over seven years being author and co-author of over 40 technical papers mostly related to fractional-order controllers. Her research area focuses on the tuning and auto-tuning of fractional-order controllers for the control of industrial processes, including servomechanisms, pneumatic and liquid level systems. She has collaborated with the CRONE (Commande Robuste Ordre Non Entier) team from the Ecole Nationale Supérieure dÉlectronique, Informatique et Radiocommunications of Bordeaux, publishing several works related to the tuning of fractional-order controllers and co-organizing the 2nd IFAC Workshop on Fractional Differentiation and its Applications (FDA06). She has also worked on the application of fractional-order controllers to the control of flexible manipulators, in collaboration with the Electrical, Electronic, Control and Communications Engineering Department of the Technic High School of Industrial Engineers of the University of Castilla La-Mancha, Spain. Her collaborations in this field also extend to the Center for Self-Organizing and Intelligent System of the Utah State University, in USA, where she was invited to deliver a research lecture on design of fractional-order controllers to Ph.D. students and a joint public lecture on this topic to members of the IEEE Control Systems Society San Diego Section. She has co-chaired international conferences and she has been a member of international program committees. She has been involved in several international and national research and industrial projects, and she has reviewed articles for several international journals and conferences of relevance.



Doctor YangQuan Chen has authored over 200 academic papers plus numerous technical reports. He co-authored two textbooks: "System Simulation Techniques with MATLAB®/Simulink" (with Dingyu Xue . Tsinghua University Press, April 2002, ISBN7-302-05341-3/TP3137, in Chinese) and "Solving Advanced Applied Mathematical Problems Using Matlab" (with Dingyu Xue. Tsinghua University Press. August 2004. 419 pages in Chinese, ISBN 7-302-09311-3/O.392); and four research monographs: "Plastic Belt for Projectiles" (with Y. Shi. Shaanxi Science and Technology Press, Jan. 1995, ISBN 7-5369-2277-9/TJ.1, in Chinese), "Iterative Learning Control " (with C. Wen . Lecture Notes in Control and Information Sciences, Springer-Verlag, Nov. 1999, ISBN: 1-85233-190-9 ), "Iterative Learning Control" (with Hyo-Sung Ahn and Kevin L. Moore. Springer, July 2007, ISBN: 978-1-84628-846-3), and "Optimal Observation for Cyber-physical Systems"(with Zhen Song, Chellury Sastry and Nazif Tas. Springer, July 2009, ISBN: 978-1-84882-655-7). His current research interests include autonomous navigation and intelligent control of a team of unmanned ground vehicles, machine vision for control and automation, distributed control systems (MAS-net : mobile actuator-sensor networks), fractional-order control, interval computation, and iterative/repetitive/adaptive learning control. Currently, he serves as an Associate Editor for IEEE Control Systems Society, Conference Editorial Board (CSSCEB ). He was also an Associate Editor of ISA Review Board for AACC 's American Control Conference ( ACC2005 ). He has been the Co-Organizer and Instructor of the Tutorial Workshop on "Fractional-order Calculus in Control and Robotics" at IEEE 2002 Conference on Decision and Control (CDC'02), and a founding member of the ASME subcommittee on "Fractional Dynamics".



Doctor Blas M. Vinagre has been working on the area of Fractional Calculus Applications for over 12 years, and he has published over 60 technical papers on this subject. He co-organized the ever first whole day Tutorial Workshop (IEEE Conference on Decision and Control, Las Vegas, December 2002) and the Symposium on Applied Fractional Calculus (Badajoz, October 2007). He has been teacher for tutorial seminars and lecturer for talks on Fractional Calculus Applications at several universities: Technical University of Kosice (Kosice, Slovak Republic 1999), Universita degli Studi di Parma (Parma, Italy 2000), Technical University of Lisbon (Lisbon, Portugal 2001), University of Seville (Seville, Spain 1999), Polytechnic University of Madrid (Madrid, Spain 2004), University of Valencia (Valencia, Spain 2005), Royal Academy of Sciences (Madrid, Spain 2005), Polytechnic University of Catalunya (Barcelona, Spain 2008). He has also been Co-Chair of the 2nd IFAC Workshop on Fractional Differentiation and its Applications, Porto, Purtugal, July 2006. He is currently involved as Principal Investigator in research projects with the objective of applying FOC to industrial processes, servomechanisms, and autonomous vehicles, and his current interest in the field also includes stability theory, optimal and adaptive control, and implementation issues using FOC. 



Doctor Dingyü Xue is a Professor of Control Engineering on the Faculty of Information Sciences and Engineering at Northeastern University in Shenyang, China. He is the author of several influential textbooks and monographs on MATLAB® and control in Chinese and two in English, cited by thousands of journal papers and theses. 



Doctor Vicente Felius research interests include multivariable and digital control systems, fractional dynamics and control, kinematic and dynamic control of rigid and flexible robots, mechatronics, and computer vision for robots. He has written about 80 technical papers in refereed international journals and more than 100 communications to international conferences about these subjects. He was awarded with the prize to the best paper published in the Pattern Recognition Journal in 2001, with the Highly Commended Award by the Industrial Robot Journal in 2007, and with the Highly Commended Award by the CLAWAR Conference in 2006. He was also awarded with the Prize to Technical Innovation ofCastilla-La Mancha (Spain) in 2003. He has also hold some leading jobs in the Spanish National Research Agency. Regarding fractional calculus, he has worked on modelling and identification of electrochemical and corrosion processes using fractional derivatives, and in the development of frequency domain control design techniques with applications to robotics, mechatronics, hydraulic canals, and electronic converters.