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Tensor Product Model Transformation in Polytopic Model-Based Control [Kõva köide]

(Chinese University of Hong Kong, Shatkin), ,
  • Formaat: Hardback, 262 pages, kõrgus x laius: 234x156 mm, kaal: 589 g, 3 Tables, black and white; 73 Illustrations, black and white
  • Sari: Automation and Control Engineering
  • Ilmumisaeg: 19-Aug-2013
  • Kirjastus: CRC Press Inc
  • ISBN-10: 1439818169
  • ISBN-13: 9781439818169
Teised raamatud teemal:
Tensor Product Model Transformation in Polytopic Model-Based ControlSuurem pilt
  • Formaat: Hardback, 262 pages, kõrgus x laius: 234x156 mm, kaal: 589 g, 3 Tables, black and white; 73 Illustrations, black and white
  • Sari: Automation and Control Engineering
  • Ilmumisaeg: 19-Aug-2013
  • Kirjastus: CRC Press Inc
  • ISBN-10: 1439818169
  • ISBN-13: 9781439818169
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781439818169.html
Märksõnad:

Tensor Product Model Transformation in Polytopic Model-Based Control offers a new perspective of control system design. Instead of relying solely on the formulation of more effective LMIs, which is the widely adopted approach in existing LMI-related studies, this cutting-edge book calls for a systematic modification and reshaping of the polytopic convex hull to achieve enhanced performance. Varying the convexity of the resulting TP canonical form is a key new feature of the approach. The book concentrates on reducing analytical derivations in the design process, echoing the recent paradigm shift on the acceptance of numerical solution as a valid form of output to control system problems. The salient features of the book include:

  • Presents a new HOSVD-based canonical representation for (qLPV) models that enables trade-offs between approximation accuracy and computation complexity
  • Supports a conceptually new control design methodology by proposing TP model transformation that offers a straightforward way of manipulating different types of convexity to appear in polytopic representation
  • Introduces a numerical transformation that has the advantage of readily accommodating models described by non-conventional modeling and identification approaches, such as neural networks and fuzzy rules
  • Presents a number of practical examples to demonstrate the application of the approach to generate control system design for complex (qLPV) systems and multiple control objectives.

The authors’ approach is based on an extended version of singular value decomposition applicable to hyperdimensional tensors. Under the approach, trade-offs between approximation accuracy and computation complexity can be performed through the singular values to be retained in the process. The use of LMIs enables the incorporation of multiple performance objectives into the control design problem and assurance of a solution via convex optimization if feasible.Tensor Product Model Transformation in Polytopic Model-Based Control includes examples and incorporates MATLAB® Toolbox TPtool. It provides a reference guide for graduate students, researchers, engineers, and practitioners who are dealing with nonlinear systems control applications.

Arvustused

" well written and easily readable. The examples and applications to 3 Degrees Of Freedom (DOFs) control schemes for helicopters, models for aeroelastic wing sections and models for controlling the behavior of suspension system in heavy trucks are the main strength of the book. for control engineers with a solid mathematical formation as well as control theorists and even applied mathematicians."zbMATH 1308 in 2015

"The book provides an introduction to a method that has potential to significantly advance the theory and practice of control system design. The modeling step is frequently the most time-consuming stage of practical control system design. The unifying TP representation of quasi LPV models described in this book has potential to make this stage more efficient as well as enabling many of the powerful LMI-based control design methods for LPV systems to be applied to practical problems."James Whidborne, Cranfield University, Bedfordshire, UK " well written and easily readable. The examples and applications to 3 Degrees Of Freedom (DOFs) control schemes for helicopters, models for aeroelastic wing sections and models for controlling the behavior of suspension system in heavy trucks are the main strength of the book. for control engineers with a solid mathematical formation as well as control theorists and even applied mathematicians." zbMATH 1308 in 2015

"The book provides an introduction to a method that has potential to significantly advance the theory and practice of control system design. The modeling step is frequently the most time-consuming stage of practical control system design. The unifying TP representation of quasi LPV models described in this book has potential to make this stage more efficient as well as enabling many of the powerful LMI-based control design methods for LPV systems to be applied to practical problems." James Whidborne, Cranfield University, Bedfordshire, UK

Preface xi
Acronyms and Abbreviations xiii
1 Introduction
1(8)
1.1 An overview
1(1)
1.2 TP model
2(1)
1.3 HOSVD-based computation
3(1)
1.4 Convex optimization via LMIs/PDC framework
4(1)
1.5 Model convexity and convex hull manipulation
5(1)
1.6 Significant paradigm changes
6(1)
1.7 Outline of the book
7(2)
I Tensor Product (TP) Model Formulation
9(108)
2 TP Model
11(10)
3 TP Model Transformation
21(12)
3.1 Introduction to HOSVD
22(4)
3.2 Transformation procedures
26(2)
3.3 The extracted model
28(1)
3.4 Addition of sampling grid lines
29(4)
4 TP Canonical Model Form
33(18)
4.1 Definition
33(2)
4.2 Numerical reconstruction
35(9)
4.3 The TORA example
44(7)
4.3.1 Equations of motion
45(2)
4.3.2 TP canonical model
47(4)
5 Approximation and Complexity Trade-Off
51(14)
5.1 TP model form of bounded order
51(1)
5.2 The nowhere dense property
52(5)
5.3 Trade-off examples
57(3)
5.3.1 A mass-spring-damper system
57(2)
5.3.2 A mass-spring-damper system with nonlinear term
59(1)
5.4 Trade-off study on the TORA example
60(5)
6 TP Model Convexity Incorporation
65(18)
6.1 TP model convexity
66(3)
6.2 Incorporation of convexity conditions
69(6)
6.2.1 Incorporating the SN condition
70(1)
6.2.2 Incorporating the NN condition
71(1)
6.2.3 Incorporating the NO condition
72(2)
6.2.4 Incorporating the RNO condition
74(1)
6.3 Alternate method for INO and RNO conditions
75(5)
6.3.1 The partial algorithm
76(2)
6.3.2 The complete algorithm
78(2)
6.4 The TORA example
80(3)
7 Introduction to the TPtool Toolbox
83(8)
7.1 Generating the TP canonical model
83(3)
7.2 Incorporating convexity conditions
86(5)
8 Centralized Model Form
91(8)
8.1 The centralized model
91(2)
8.1.1 Mathematical properties
92(1)
8.1.2 Control properties
93(1)
8.1.3 Computational advantages
93(1)
8.2 Illustrating examples
93(6)
9 Computational Relaxed TP Model Transformation
99(18)
9.1 SVD-based column equivalence
101(3)
9.2 Modified transformation algorithm
104(5)
9.3 Evaluation of computational reduction
109(3)
9.3.1 Discretization complexity
109(1)
9.3.2 HOSVD computation
110(1)
9.3.3 Tensor product computation
111(1)
9.4 Examples
112(5)
9.4.1 A simple numerical example
112(1)
9.4.2 The double inverted pendulum example
112(5)
II TP Model-Based Control System Design
117(36)
10 Overview of TP Model-Based Design Strategy
119(6)
11 LMI Theorems under the PDC Framework
125(22)
11.1 LMIs for control system design
125(6)
11.1.1 Definition of LMIs
126(2)
11.1.2 Constraints expressed via LMIs
128(2)
11.1.3 Generic problems for LMIs
130(1)
11.2 LMI optimization under the PDC framework
131(6)
11.2.1 Lyapunov stability criteria
132(1)
11.2.2 Control design for stability
133(1)
11.2.3 Multiobjective control optimization
134(1)
11.2.4 Simultaneous observer/controller design
135(2)
11.3 TP model-based control design procedures
137(1)
11.4 LMI-based control design for the TORA example
138(9)
11.4.1 Control specifications
140(1)
11.4.2 State feedback control design
140(2)
11.4.3 Observer-based output feedback control design
142(5)
12 Convex Hull Manipulation
147(6)
12.1 Nonlinear sensitivity of control solutions
148(2)
12.2 Conservativeness of control solutions
150(3)
III Control Design Examples
153(64)
13 Control Design with TPtool Toolbox
155(2)
14 2-D Prototypical Aeroelastic Wing Section with Structural Nonlinearity
157(24)
1.4.1 Dynamics modeling
158(4)
14.2 The TP model
162(2)
14.3 State feedback control design
164(7)
14.3.1 Controller for asymptotic stabilization
165(2)
14.3.2 Controller for decay rate control
167(1)
14.3.3 Controller for constraint on the control value
167(1)
14.3.4 Comparison to other control solutions
167(4)
14.4 Observer-based output feedback control design
171(2)
14.4.1 An alternative TP model
171(1)
14.4.2 Control system design
172(1)
14.4.3 Control performance
173(1)
14.5 Convex hull manipulation
173(4)
14.6 Convex hull geometry
177(4)
14.6.1 Effects on LMI-based controller performance
177(1)
14.6.2 Effects on LMI-based observer performance
178(3)
15 3-D Prototypical Aeroelastic Wing Section with Structural Nonlinearity
181(14)
15.1 Dynamics modeling
182(3)
15.2 The TP model
185(2)
15.3 LMI-based output feedback control design
187(8)
15.3.1 Controller 1: Asymptotic stabilization
188(2)
15.3.2 Controller 2: Constraint on the control value
190(1)
15.3.3 Control performance
190(5)
16 3-DoF Helicopter with Four Propellers
195(12)
16.1 Dynamics Modeling
195(5)
16.1.1 A simplified model
199(1)
16.1.2 Modeling of uncertainty
199(1)
16.2 The TP model
200(2)
16.3 Control system design
202(2)
16.4 Control performance
204(3)
17 Heavy Vehicle Rollover Prevention Problem
207(10)
17.1 Problem introduction
207(1)
17.2 A qLPV model for heavy vehicles
208(4)
17.3 The TP model
212(1)
17.4 Control system design and performance
212(5)
References 217(12)
Index 229
Peter Beranyi, Ph.D, D. Sc, is head of the Computer and Automation Research Institute of the Hungarian Academy of Sciences and a professor at the Budapest University of Technology and Economics. He received his D.Sc in Informatics, his Ph.D. in Electrical Engineering, his M.Sc. in Education of Engineering Science, and his M.Sc. in Electrical Engineering at Budapest University of Technology and Economics. His research interest is on LPV- and LMI-based control design, modeling based on TP functions, fuzzy modeling, fuzzy rule interpolation, and calculation complexity reduction of various model types. He has written 48 journal papers for 262 publications.



Yeung Yam, is a professor in the Department of Mechanical and Automation Engineering at the Chinese University of Hong Kong. He obtained his B.Sc. from the Chinese University of Hong Kong, his M.Sc. from the University of Akron, Ohio, USA and his M.Sc., D.Sc. from the Massachusetts Institute of Technology, Cambridge, Massachusetts, USA. He has published over 100 technical papers in various areas of research, including human skill acquisition and analysis, dynamics modeling, control, system identification, fuzzy approximation, and intelligent and autonomous systems.



Peter Valarki, is a professor at the Budapest University of Technology and Economics. He graduated in mechanical engineering in 1971 at the Faculty of Transportation Engineering at the Technical University of Budapest, now the Budapest University of Technology and Economics. He also earned his Ph.D., his C.Sc. and his D.Sc. He is a founding member of the Hungarian Academy of Engineering and the main topics of his research field are the stochastic control theory, statistical system identification, and computational intelligency. He is the co-author of 10 books and more than 250 other scientific and technical publications.