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E-raamat: PID Passivity-Based Control of Nonlinear Systems with Applications

(University of Groningen, The Netherlands), (Instituto Tecnologico Autonomo de Mexico), (Instituto Tecnologico Autonomo de Mexico), (The University of Newcastle, Australia)
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  • Ilmumisaeg: 03-Sep-2021
  • Kirjastus: Wiley-IEEE Press
  • Keel: eng
  • ISBN-13: 9781119694182
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PID Passivity-Based Control of Nonlinear Systems with ApplicationsSuurem pilt
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 03-Sep-2021
  • Kirjastus: Wiley-IEEE Press
  • Keel: eng
  • ISBN-13: 9781119694182
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"This book provides the theoretical foundations required to design this class of controllers in diverse practical control applications. To that end, the authors present several systematic methodologies of control design and their formal justification in term of passivity and Lyapunov Theory. The first chapters cover the general framework for PID-PBC design for nonlinear systems, and subsequent chapters introduce the specialization of the control design to broad range of practical applications, including power electronic, electrical drives, electrical circuits and mechanical and process control systems. Additionally, fundamental concepts related to PID regulators, passivity theory, Lyapunov stability and port-Hamiltonian systems are revisited."--

Explore the foundational and advanced subjects associated with proportional-integral-derivative controllers from leading authors in the field 

In PID Passivity-Based Control of Nonlinear Systems with Applications, expert researchers and authors Drs. Romeo Ortega, Jose Guadalupe Romero, Pablo Borja, and Alejandro Donaire deliver a comprehensive and detailed discussion of the most crucial and relevant concepts in the analysis and design of proportional-integral-derivative controllers using passivity techniques. The accomplished authors present a formal treatment of the recent research in the area and offer readers practical applications of the developed methods to physical systems, including electrical, mechanical, electromechanical, power electronics, and process control. 

The book offers the material with minimal mathematical background, making it relevant to a wide audience. Familiarity with the theoretical tools reported in the control systems literature is not necessary to understand the concepts contained within. You’ll learn about a wide range of concepts, including disturbance rejection via PID control, PID control of mechanical systems, and Lyapunov stability of PID controllers. 

Readers will also benefit from the inclusion of: 

  • A thorough introduction to a class of physical systems described in the port-Hamiltonian form and a presentation of the systematic procedures to design PID-PBC for them 
  • An exploration of the applications to electrical, electromechanical, and process control systems of Lyapunov stability of PID controllers 
  • Practical discussions of the regulation and tracking of bilinear systems via PID control and their application to power electronics and thermal process control 
  • A concise treatment of the characterization of passive outputs, incremental models, and Port Hamiltonian and Euler-Lagrange systems 

Perfect for senior undergraduate and graduate students studying control systems, PID Passivity-Based Control will also earn a place in the libraries of engineers who practice in this area and seek a one-stop and fully updated reference on the subject. 

Author Biographies xiii
Preface xvii
Acknowledgments xxi
Acronyms xxiii
Notation xxv
1 Introduction
1(4)
2 Motivation and Basic Construction of PID Passivity-Based Control
5(10)
2.1 L2-Stability and Output Regulation to Zero
5(2)
2.2 Well-Posedness Conditions
7(1)
2.3 PID-PBC and the Dissipation Obstacle
8(2)
2.3.1 Passive Systems and the Dissipation Obstacle
8(1)
2.3.2 Steady-State Operation and the Dissipation Obstacle
9(1)
2.4 PI-PBC with y0 and Control by Interconnection
10(5)
Bibliography
12(3)
3 Use of Passivity for Analysis and Tuning of PIDs: Two Practical Examples
15(32)
3.1 Tuning of the PI Gains for Control of Induction Motors
16(10)
3.1.1 Problem Formulation
18(2)
3.1.2 Change of Coordinates
20(2)
3.1.3 Tuning Rules and Performance Intervals
22(4)
3.1.4 Concluding Remarks
26(1)
3.2 PI-PBC of a Fuel Cell System
26(21)
3.2.1 Control Problem Formulation
29(4)
3.2.2 Limitations of Current Controllers and the Role of Passivity
33(1)
3.2.3 Model Linearization and Useful Properties
34(2)
3.2.4 Main Result
36(2)
3.2.5 An Asymptotically Stable PI-PBC
38(2)
3.2.6 Simulation Results
40(2)
3.2.7 Concluding Remarks and Future Work
42(2)
Bibliography
44(3)
4 PIO-PBC for Nonzero Regulated Output Reference
47(40)
4.1 PI-PBC for Global Tracking
48(4)
4.1.1 PI Global Tracking Problem
49(1)
4.1.2 Construction of a Shifted Passive Output
50(1)
4.1.3 A PI Global Tracking Controller
51(1)
4.2 Conditions for Shifted Passivity of General Nonlinear Systems
52(3)
4.2.1 Shifted Passivity Definition
52(1)
4.2.2 Main Results
53(2)
4.3 Conditions for Shifted Passivity of Port-Hamiltonian Systems
55(5)
4.3.1 Problems Formulation
55(2)
4.3.2 Shifted Passivity
57(1)
4.3.3 Shifted Passifiability via Output-Feedback
58(1)
4.3.4 Stability of the Forced Equilibria
58(1)
4.3.5 Application to Quadratic pH Systems
59(1)
4.4 PI-PBC of Power Converters
60(5)
4.4.1 Model of the Power Converters
60(1)
4.4.2 Construction of a Shifted Passive Output
61(1)
4.4.3 PI Stabilization
62(1)
4.4.4 Application to a Quadratic Boost Converter
63(2)
4.5 PI-PBC of HVDC Power Systems
65(5)
4.5.1 Background
65(2)
4.5.2 Port-Hamiltonian Model of the System
67(1)
4.5.3 Main Result
68(1)
4.5.4 Relation of PI-PBC with Akagi's PQ Method
69(1)
4.6 PI-PBC of Wind Energy Systems
70(7)
4.6.1 Background
70(1)
4.6.2 System Model
71(3)
4.6.3 Control Problem Formulation
74(1)
4.6.4 Proposed PI-PBC
75(2)
4.7 Shifted Passivity of Pl-Controlled Permanent Magnet Synchronous Motors
77(10)
4.7.1 Background
77(1)
4.7.2 Motor Models
78(2)
4.7.3 Problem Formulation
80(1)
4.7.4 Main Result
81(1)
4.7.5 Conclusions and Future Research
81(1)
Bibliography
82(5)
5 Parameterization of All Passive Outputs for Port-Hamiltonian Systems
87(8)
5.1 Parameterization of All Passive Outputs
87(2)
5.2 Some Particular Cases
89(1)
5.3 Two Additional Remarks
90(1)
5.4 Examples
91(4)
5.4.1 A Level Control System
91(1)
5.4.2 A Microelectromechanical Optical Switch
92(1)
Bibliography
93(2)
6 Lyapunov Stabilization of Port-Hamiltonian Systems
95(20)
6.1 Generation of Lyapunov Functions
96(3)
6.1.1 Basic PDE
97(1)
6.1.2 Lyapunov Stability Analysis
98(1)
6.2 Explicit Solution of the PDE
99(4)
6.2.1 The Power Shaping Output
99(1)
6.2.2 A More General Solution
100(1)
6.2.3 On the Use of Multipliers
101(2)
6.3 Derivative Action on Relative Degree Zero Outputs
103(3)
6.3.1 Preservation of the Port-Hamiltonian Structure of I-PBC
103(1)
6.3.2 Projection of the New Passive Output
104(1)
6.3.3 Lyapunov Stabilization with the New PID-PBC
105(1)
6.4 Examples
106(9)
6.4.1 A Microelectromechanical Optical Switch (Continued)
106(1)
6.4.2 Boost Converter
107(2)
6.4.3 Two-Dimensional Controllable LTI Systems
109(1)
6.4.4 Control by Interconnection vs. PI-PBC
110(1)
6.4.5 The Use of the Derivative Action
111(1)
Bibliography
112(3)
7 Underactuated Mechanical Systems
115(38)
7.1 Historical Review and
Chapter Contents
115(3)
7.1.1 Potential Energy Shaping of Fully Actuated Systems
115(2)
7.1.2 Total Energy Shaping of Underactuated Systems
117(1)
7.1.3 Two Formulations of PID-PBC
117(1)
7.2 Shaping the Energy with a PID
118(2)
7.3 PID-PBC of Port-Hamiltonian Systems
120(7)
7.3.1 Assumptions on the System
120(1)
7.3.2 A Suitable Change of Coordinates
121(1)
7.3.3 Generating New Passive Outputs
122(2)
7.3.4 Projection of the Total Storage Function
124(1)
7.3.5 Main Stability Result
125(2)
7.4 PID-PBC of Euler-Lagrange Systems
127(2)
7.4.1 Passive Outputs for Euler-Lagrange Systems
127(1)
7.4.2 Passive Outputs for Euler-Lagrange Systems in Spong's Normal Form
128(1)
7.5 Extensions
129(2)
7.5.1 Tracking Constant Speed Trajectories
129(1)
7.5.2 Removing the Cancellation of Va(qa)
130(1)
7.5.3 Enlarging the Class of Integral Actions
131(1)
7.6 Examples
131(6)
7.6.1 Tracking for Inverted Pendulum on a Cart
132(1)
7.6.2 Cart-Pendulum on an Inclined Plane
133(4)
1.1 PID-PBC of Constrained Euler-Lagrange Systems
137(16)
7.7.1 System Model and Problem Formulation
140(2)
1.1.2 Reduced Purely Differential Model
142(1)
7.7.3 Design of the PID-PBC
143(2)
1.1.4 Main Stability Result
145(1)
7.7.5 Simulation Results
146(1)
7.7.6 Experimental Results
147(3)
Bibliography
150(3)
8 Disturbance Rejection in Port-Hamiltonian Systems
153(44)
8.1 Some Remarks on Notation and Assignable Equilibria
154(2)
8.1.1 Notational Simplifications
154(1)
8.1.2 Assignable Equilibria for Constant d
155(1)
8.2 Integral Action on the Passive Output
156(1)
8.3 Solution Using Coordinate Changes
157(5)
8.3.1 A Feedback Equivalence Problem
158(2)
8.3.2 Local Solutions of the Feedback Equivalent Problem
160(1)
8.3.3 Stability of the Closed-Loop
161(1)
8.4 Solution Using Nonseparable Energy Functions
162(5)
8.4.1 Matched and Unmatched Disturbances
162(2)
8.4.2 Robust Matched Disturbance Rejection
164(3)
8.5 Robust Integral Action for Fully Actuated Mechanical Systems
167(5)
8.6 Robust Integral Action for Underactuated Mechanical Systems
172(5)
8.6.1 Standard Interconnection and Damping Assignment PBC
173(2)
8.6.2 Main Result
175(2)
8.7 A New Robust Integral Action for Underactuated Mechanical Systems
177(2)
8.7.1 System Model
177(1)
8.7.2 Coordinate Transformation
177(1)
8.7.3 Verification of Requisites
178(1)
8.7 A Robust Integral Action Controller
179(1)
8.8 Examples
179(18)
8.8.1 Mechanical Systems with Constant Inertia Matrix
180(1)
8.8.2 Prismatic Robot
180(4)
8.8.3 The Acrobot System
184(4)
8.8.4 Disk on Disk System
188(3)
8.8.5 Damped Vertical Take-off and Landing Aircraft
191(2)
Bibliography
193(4)
Appendix A Passivity and Stability Theory for State-Space Systems
197(4)
A.1 Characterization of Passive Systems
197(1)
A.2 Passivity Theorem
198(1)
A.3 Lyapunov Stability of Passive Systems
199(2)
Bibliography
200(1)
Appendix B Two Stability Results and Assignable Equilibria
201(2)
B.1 Two Stability Results
201(1)
B.2 Assignable Equilibria
202(1)
Bibliography
202(1)
Appendix C Some Differential Geometric Results
203(2)
C.1 Invariant Manifolds
203(1)
C.2 Gradient Vector Fields
204(1)
C.3 A Technical Lemma
204(1)
Bibliography
204(1)
Appendix D Port-Hamiltonian Systems
205(4)
D.1 Definition of Port-Hamiltonian Systems and Passivity Property
205(1)
D.2 Physical Examples
206(1)
D.2.1 Mechanical Systems
206(1)
D.2.2 Electromechanical Systems
206(1)
D.2.3 Power Converters
207(1)
D.3 Euler-Lagrange Models
207(1)
D.4 Port-Hamiltonian Representation of GAS Systems
208(1)
Bibliography
208(1)
Index 209
ROMEO ORTEGA, PhD, is a full-time professor and researcher at the Mexico Autonomous Institute of Technology, Mexico. He is a Fellow Member of the IEEE since 1999. He has served as chairman on several IFAC and IEEE committees and participated in various editorial boards of international journals.

JOSÉ GUADALUPE ROMERO, PhD, is a full-time professor and researcher at the Mexico Autonomous Institute of Technology, Mexico. His research interests are focused on nonlinear and adaptive control, stability analysis, and the state estimation problem.

PABLO BORJA, PhD, is a Postdoctoral researcher at the University of Groningen, Netherlands. His research interests encompass nonlinear systems, passivity-based control, and model reduction.

ALEJANDRO DONAIRE, PhD, is a full-time academic at the University of Newcastle, Australia. His research interests include nonlinear systems, passivity, and control theory.
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