PID Passivity-Based Control of Nonlinear Systems with Applications

✍ Scribed by Romeo Ortega, Jose Guadalupe Romero, Pablo Borja, Alejandro Donaire

• Publisher: Wiley-IEEE Press
• Year: 2021
• Tongue: English
• Leaves: 243
• Edition: 1
• Category: Library

✦ Synopsis

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. 

✦ Table of Contents

Cover
Title Page
Copyright
Contents
Author Biographies
Preface
Acknowledgments
Acronyms
Notation
Chapter 1 Introduction
Chapter 2 Motivation and Basic Construction of PID Passivity‐Based Control
2.1 ℒ2‐Stability and Output Regulation to Zero
2.2 Well‐Posedness Conditions
2.3 PID‐PBC and the Dissipation Obstacle
2.3.1 Passive Systems and the Dissipation Obstacle
2.3.2 Steady‐State Operation and the Dissipation Obstacle
2.4 PI‐PBC with y0 and Control by Interconnection
Bibliography
Chapter 3 Use of Passivity for Analysis and Tuning of PIDs: Two Practical Examples
3.1 Tuning of the PI Gains for Control of Induction Motors
3.1.1 Problem Formulation
3.1.2 Change of Coordinates
3.1.3 Tuning Rules and Performance Intervals
3.1.4 Concluding Remarks
3.2 PI‐PBC of a Fuel Cell System
3.2.1 Control Problem Formulation
3.2.2 Limitations of Current Controllers and the Role of Passivity
3.2.3 Model Linearization and Useful Properties
3.2.4 Main Result
3.2.5 An Asymptotically Stable PI‐PBC
3.2.6 Simulation Results
3.2.7 Concluding Remarks and Future Work
Bibliography
Chapter 4 PID‐PBC for Nonzero Regulated Output Reference
4.1 PI‐PBC for Global Tracking
4.1.1 PI Global Tracking Problem
4.1.2 Construction of a Shifted Passive Output
4.1.3 A PI Global Tracking Controller
4.2 Conditions for Shifted Passivity of General Nonlinear Systems
4.2.1 Shifted Passivity Definition
4.2.2 Main Results
4.3 Conditions for Shifted Passivity of Port‐Hamiltonian Systems
4.3.1 Problems Formulation
4.3.2 Shifted Passivity
4.3.3 Shifted Passifiability via Output‐Feedback
4.3.4 Stability of the Forced Equilibria
4.3.5 Application to Quadratic pH Systems
4.4 PI‐PBC of Power Converters
4.4.1 Model of the Power Converters
4.4.2 Construction of a Shifted Passive Output
4.4.3 PI Stabilization
4.4.4 Application to a Quadratic Boost Converter
4.5 PI‐PBC of HVDC Power Systems
4.5.1 Background
4.5.2 Port‐Hamiltonian Model of the System
4.5.3 Main Result
4.5.4 Relation of PI‐PBC with Akagi's PQ Method
4.6 PI‐PBC of Wind Energy Systems
4.6.1 Background
4.6.2 System Model
4.6.3 Control Problem Formulation
4.6.4 Proposed PI‐PBC
4.7 Shifted Passivity of PI‐Controlled Permanent Magnet Synchronous Motors
4.7.1 Background
4.7.2 Motor Models
4.7.3 Problem Formulation
4.7.4 Main Result
4.7.5 Conclusions and Future Research
Bibliography
Chapter 5 Parameterization of All Passive Outputs for Port‐Hamiltonian Systems
5.1 Parameterization of All Passive Outputs
5.2 Some Particular Cases
5.3 Two Additional Remarks
5.4 Examples
5.4.1 A Level Control System
5.4.2 A Microelectromechanical Optical Switch
Bibliography
Chapter 6 Lyapunov Stabilization of Port‐Hamiltonian Systems
6.1 Generation of Lyapunov Functions
6.1.1 Basic PDE
6.1.2 Lyapunov Stability Analysis
6.2 Explicit Solution of the PDE
6.2.1 The Power Shaping Output
6.2.2 A More General Solution
6.2.3 On the Use of Multipliers
6.3 Derivative Action on Relative Degree Zero Outputs
6.3.1 Preservation of the Port‐Hamiltonian Structure of I‐PBC
6.3.2 Projection of the New Passive Output
6.3.3 Lyapunov Stabilization with the New PID‐PBC
6.4 Examples
6.4.1 A Microelectromechanical Optical Switch (Continued)
6.4.2 Boost Converter
6.4.3 Two‐Dimensional Controllable LTI Systems
6.4.4 Control by Interconnection vs. PI‐PBC
6.4.5 The Use of the Derivative Action
Bibliography
Chapter 7 Underactuated Mechanical Systems
7.1 Historical Review and Chapter Contents
7.1.1 Potential Energy Shaping of Fully Actuated Systems
7.1.2 Total Energy Shaping of Underactuated Systems
7.1.3 Two Formulations of PID‐PBC
7.2 Shaping the Energy with a PID
7.3 PID‐PBC of Port‐Hamiltonian Systems
7.3.1 Assumptions on the System
7.3.2 A Suitable Change of Coordinates
7.3.3 Generating New Passive Outputs
7.3.4 Projection of the Total Storage Function
7.3.5 Main Stability Result
7.4 PID‐PBC of Euler‐Lagrange Systems
7.4.1 Passive Outputs for Euler–Lagrange Systems
7.4.2 Passive Outputs for Euler–Lagrange Systems in Spong's Normal Form
7.5 Extensions
7.5.1 Tracking Constant Speed Trajectories
7.5.2 Removing the Cancellation of Va(qa)
7.5.3 Enlarging the Class of Integral Actions
7.6 Examples
7.6.1 Tracking for Inverted Pendulum on a Cart
7.6.2 Cart‐Pendulum on an Inclined Plane
7.7 PID‐PBC of Constrained Euler–Lagrange Systems
7.7.1 System Model and Problem Formulation
7.7.2 Reduced Purely Differential Model
7.7.3 Design of the PID‐PBC
7.7.4 Main Stability Result
7.7.5 Simulation Results
7.7.6 Experimental Results
Bibliography
Chapter 8 Disturbance Rejection in Port‐Hamiltonian Systems
8.1 Some Remarks on Notation and Assignable Equilibria
8.1.1 Notational Simplifications
8.1.2 Assignable Equilibria for Constant d
8.2 Integral Action on the Passive Output
8.3 Solution Using Coordinate Changes
8.3.1 A Feedback Equivalence Problem
8.3.2 Local Solutions of the Feedback Equivalent Problem
8.3.3 Stability of the Closed‐Loop
8.4 Solution Using Nonseparable Energy Functions
8.4.1 Matched and Unmatched Disturbances
8.4.2 Robust Matched Disturbance Rejection
8.5 Robust Integral Action for Fully Actuated Mechanical Systems
8.6 Robust Integral Action for Underactuated Mechanical Systems
8.6.1 Standard Interconnection and Damping Assignment PBC
8.6.2 Main Result
8.7 A New Robust Integral Action for Underactuated Mechanical Systems
8.7.1 System Model
8.7.2 Coordinate Transformation
8.7.3 Verification of Requisites
8.7.4 Robust Integral Action Controller
8.8 Examples
8.8.1 Mechanical Systems with Constant Inertia Matrix
8.8.2 Prismatic Robot
8.8.3 The Acrobot System
8.8.4 Disk on Disk System
8.8.5 Damped Vertical Take‐off and Landing Aircraft
Bibliography
Appendix A Passivity and Stability Theory for State‐Space Systems
A.1 Characterization of Passive Systems
A.2 Passivity Theorem
A.3 Lyapunov Stability of Passive Systems
Bibliography
Appendix B Two Stability Results and Assignable Equilibria
B.1 Two Stability Results
B.2 Assignable Equilibria
Bibliography
Appendix C Some Differential Geometric Results
C.1 Invariant Manifolds
C.2 Gradient Vector Fields
C.3 A Technical Lemma
Bibliography
Appendix D Port–Hamiltonian Systems
D.1 Definition of Port‐Hamiltonian Systems and Passivity Property
D.2 Physical Examples
D.2.1 Mechanical Systems
D.2.2 Electromechanical Systems
D.2.3 Power Converters
D.3 Euler–Lagrange Models
D.4 Port‐Hamiltonian Representation of GAS Systems
Bibliography
Index
EULA