Romeo Ortega - PID Passivity-Based Control of Nonlinear Systems with Applications

1 Cover

2 Series Page IEEE Press 445 Hoes Lane Piscataway, NJ 08854 IEEE Press Editorial Board Ekram Hossain, Editor in Chief Jón Atli Benediktsson Xiaoou Li Jeffrey Reed Anjan Bose Lian Yong Diomidis Spinellis David Alan Grier Andreas Molisch Sarah Spurgeon Elya B. Joffe Saeid Nahavandi Ahmet Murat Tekalp

3 Title Page PID Passivity‐Based Control of Nonlinear Systems with Applications Romeo OrtegaInstituto Tecnológico Autónomo de México José Guadalupe RomeroInstituto Tecnológico Autónomo de México Pablo BorjaUniversity of Groningen Alejandro DonaireThe University of Newcastle

4 Copyright

5 Dedication

6 Author Biographies

7 Preface Bibliography

8 Acknowledgments

9 Acronyms

10 Notation

11 1 Introduction

12 2 Motivation and Basic Construction of PID Passivity‐Based Control 2.1 ‐Stability and Output Regulation to Zero 2.2 Well‐Posedness Conditions 2.3 PID‐PBC and the Dissipation Obstacle 2.4 PI‐PBC with and Control by Interconnection Bibliography Notes

13 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 3.2 PI‐PBC of a Fuel Cell System Bibliography Notes

14 4 PID‐PBC for Nonzero Regulated Output Reference 4.1 PI‐PBC for Global Tracking 4.2 Conditions for Shifted Passivity of General Nonlinear Systems 4.3 Conditions for Shifted Passivity of Port‐Hamiltonian Systems 4.4 PI‐PBC of Power Converters 4.5 PI‐PBC of HVDC Power Systems 4.6 PI‐PBC of Wind Energy Systems 4.7 Shifted Passivity of PI‐Controlled Permanent Magnet Synchronous Motors Bibliography Notes

15 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 Bibliography Note

16 6 Lyapunov Stabilization of Port‐Hamiltonian Systems 6.1 Generation of Lyapunov Functions 6.2 Explicit Solution of the PDE 6.3 Derivative Action on Relative Degree Zero Outputs 6.4 Examples Bibliography Notes

17 7 Underactuated Mechanical Systems 7.1 Historical Review and Chapter Contents 7.2 Shaping the Energy with a PID 7.3 PID‐PBC of Port‐Hamiltonian Systems 7.4 PID‐PBC of Euler‐Lagrange Systems 7.5 Extensions 7.6 Examples 7.7 PID‐PBC of Constrained Euler–Lagrange Systems Bibliography Notes

18 8 Disturbance Rejection in Port‐Hamiltonian Systems 8.1 Some Remarks on Notation and Assignable Equilibria 8.2 Integral Action on the Passive Output 8.3 Solution Using Coordinate Changes 8.4 Solution Using Nonseparable Energy Functions 8.5 Robust Integral Action for Fully Actuated Mechanical Systems 8.6 Robust Integral Action for Underactuated Mechanical Systems 8.7 A New Robust Integral Action for Underactuated Mechanical Systems 8.8 Examples Bibliography Notes

19 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 Note

20 Appendix B Two Stability Results and Assignable EquilibriaB.1 Two Stability Results B.2 Assignable Equilibria Bibliography

21 Appendix C Some Differential Geometric Results C.1 Invariant Manifolds C.2 Gradient Vector Fields C.3 A Technical Lemma Bibliography

22 Appendix D Port–Hamiltonian Systems D.1 Definition of Port‐Hamiltonian Systems and Passivity Property D.2 Physical Examples D.3 Euler–Lagrange Models D.4 Port‐Hamiltonian Representation of GAS Systems Bibliography

23 Index

24 End User License Agreement

1 Chapter 7Table 7.1 System parameters.Table 7.2 Initial conditions.Table 7.3 Gains sets.

1 Chapter 2 Figure 2.1 Block diagram representation of the closed‐loop system of Proposi...

2 Chapter 3Figure 3.1 Feedback decomposition of the closed‐loop system.Figure 3.2 Compressor map: the curves are parameterized by , and grow when ...Figure 3.3 Convergence of the three states to the equilibrium point.Figure 3.4 Simulation response of the closed‐loop system with the PI control...

3 Chapter 4Figure 4.1 Schematic of the quadratic boost converter.Figure 4.2 Schematic diagram of the equivalent circuit of a VSR in frame....Figure 4.3 Wind energy system.Figure 4.4 Function .

4 Chapter 5Figure 5.1 Two‐tanks system.

5 Chapter 7Figure 7.1 Time histories of the (a) position of the cart and (b) angle of...Figure 7.2 Time histories of the (a) velocity of the cart and (b) angular ...Figure 7.3 Time histories of the (a) input force and (b) the nonlinear gai...Figure 7.4 Time histories of the (a) position of the cart and (b) angle of...Figure 7.5 Time histories of the (a) velocity of the cart and (b) angular ...Figure 7.6 Time histories of the (a) input force and (b) the nonlinear gai...Figure 7.7 Time histories of the (a) position of the cart and (b) angle of...Figure 7.8 Time histories of the (a) velocity of the cart and (b) angular ...Figure 7.9 Time histories of (a) the input force and (b) the nonlinear gai...Figure 7.10 Captures of a video animation of the cart‐pendulum on an incline...Figure 7.11 Single ultraflexible link with base excitation.Figure 7.12 Simulation results for .Figure 7.13 Simulation results for .Figure 7.14 Simulation results for .Figure 7.15 Inverted flexible pendulum.Figure 7.16 Comparison of simulation and experimental results for .

6 Chapter 8Figure 8.1 Graph of the state space showing two sheets of the invariant foli...Figure 8.2 (a, b) Angle of the arm