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.

• Author Biographies xvPreface xixAcknowledgments xxiiiAcronyms xxvNotation xxix1 Introduction 12 Motivation and Basic Construction of PID Passivity-based Control 52.1 L2-Stability and Output Regulation to Zero 62.2 Well-Posedness Conditions 92.3 PID-PBC and the Dissipation Obstacle 102.3.1 Passive systems and the dissipation obstacle 112.3.2 Steady-state operation and the dissipation obstacle 122.4 PI-PBC with y0 and Control by Interconnection 143 Use of Passivity for Analysis and Tuning of PIDs: Two Practical Examples 193.1 Tuning of the PI Gains for Control of Induction Motors 213.1.1 Problem formulation 233.1.2 Change of coordinates 273.1.3 Tuning rules and performance intervals 303.1.4 Concluding remarks 353.2 PI-PBC of a Fuel Cell System 363.2.1 Control problem formulation 413.2.2 Limitations of current controllers and the role of passivity 463.2.3 Model linearization and useful properties 483.2.4 Main result 503.2.5 An asymptotically stable PI-PBC 543.2.6 Simulation results 573.2.7 Concluding remarks and future work 584 PID-PBC for Nonzero Regulated Output Reference 614.1 PI-PBC for Global Tracking 634.1.1 PI global tracking problem 634.1.2 Construction of a shifted passive output 654.1.3 A PI global tracking controller 674.2 Conditions for Shifted Passivity of General Nonlinear Systems 684.2.1 Shifted passivity definition 694.2.2 Main results 704.3 Conditions for Shifted Passivity of port-Hamiltonian Systems 734.3.1 Problems formulation 744.3.2 Shifted passivity 754.3.3 Shifted passifiability via output-feedback 774.3.4 Stability of the forced equilibria 784.3.5 Application to quadratic pH systems 794.4 PI-PBC of Power Converters 814.4.1 Model of the power converters 814.4.2 Construction of a shifted passive output 824.4.3 PI stabilization 854.4.4 Application to a quadratic boost converter 864.5 PI-PBC of HVDC Power Systems 894.5.1 Background 894.5.2 Port-Hamiltonian model of the system 914.5.3 Main result 934.5.4 Relation of PI-PBC with Akagi’s PQ method 954.6 PI-PBC of Wind Energy Systems 964.6.1 Background 964.6.2 System model 984.6.3 Control problem formulation 1024.6.4 Proposed PI-PBC 1044.7 Shifted Passivity of PI-Controlled Permanent Magnet Synchronous Motors 1074.7.1 Background 1074.7.2 Motor models 1084.7.3 Problem formulation 1114.7.4 Main result 1134.7.5 Conclusions and future research 1145 Parameterization of All Passive Outputs for port-Hamiltonian Systems 1155.1 Parameterization of all Passive Outputs 1165.2 Some Particular Cases 1185.3 Two Additional Remarks 1205.4 Examples 1215.4.1 A level control system 1215.4.2 A microelectromechanical optical switch 1236 Lyapunov Stabilization of port-Hamiltonian Systems 1256.1 Generation of Lyapunov Functions 1276.1.1 Basic PDE 1286.1.2 Lyapunov stability analysis 1296.2 Explicit Solution of the PDE 1316.2.1 The power shaping output 1326.2.2 A more general solution 1336.2.3 On the use of multipliers 1356.3 Derivative Action on Relative Degree Zero Outputs 1376.3.1 Preservation of the port-Hamiltonian Structure of I-PBC 1386.3.2 Projection of the new passive output 1406.3.3 Lyapunov stabilization with the new PID-PBC 1416.4 Examples 1426.4.1 A microelectromechanical optical switch (continued) 1436.4.2 Boost converter 1446.4.3 2-dimensional controllable LTI systems 1466.4.4 Control by Interconnection vs PI-PBC 1486.4.5 The use of the derivative action 1507 Underactuated Mechanical Systems 1537.1 Historical Review and Chapter Contents 1537.1.1 Potential energy shaping of fully actuated systems 1547.1.2 Total energy shaping of underactuated systems 1567.1.3 Two formulations of PID-PBC 1577.2 Shaping the Energy with a PID 1587.3 PID-PBC of port-Hamiltonian Systems 1617.3.1 Assumptions on the system 1617.3.2 A suitable change of coordinates 1637.3.3 Generating new passive outputs 1657.3.4 Projection of the total storage function 1677.3.5 Main stability result 1697.4 PID-PBC of Euler-Lagrange Systems 1727.4.1 Passive outputs for Euler-Lagrange systems 1737.4.2 Passive outputs for Euler-Lagrange systems in Spong’s normal form 1757.5 Extensions 1767.5.1 Tracking constant speed trajectories 1767.5.2 Removing the cancellation of Va(qa) 1787.5.3 Enlarging the class of integral actions 1797.6 Examples 1807.6.1 Tracking for inverted pendulum on a cart 1807.6.2 Cart-pendulum on an inclined plane 1827.7 PID-PBC of Constrained Euler-Lagrange Systems 1907.7.1 System model and problem formulation 1917.7.2 Reduced purely differential model 1957.7.3 Design of the PID-PBC 1967.7.4 Main stability result 1997.7.5 Simulation Results 2007.7.6 Experimental Results 2028 Disturbance Rejection in port-Hamiltonian Systems 2078.1 Some Remarks On Notation and Assignable Equilibria 2098.1.1 Notational simplifications 2098.1.2 Assignable equilibria for constant d 2108.2 Integral Action on the Passive Output 2118.3 Solution Using Coordinate Changes 2148.3.1 A feedback equivalence problem 2148.3.2 Local solutions of the feedback equivalent problem 2178.3.3 Stability of the closed–loop 2198.4 Solution Using Nonseparable Energy Functions 2218.4.1 Matched and unmatched disturbances 2228.4.2 Robust matched disturbance rejection 2258.5 Robust Integral Action for Fully Actuated Mechanical Systems 2308.6 Robust Integral Action for Underactuated Mechanical Systems 2378.6.1 Standard interconnection and damping assignment PBC 2398.6.2 Main result 2418.7 A New Robust Integral Action for Underactuated Mechanical Systems 2448.7.1 System model 2448.7.2 Coordinate transformation 2458.7.3 Verification of requisites 2468.7.4 Robust integral action controller 2488.8 Examples 2488.8.1 Mechanical systems with constant inertia matrix 2498.8.2 Prismatic robot 2508.8.3 The Acrobot system 2558.8.4 Disk on disk system 2608.8.5 Damped vertical take-off and landing aircraft 265A Passivity and Stability Theory for State-Space Systems 269A.1 Characterization of Passive Systems 269A.2 Passivity Theorem 271A.3 Lyapunov Stability of Passive Systems 273B Two Stability Results and Assignable Equilibria 275B.1 Two Stability Results 275B.2 Assignable Equilibria 276C Some Differential Geometric Results 279C.1 Invariant Manifolds 279C.2 Gradient Vector Fields 280C.3 A Technical Lemma 281D Port-Hamiltonian Systems 283D.1 Definition of port-Hamiltonian Systems and Passivity Property 283D.2 Physical Examples 284D.3 Euler-Lagrange Models 286D.4 Port-Hamiltonian Representation of GAS Systems 288Index 309

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.

• Author Biographies xvPreface xixAcknowledgments xxiiiAcronyms xxvNotation xxix1 Introduction 12 Motivation and Basic Construction of PID Passivity-based Control 52.1 L2-Stability and Output Regulation to Zero 62.2 Well-Posedness Conditions 92.3 PID-PBC and the Dissipation Obstacle 102.3.1 Passive systems and the dissipation obstacle 112.3.2 Steady-state operation and the dissipation obstacle 122.4 PI-PBC with y0 and Control by Interconnection 143 Use of Passivity for Analysis and Tuning of PIDs: Two Practical Examples 193.1 Tuning of the PI Gains for Control of Induction Motors 213.1.1 Problem formulation 233.1.2 Change of coordinates 273.1.3 Tuning rules and performance intervals 303.1.4 Concluding remarks 353.2 PI-PBC of a Fuel Cell System 363.2.1 Control problem formulation 413.2.2 Limitations of current controllers and the role of passivity 463.2.3 Model linearization and useful properties 483.2.4 Main result 503.2.5 An asymptotically stable PI-PBC 543.2.6 Simulation results 573.2.7 Concluding remarks and future work 584 PID-PBC for Nonzero Regulated Output Reference 614.1 PI-PBC for Global Tracking 634.1.1 PI global tracking problem 634.1.2 Construction of a shifted passive output 654.1.3 A PI global tracking controller 674.2 Conditions for Shifted Passivity of General Nonlinear Systems 684.2.1 Shifted passivity definition 694.2.2 Main results 704.3 Conditions for Shifted Passivity of port-Hamiltonian Systems 734.3.1 Problems formulation 744.3.2 Shifted passivity 754.3.3 Shifted passifiability via output-feedback 774.3.4 Stability of the forced equilibria 784.3.5 Application to quadratic pH systems 794.4 PI-PBC of Power Converters 814.4.1 Model of the power converters 814.4.2 Construction of a shifted passive output 824.4.3 PI stabilization 854.4.4 Application to a quadratic boost converter 864.5 PI-PBC of HVDC Power Systems 894.5.1 Background 894.5.2 Port-Hamiltonian model of the system 914.5.3 Main result 934.5.4 Relation of PI-PBC with Akagi’s PQ method 954.6 PI-PBC of Wind Energy Systems 964.6.1 Background 964.6.2 System model 984.6.3 Control problem formulation 1024.6.4 Proposed PI-PBC 1044.7 Shifted Passivity of PI-Controlled Permanent Magnet Synchronous Motors 1074.7.1 Background 1074.7.2 Motor models 1084.7.3 Problem formulation 1114.7.4 Main result 1134.7.5 Conclusions and future research 1145 Parameterization of All Passive Outputs for port-Hamiltonian Systems 1155.1 Parameterization of all Passive Outputs 1165.2 Some Particular Cases 1185.3 Two Additional Remarks 1205.4 Examples 1215.4.1 A level control system 1215.4.2 A microelectromechanical optical switch 1236 Lyapunov Stabilization of port-Hamiltonian Systems 1256.1 Generation of Lyapunov Functions 1276.1.1 Basic PDE 1286.1.2 Lyapunov stability analysis 1296.2 Explicit Solution of the PDE 1316.2.1 The power shaping output 1326.2.2 A more general solution 1336.2.3 On the use of multipliers 1356.3 Derivative Action on Relative Degree Zero Outputs 1376.3.1 Preservation of the port-Hamiltonian Structure of I-PBC 1386.3.2 Projection of the new passive output 1406.3.3 Lyapunov stabilization with the new PID-PBC 1416.4 Examples 1426.4.1 A microelectromechanical optical switch (continued) 1436.4.2 Boost converter 1446.4.3 2-dimensional controllable LTI systems 1466.4.4 Control by Interconnection vs PI-PBC 1486.4.5 The use of the derivative action 1507 Underactuated Mechanical Systems 1537.1 Historical Review and Chapter Contents 1537.1.1 Potential energy shaping of fully actuated systems 1547.1.2 Total energy shaping of underactuated systems 1567.1.3 Two formulations of PID-PBC 1577.2 Shaping the Energy with a PID 1587.3 PID-PBC of port-Hamiltonian Systems 1617.3.1 Assumptions on the system 1617.3.2 A suitable change of coordinates 1637.3.3 Generating new passive outputs 1657.3.4 Projection of the total storage function 1677.3.5 Main stability result 1697.4 PID-PBC of Euler-Lagrange Systems 1727.4.1 Passive outputs for Euler-Lagrange systems 1737.4.2 Passive outputs for Euler-Lagrange systems in Spong’s normal form 1757.5 Extensions 1767.5.1 Tracking constant speed trajectories 1767.5.2 Removing the cancellation of Va(qa) 1787.5.3 Enlarging the class of integral actions 1797.6 Examples 1807.6.1 Tracking for inverted pendulum on a cart 1807.6.2 Cart-pendulum on an inclined plane 1827.7 PID-PBC of Constrained Euler-Lagrange Systems 1907.7.1 System model and problem formulation 1917.7.2 Reduced purely differential model 1957.7.3 Design of the PID-PBC 1967.7.4 Main stability result 1997.7.5 Simulation Results 2007.7.6 Experimental Results 2028 Disturbance Rejection in port-Hamiltonian Systems 2078.1 Some Remarks On Notation and Assignable Equilibria 2098.1.1 Notational simplifications 2098.1.2 Assignable equilibria for constant d 2108.2 Integral Action on the Passive Output 2118.3 Solution Using Coordinate Changes 2148.3.1 A feedback equivalence problem 2148.3.2 Local solutions of the feedback equivalent problem 2178.3.3 Stability of the closed–loop 2198.4 Solution Using Nonseparable Energy Functions 2218.4.1 Matched and unmatched disturbances 2228.4.2 Robust matched disturbance rejection 2258.5 Robust Integral Action for Fully Actuated Mechanical Systems 2308.6 Robust Integral Action for Underactuated Mechanical Systems 2378.6.1 Standard interconnection and damping assignment PBC 2398.6.2 Main result 2418.7 A New Robust Integral Action for Underactuated Mechanical Systems 2448.7.1 System model 2448.7.2 Coordinate transformation 2458.7.3 Verification of requisites 2468.7.4 Robust integral action controller 2488.8 Examples 2488.8.1 Mechanical systems with constant inertia matrix 2498.8.2 Prismatic robot 2508.8.3 The Acrobot system 2558.8.4 Disk on disk system 2608.8.5 Damped vertical take-off and landing aircraft 265A Passivity and Stability Theory for State-Space Systems 269A.1 Characterization of Passive Systems 269A.2 Passivity Theorem 271A.3 Lyapunov Stability of Passive Systems 273B Two Stability Results and Assignable Equilibria 275B.1 Two Stability Results 275B.2 Assignable Equilibria 276C Some Differential Geometric Results 279C.1 Invariant Manifolds 279C.2 Gradient Vector Fields 280C.3 A Technical Lemma 281D Port-Hamiltonian Systems 283D.1 Definition of port-Hamiltonian Systems and Passivity Property 283D.2 Physical Examples 284D.3 Euler-Lagrange Models 286D.4 Port-Hamiltonian Representation of GAS Systems 288Index 309

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.

• Author Biographies xvPreface xixAcknowledgments xxiiiAcronyms xxvNotation xxix1 Introduction 12 Motivation and Basic Construction of PID Passivity-based Control 52.1 L2-Stability and Output Regulation to Zero 62.2 Well-Posedness Conditions 92.3 PID-PBC and the Dissipation Obstacle 102.3.1 Passive systems and the dissipation obstacle 112.3.2 Steady-state operation and the dissipation obstacle 122.4 PI-PBC with y0 and Control by Interconnection 143 Use of Passivity for Analysis and Tuning of PIDs: Two Practical Examples 193.1 Tuning of the PI Gains for Control of Induction Motors 213.1.1 Problem formulation 233.1.2 Change of coordinates 273.1.3 Tuning rules and performance intervals 303.1.4 Concluding remarks 353.2 PI-PBC of a Fuel Cell System 363.2.1 Control problem formulation 413.2.2 Limitations of current controllers and the role of passivity 463.2.3 Model linearization and useful properties 483.2.4 Main result 503.2.5 An asymptotically stable PI-PBC 543.2.6 Simulation results 573.2.7 Concluding remarks and future work 584 PID-PBC for Nonzero Regulated Output Reference 614.1 PI-PBC for Global Tracking 634.1.1 PI global tracking problem 634.1.2 Construction of a shifted passive output 654.1.3 A PI global tracking controller 674.2 Conditions for Shifted Passivity of General Nonlinear Systems 684.2.1 Shifted passivity definition 694.2.2 Main results 704.3 Conditions for Shifted Passivity of port-Hamiltonian Systems 734.3.1 Problems formulation 744.3.2 Shifted passivity 754.3.3 Shifted passifiability via output-feedback 774.3.4 Stability of the forced equilibria 784.3.5 Application to quadratic pH systems 794.4 PI-PBC of Power Converters 814.4.1 Model of the power converters 814.4.2 Construction of a shifted passive output 824.4.3 PI stabilization 854.4.4 Application to a quadratic boost converter 864.5 PI-PBC of HVDC Power Systems 894.5.1 Background 894.5.2 Port-Hamiltonian model of the system 914.5.3 Main result 934.5.4 Relation of PI-PBC with Akagi’s PQ method 954.6 PI-PBC of Wind Energy Systems 964.6.1 Background 964.6.2 System model 984.6.3 Control problem formulation 1024.6.4 Proposed PI-PBC 1044.7 Shifted Passivity of PI-Controlled Permanent Magnet Synchronous Motors 1074.7.1 Background 1074.7.2 Motor models 1084.7.3 Problem formulation 1114.7.4 Main result 1134.7.5 Conclusions and future research 1145 Parameterization of All Passive Outputs for port-Hamiltonian Systems 1155.1 Parameterization of all Passive Outputs 1165.2 Some Particular Cases 1185.3 Two Additional Remarks 1205.4 Examples 1215.4.1 A level control system 1215.4.2 A microelectromechanical optical switch 1236 Lyapunov Stabilization of port-Hamiltonian Systems 1256.1 Generation of Lyapunov Functions 1276.1.1 Basic PDE 1286.1.2 Lyapunov stability analysis 1296.2 Explicit Solution of the PDE 1316.2.1 The power shaping output 1326.2.2 A more general solution 1336.2.3 On the use of multipliers 1356.3 Derivative Action on Relative Degree Zero Outputs 1376.3.1 Preservation of the port-Hamiltonian Structure of I-PBC 1386.3.2 Projection of the new passive output 1406.3.3 Lyapunov stabilization with the new PID-PBC 1416.4 Examples 1426.4.1 A microelectromechanical optical switch (continued) 1436.4.2 Boost converter 1446.4.3 2-dimensional controllable LTI systems 1466.4.4 Control by Interconnection vs PI-PBC 1486.4.5 The use of the derivative action 1507 Underactuated Mechanical Systems 1537.1 Historical Review and Chapter Contents 1537.1.1 Potential energy shaping of fully actuated systems 1547.1.2 Total energy shaping of underactuated systems 1567.1.3 Two formulations of PID-PBC 1577.2 Shaping the Energy with a PID 1587.3 PID-PBC of port-Hamiltonian Systems 1617.3.1 Assumptions on the system 1617.3.2 A suitable change of coordinates 1637.3.3 Generating new passive outputs 1657.3.4 Projection of the total storage function 1677.3.5 Main stability result 1697.4 PID-PBC of Euler-Lagrange Systems 1727.4.1 Passive outputs for Euler-Lagrange systems 1737.4.2 Passive outputs for Euler-Lagrange systems in Spong’s normal form 1757.5 Extensions 1767.5.1 Tracking constant speed trajectories 1767.5.2 Removing the cancellation of Va(qa) 1787.5.3 Enlarging the class of integral actions 1797.6 Examples 1807.6.1 Tracking for inverted pendulum on a cart 1807.6.2 Cart-pendulum on an inclined plane 1827.7 PID-PBC of Constrained Euler-Lagrange Systems 1907.7.1 System model and problem formulation 1917.7.2 Reduced purely differential model 1957.7.3 Design of the PID-PBC 1967.7.4 Main stability result 1997.7.5 Simulation Results 2007.7.6 Experimental Results 2028 Disturbance Rejection in port-Hamiltonian Systems 2078.1 Some Remarks On Notation and Assignable Equilibria 2098.1.1 Notational simplifications 2098.1.2 Assignable equilibria for constant d 2108.2 Integral Action on the Passive Output 2118.3 Solution Using Coordinate Changes 2148.3.1 A feedback equivalence problem 2148.3.2 Local solutions of the feedback equivalent problem 2178.3.3 Stability of the closed–loop 2198.4 Solution Using Nonseparable Energy Functions 2218.4.1 Matched and unmatched disturbances 2228.4.2 Robust matched disturbance rejection 2258.5 Robust Integral Action for Fully Actuated Mechanical Systems 2308.6 Robust Integral Action for Underactuated Mechanical Systems 2378.6.1 Standard interconnection and damping assignment PBC 2398.6.2 Main result 2418.7 A New Robust Integral Action for Underactuated Mechanical Systems 2448.7.1 System model 2448.7.2 Coordinate transformation 2458.7.3 Verification of requisites 2468.7.4 Robust integral action controller 2488.8 Examples 2488.8.1 Mechanical systems with constant inertia matrix 2498.8.2 Prismatic robot 2508.8.3 The Acrobot system 2558.8.4 Disk on disk system 2608.8.5 Damped vertical take-off and landing aircraft 265A Passivity and Stability Theory for State-Space Systems 269A.1 Characterization of Passive Systems 269A.2 Passivity Theorem 271A.3 Lyapunov Stability of Passive Systems 273B Two Stability Results and Assignable Equilibria 275B.1 Two Stability Results 275B.2 Assignable Equilibria 276C Some Differential Geometric Results 279C.1 Invariant Manifolds 279C.2 Gradient Vector Fields 280C.3 A Technical Lemma 281D Port-Hamiltonian Systems 283D.1 Definition of port-Hamiltonian Systems and Passivity Property 283D.2 Physical Examples 284D.3 Euler-Lagrange Models 286D.4 Port-Hamiltonian Representation of GAS Systems 288Index 309