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

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 Equilibria B.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

List of Tables

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

List of Illustrations

1 Chapter 2Figure 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

and position of the hand

, and (c, d) ...Figure 8.3 (a, b) States of the controller, (c, d) control torque on the arm...Figure 8.4 (a, b) Angle of the arm

and position of the hand

, and (c, d) ...Figure 8.5 (a, b) States of the controller, (c, d) control torque on the arm...Figure 8.6 Time histories of the Acrobot angles

and

with the IDA‐PBC plu...Figure 8.7 Time histories of the Acrobot angular velocities

and

with the...Figure 8.8 Time history of the matched disturbance

, and the controller sta...Figure

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