Passivity-based Control of Euler-Lagrange Systems:

xiv
CONTENTS
4.1 A rotational/translational proof mass actuator . . . . . . . . . 30
4.2 Levitated ball . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.3 Flexible joints robots . . . . . . . . . . . . . . . . . . . . . . . 34
4.4 The Dung system . . . . . . . . . . . . . . . . . . . . . . . . 35
4.5 A marine surface vessel . . . . . . . . . . . . . . . . . . . . . . 36
5 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
I Mechanical Systems 39
3 Set-point regulation 41
1 State feedback control of fully-actuated systems . . . . . . . . . . . . 42
1.1 A basic result: The PD controller . . . . . . . . . . . . . . . . 42
1.2 An introductory example . . . . . . . . . . . . . . . . . . . . . 44
1.3 Physical interpretation and literature review . . . . . . . . . . 46
2 Output feedback stabilization of underactuated systems . . . . . . . . 48
2.1 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.2 Problem formulation . . . . . . . . . . . . . . . . . . . . . . . 48
2.3 Euler{Lagrange controllers . . . . . . . . . . . . . . . . . . . . 49
2.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3 Bounded output feedback regulation . . . . . . . . . . . . . . . . . . 61
3.1 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.2 Problem formulation . . . . . . . . . . . . . . . . . . . . . . . 61
3.3 Globally stabilizing saturated EL controllers . . . . . . . . . . 63
3.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4 Set-point regulation under parameter uncertainty . . . . . . . . . . . 75
4.1 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.2 Adaptive control . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.3 Linear PID control . . . . . . . . . . . . . . . . . . . . . . . . 79
4.4 Nonlinear PID control . . . . . . . . . . . . . . . . . . . . . . 82
4.5 Output feedback regulation: The PI 2 Dcontroller . . . . . . . 85
5 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91