Passivity-based Control of Euler-Lagrange Systems:

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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
CONTENTS xv 4 Trajectory tracking control 93 1 State feedback control of fully-actuated systems . . . . . . . . . . . . 94 1.1 The PD+ controller . . . . . . . . . . . . . . . . . . . . . . . . 95 1.2 The Slotine and Li controller . . . . . . . . . . . . . . . . . . . 96 2 Adaptive trajectory tracking . . . . . . . . . . . . . . . . . . . . . . . 97 2.1 Adaptive controller of Slotine and Li . . . . . . . . . . . . . . 97 2.2 A robust adaptive controller . . . . . . . . . . . . . . . . . . . 98 3 State feedback of underactuated systems . . . . . . . . . . . . . . . . 100 3.1 Model and problem formulation . . . . . . . . . . . . . . . . . 100 3.2 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . 101 3.3 A passivity{based controller . . . . . . . . . . . . . . . . . . . 102 3.4 Comparison with backstepping and cascaded designs . . . . . 104 3.5 Acontroller without jerk measurements . . . . . . . . . . . . . 105 4 Output feedback of fully-actuated systems . . . . . . . . . . . . . . . 108 4.1 Semiglobal tracking control of robot manipulators . . . . . . . 109 4.2 Discussion on global tracking . . . . . . . . . . . . . . . . . . 110 5 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 6 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 5 Adaptive disturbance attenuation: Friction compensation 115 1 Adaptive friction compensation . . . . . . . . . . . . . . . . . . . . . 116 1.1 The LuGre friction model . . . . . . . . . . . . . . . . . . . . 117 1.2 DC motor with friction . . . . . . . . . . . . . . . . . . . . . . 119 1.3 Robot manipulator . . . . . . . . . . . . . . . . . . . . . . . . 122 1.4 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 2 State-space passiable systems with disturbances . . . . . . . . . . . 127 2.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 2.2 A theorem for passiable ane nonlinear systems . . . . . . . 129 3 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
Page 1: Passivity-based Control of Euler-La
Page 5 and 6: Preface By its own denition the nal
Page 7 and 8: Preface ix DC power converters. In
Page 9 and 10: xi gratitude to the french CNRS, wh
Page 11: Contents Notation xxxi 1 Introducti
Page 15 and 16: CONTENTS xvii 5.1 Feedback control
Page 17 and 18: CONTENTS xix 3.8 Denitions of desir
Page 19 and 20: CONTENTS xxi 3 Assumptions . . . .

Passivity-based Control of Euler-Lagrange Systems:

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