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