Passivity-based Control of Euler-Lagrange Systems: Mechanical, Electrical and Electromechanical Applications

The essence of this work is the control of electromechanical systems, such as manipulators, electric machines, and power converters. The common thread that links together the results presented here is the passivity property, which is at present in numerous electrical and mechanical systems, and which has great relevance in control engineering at this time. Amongst other topics, the authors cover: Euler-Lagrange Systems, Mechanical Systems, Generalised AC Motors, Induction Motor Control, Robots with AC Drives, and Perspectives and Open Problems. The authors have extensive experience of research and application in the field of control of electromechanical systems, which they have summarised here in this self-contained volume. While written in a strictly mathematical way, it is also elementary, and will be accessible to a wide-ranging audience, including graduate students as well as practitioners and researchers in this field.

Table of Contents:
1 Introduction.- 2 Euler-Lagrange systems.- 3 Set-point regulation.- 4 Trajectory tracking control.- 5 Adaptive disturbance attenuation: Friction compensation.- 6 Modeling of switched DC-to-DC power converters.- 7 Passivity-based control of DC-to-DC power converters.- 8 Nested-loop passivity-based control: An illustrative example.- 9 Generalized AC motor.- 10 Voltage-fed induction motors.- 11 Current-fed induction motors.- 12 Feedback interconnected systems: Robots with AC drives.- 13 Other applications and current research.- A Dissipativity and passivity.- 1 Circuit example.- 3 Passivity and finite-gain stability.- 4 Feedback systems.- 5 Internal stability and passivity.- 6 The Kalman-Yakubovich-Popov lemma.- B Derivation of the Euler-Lagrange equations.- 1 Generalized coordinates and velocities.- 2 Hamilton’s principle.- 3 From Hamilton’s principle to the EL equations.- 4 EL equations for non-conservative systems.- 5 List of generalized variables.- 6 Hamiltonian formulation.- C Background material.- D Proofs.- 3 The BP transformation.- 3.1 Proof of Proposition 9.20.- 3.2 A Lemma on the BP Transformation.- 4 Proof of Eqs. (10.41) and (10.77).- 4.1 A theorem on positivity of a block matrix.- 4.2 Proof of Eq. (10.77).- 4.3 Proof of Eq. (10.41).- 5 Derivation of Eqs. (10.55) and (10.56).- 5.1 Derivation of Eq. (10.55).- 5.2 Derivation of Eq. (10.56).- 6 Boundedness of all signals for indirect FOC.- 6.1 Proof of Proposition 11.10.