A passivity‐based control of Euler‐Lagrange systems with a non‐quadratic Lagrangian | Zendy

Jungnickel U. | Zendy; Kielau G. | Zendy; Maißer P. | Zendy; Müller A. | Zendy

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A passivity‐based control of Euler‐Lagrange systems with a non‐quadratic Lagrangian

Author(s) -

Jungnickel U.,

Kielau G.,

Maißer P.,

Müller A.

Publication year - 2008

Publication title -

zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 51

eISSN - 1521-4001

pISSN - 0044-2267

DOI - 10.1002/zamm.200800029

Subject(s) - passivity , legendre transformation , kinetic energy , control theory (sociology) , mathematics , quadratic equation , trajectory , mathematical analysis , computer science , classical mechanics , control (management) , physics , geometry , astronomy , artificial intelligence , electrical engineering , engineering

In this paper, the classical augmented PD control method is extended to a passivity‐based control of Euler‐Lagrange systems with a non‐quadratic Lagrangian. It is assumed that the systems are fully actuated. The problem is treated with two geometrically different approaches. The first approach is dealing with state space control in the configuration space by introducing the kinetic energy via the Legendre transformation of the kinetic co‐energy. The second approach considers the system's dynamics in the event space endowed with a Finsler metric based on the kinetic co‐energy. It is shown that the control laws of both approaches achieve uniformly asymptotically stable trajectory tracking.

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