Stabilization of a class of underactuated mechanical systems via total energy shaping

Author

Gómez-Estern, Fabio ; Ortega, Romeo ; Rubio, Francisco R. ; Aracil, Javier

Author_Institution

Ing. de Sistemas y Automatica, Escuela Superior de Ingenieros, Seville, Spain

Volume

2

fYear

2001

fDate

2001

Firstpage

1137

Abstract

In this paper a system of ODEs and a method for its solution are proposed for passivity-based stabilization of a class of underactuated mechanical systems. This method simplifies the PDEs imposed by the passivity-based control via interconnection and damping assignment (IDA-PBC) technique. For a class of mechanical systems satisfying some mathematical properties the PDEs are reduced to a simple set of nonlinear ODEs. A general solution for these equations in the 2-DOF case is presented, through a new parametrization of the closed loop inertia matrix. Two examples illustrate the method, achieving kinetic and potential energy shaping in a straightforward manner. The simulation analysis in comparison with recent studies highlight the advantages of these techniques

Keywords

differential equations; nonlinear control systems; stability; IDA-PBC technique; PDE; closed loop inertia matrix; damping assignment; interconnection; kinetic energy shaping; nonlinear ODE; passivity-based control; passivity-based stabilization; potential energy shaping; total energy shaping; underactuated mechanical systems stabilization; Control systems; Damping; Design methodology; Lighting control; Mechanical systems; Nonlinear control systems; Nonlinear equations; Potential energy; Power system interconnection; Shape control;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2001. Proceedings of the 40th IEEE Conference on

Conference_Location

Orlando, FL

Print_ISBN

0-7803-7061-9

Type

conf

DOI

10.1109/.2001.981038

Filename

981038