Brief paper: Power-based control of physical systems

Authors:
Eloísa García-Canseco;Dimitri Jeltsema;Romeo Ortega;Jacquelien M. A. Scherpen
Affiliations:
Eindhoven University of Technology, Faculty of Mechanical Engineering, CST, PO Box 513, 5600MB Eindhoven, The Netherlands;Delft Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands;Laboratoire des Signaux et Systèmes, Supélec, Plateau de Moulon, 91192, Gif-sur-Yvette, cedex, France;Faculty of Mathematics and Natural Sciences, ITM, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
Venue:
Automatica (Journal of IFAC)
Year:
2010

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Abstract

It is well known that energy-balancing control is stymied by the presence of pervasive dissipation. To overcome this problem in electrical circuits, the alternative paradigm of power shaping was introduced in Ortega, Jeltsema, and Scherpen (2003) -where, as suggested by its name, stabilization is achieved shaping a function akin to the power instead of the energy function. In this paper we extend this technique to general nonlinear systems. The method relies on the solution of a PDE, which identifies the open-loop storage function. We show through some physical examples, that the power-shaping methodology yields storage functions which have units of power. To motivate the application of this control technique we illustrate the procedure with two case studies: a tunnel diode circuit and a two-tanks system.