DocumentCode :
800098
Title :
Power shaping: a new paradigm for stabilization of nonlinear RLC circuits
Author :
Ortega, R. ; Jeltsema, D. ; Scherpen, J.M.A.
Author_Institution :
Lab. des Signaux et Syst., Gif-sur-Yvette, France
Volume :
48
Issue :
10
fYear :
2003
Firstpage :
1762
Lastpage :
1767
Abstract :
It is well known that arbitrary interconnections of passive (possibly nonlinear) resistors, inductors, and capacitors define passive systems, with port variables the external source voltages and currents, and storage function the total stored energy. In this note, we prove that for a class of RLC circuits with convex energy function and weak electromagnetic coupling it is possible to "add a differentiation" to the port terminals preserving passivity - with a new storage function that is directly related to the circuit power. The result is of interest in circuits theory, but also has applications in control as it suggests the paradigm of power shaping stabilization as an alternative to the well-known method of energy shaping. We show in this note that, in contrast with energy shaping designs, power shaping is not restricted to systems without pervasive dissipation and naturally allows to add "derivative" actions in the control. These important features, that stymie the applicability of energy shaping control, make power shaping very practically appealing. To establish our results we exploit the geometric property that voltages and currents in RLC circuits live in orthogonal spaces, i.e., Tellegen\´s theorem, and heavily rely on the seminal paper of Brayton and Moser in 1964.
Keywords :
RLC circuits; interconnections; RLC circuits; convex energy function; interconnections; nonlinear RLC circuits; nonlinear control; stability theory; total stored energy; Capacitors; Electromagnetic coupling; Energy storage; Inductors; Integrated circuit interconnections; Power system interconnection; RLC circuits; Resistors; Shape control; Voltage;
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/TAC.2003.817918
Filename :
1235380
Link To Document :
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