2009
DOI: 10.1007/s00034-009-9103-x
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Proportional Plus Integral Control for Set-Point Regulation of a Class of Nonlinear RLC Circuits

Abstract: In this paper we identify graph-theoretic conditions which allow us to write a nonlinear RLC circuit as port-Hamiltonian with constant input matrices. We show that under additional monotonicity conditions on the network's components, the circuit enjoys the property of relative passivity, an extended notion of classical passivity. The property of relative passivity is then used to build simple, yet robust and globally stable, proportional plus integral controllers.

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Cited by 21 publications
(8 citation statements)
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“…The first approach has been pursued in [7] and [26] for mechanical systems and in [2] for general port-Hamiltonian (pH) systems. PID-PBCs have been designed following the second line of research in [5], [12], and [27] for power converters, in [17] for photovoltaic systems, and in [4] for general RLC circuits. The addition of integral actions has also been proposed to robustify PBCs, vis-à-vis external disturbances, in [6], [10], [22], and [25].…”
Section: Introductionmentioning
confidence: 99%
“…The first approach has been pursued in [7] and [26] for mechanical systems and in [2] for general port-Hamiltonian (pH) systems. PID-PBCs have been designed following the second line of research in [5], [12], and [27] for power converters, in [17] for photovoltaic systems, and in [4] for general RLC circuits. The addition of integral actions has also been proposed to robustify PBCs, vis-à-vis external disturbances, in [6], [10], [22], and [25].…”
Section: Introductionmentioning
confidence: 99%
“…One way to overcome this difficulty has been presented in the nowadays classical F.O.C [10]. There, the field orientation objective…”
Section: Desired Current Behaviormentioning
confidence: 99%
“…Our main result is an extension, to the problem of tracking trajectories, of Jayawardhana et al (2007); Sanders and Verghese (1992) that treat the regulation case. See also Castaños et al (2009) for its application to PI stabilization of RLC circuits and Hernandez-Gomez et al (2010) where the result is used in power converters.…”
Section: Introductionmentioning
confidence: 99%