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Bifurcation analysis of a Lyapunov-based controlled boost converter
Spinetti Rivera, Mario de Jesús; Olm Miras, Josep Maria; Biel Solé, Domingo; Fossas Colet, Enric
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV; Universitat Politècnica de Catalunya. Departament d'Enginyeria Electrònica; Universitat Politècnica de Catalunya. Departament d'Enginyeria de Sistemes, Automàtica i Informàtica Industrial; Universitat Politècnica de Catalunya. ACES - Control Avançat de Sistemes d´Energia
Lyapunov-based controlled boost converters have a unique equilibrium point, which is globally asymptotically stable, for known resistive loads. This article investigates the dynamic behaviors that appear in the system when the nominal load differs from the actual one and no action is taken by the controller to compensate for the mismatch. Exploiting the fact that the closed-loop system is, in fact, planar and quadratic, one may provide not only local but also global stability results: specifically, it is proved that the number of equilibria of the converter may grow up to three and that, in any case, the system trajectories are always bounded, i.e. it is a bounded quadratic system. The possible phase portraits of the closed-loop system are also characterized in terms of the selected bifurcation parameters, namely, the actual load value and the gain of the control law. Accordingly, the analysis allows the numerical illustration of many bifurcation phenomena that appear in bounded quadratic systems through a physical example borrowed from power electronics.
Àrees temàtiques de la UPC::Enginyeria electrònica::Electrònica de potència::Convertidors de corrent elèctric
Àrees temàtiques de la UPC::Matemàtiques i estadística
Electric current converters
Lyapunov functions
Boost converter
Lyapunov-based control
Bifurcations
Bounded quadratic systems
Convertidors de corrent elèctric
Lyapunov, Funcions de
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
info:eu-repo/semantics/publishedVersion
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