Bounding the output error in a buck power converter using perturbation theory

We show the main results obtained when applying the average theory to Zero Average Dynamic control technique in a buck power converter with pulse-width modulation (PWM). In particular, we have obtained the bound values for output error and sliding surface. The PWM with centered and lateral pulse configurations were analyzed. The analytical results have confirmed the numerical and experimental results already obtained in previous publications. Moreover, through an important lemma, we have generalized the theory for any stable second-order system with relative degree 2, using properties related to transformations and stability of linear systems.Peer Reviewe

Two-parameter bifurcation analysis of the buck converter

This paper is concerned with the analysis of two-parameter bifurcation phenomena in the buck power converter. It is shown that the complex dynamics of the converter can be unfolded by considering higher codimension bifurcation points in two-parameter space. Specifically, standard smooth bifurcations are shown to merge with discontinuity-induced bifurcation (DIB) curves, giving rise to intricate bifurcation scenarios. The analytical results are compared with those obtained numerically, showing excellent agreement between the analytical predictions and the numerical observations. The existence of these two-parameter bifurcation phenomena involving DIBs and smooth bifurcations, predicted in [P. Kowalczyk et al., Internat. J. Bifur. Chaos Appl. Sci. Engrg., 16 (2006), pp. 601–629; A. Colombo and F. Dercole, SIAM J. Appl. Dyn. Syst., submitted], is confirmed in this important class of systems.Postprint (published version

Implementación de una nueva técnica de control digital para convertidores dc-dc y dc-ac

En este trabajo se presentan resultados experimentales que confirman la validez de una nueva técnica de control digital, por modulación de ancho de pulso (PWM-Digital), para convertidores de potencia DC-DC y DC-AC. El controlador PWM-Digital combina el esquema de control por promedio cero de la dinámica del error (ZAD), ya reportado en la literatura, con el esquema de control por inducción al punto fijo (FPIC) aún en fase de experimentación. El diseño ha sido validado experimentalmente, usando la plataforma digital DSpace , en convertidores DC-DC y DC-AC de baja potencia. Los diagramas de bifurcaciones, calculados numéricamente en la etapa de diseño, concuerdan en un alto porcentaje con los obtenidos en la etapa experimental. Cuando el sistema opera en zona estable se obtiene buen comportamiento a la salida (regulación en el caso DC-DC y rastreo en el caso DC-AC), con bajo error y rechazo a perturbaciones

Generalization of zad strategy: an application to a dc-dc buck converter

The Zero Average Dynamics (ZAD) strategy has been reported in the last decade as an alternative for controlling power converters. This technique has the advantage of guaranteeing fi xed frequency switching. However, the stability of the controller is highly dependent on the load value, and when the stability is lost, the fi xed frequency switching is lost too. In this paper we generalize ZAD strategy using the probabilities framework through the expectation operator. Thus, we recover classical sliding mode control classical ZAD strategy, and new control methods can be defined, which are more stable than the others previously used. For this reason, this technique is entitled Generalized Zero Average Dynamics (GZAD). We will show several simulations regarding an application to a DC-DC Buck converter within the generalized ZAD strategy, which cannot be deduced from the classical ZAD. Numerical simulations show good regulation features and a wide range of stability

Transition from periodicity to chaos in a PWM-controlled buck converter with ZAD strategy

The transition from periodicity to chaos in a DC-DC Buck power converter is studied in this paper. The converter is controlled through a direct Pulse Width Modulation (PWM) in order to regulate the error dynamics at zero. Results show robustness with low output error and a fixed switching frequency. Furthermore, some rich dynamics appear as the constant associated with the first order error dynamics decreases. Finally, a transition from periodicity to chaos is observed. This paper describes this transition and the bifurcations in the converter. Chaos appears in the system with a stretching and folding mechanism. It can be observed in the one-dimensional Poincaré map of the inductor current. This Poincaré map converges to a tent map with the variation of the system parameter ks.Peer Reviewe

Transition from periodicity to chaos in a PWM-controlled buck converter with ZAD strategy

The transition from periodicity to chaos in a DC-DC Buck power converter is studied in this paper. The converter is controlled through a direct Pulse Width Modulation (PWM) in order to regulate the error dynamics at zero. Results show robustness with low output error and a fixed switching frequency. Furthermore, some rich dynamics appear as the constant associated with the first order error dynamics decreases. Finally, a transition from periodicity to chaos is observed. This paper describes this transition and the bifurcations in the converter. Chaos appears in the system with a stretching and folding mechanism. It can be observed in the one-dimensional Poincaré map of the inductor current. This Poincaré map converges to a tent map with the variation of the system parameter ks.Peer Reviewe