Fabiola Angulo

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 Poincare map of the inductor current. This Poincare map converges to a tent map with the variation of the system parameter ks.

Feedback control of limit cycles: a switching control strategy based on nonsmooth bifurcation theory

In this paper, we present a method to control limit cycles in smooth planar systems making use of the theory of nonsmooth bifurcations. By designing an appropriate switching controller, the occurrence of a corner-collision bifurcation is induced on the system and the amplitude and stability properties of the target limit cycle are controlled. The technique is illustrated through a representative example.

Two-Parameter Discontinuity-Induced Bifurcation Curves in a ZAD-Strategy-Controlled DC–DC Buck Converter

The dynamics of a zero-average dynamic strategy controlled dc-dc Buck converter, modelled by a set of differential equations with discontinuous right-hand side is studied. Period-doubling and corner-collision bifurcations are found to occur close to each other under small parameter variations. Closer examination of the parameter space leads to the discovery of a novel bifurcation. This type of bifurcation has not been reported so far in the literature and it corresponds to a corner-collision bifurcation of a nonhyperbolic cycle. The bifurcation boundaries are computed analytically in this paper and the system dynamics are unfolded close to the novel bifurcation point.

STABILIZING A TWO-CELL DC-DC BUCK CONVERTER BY FIXED POINT INDUCED CONTROL

In this paper, we study nonlinear and bifurcation behavior of a two-cell DC-DC buck power electronic converter. The system shows nonsmooth period doubling bifurcation and chaotic phenomena in a certain zone of parameter space. This zone is located both analytically and from numerical simulations. One-dimensional, two-dimensional bifurcation diagrams and Lyapunov exponent spectrum are used to detect the different dynamic behaviors of the system. The Fixed Point Induced Control (FPIC) technique is applied to the system in order to widen the stability zone. The performance of the FPIC technique applied to the stabilization of a two-cell DC-DC buck converter is analyzed. With this technique, stabilization is achieved without changing the fixed point. The robustness in the presence of a noisy environment is checked by numerical simulations by considering different noise levels.

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.

STABILIZATION OF CHAOS WITH FPIC: APPLICATION TO ZAD-STRATEGY BUCK CONVERTERS

Abstract In this paper a new design for controlling dynamical systems has been applied to buck converters driven with a PWM centered pulse and (Zero Average Dynamics) ZAD-strategy. Chaotic operation has been stabilized with the so-called Fixed Point Induced Control (FPIC) technique. Also, the same converter with delay whose 1-periodic orbit is always unstable, has been stabilized. Simulations are compared with the TDAS stabilization technique. Once a 1-periodic orbit has been stabilized, the dynamics shows the same characteristics and advantages of the ZAD design, such as robustness, fixed switching frequency (with zero average on the sliding surface) and a low output error.

Chaos stabilization with TDAS and FPIC in a buck converter controlled by lateral PWM and ZAD

In this paper the performance of TDAS (time-delay autosynchronization) and FPIC (fixed point induced control) techniques, controlling chaos in the buck converter is analyzed. With these techniques, the stabilization of the 1-periodic orbit in the buck converter is controlled by lateral PWM (pulse width modulation) and ZAD (zero average dynamics) strategies.

Adaptive Ramp Technique for Controlling Chaos and Subharmonic Oscillations in DC–DC Power Converters

We propose an adaptive ramp control strategy with self-tuning offset and amplitude, as a simple yet effective solution for controlling dc-dc power converters despite load and input voltage variations. It is shown that our control technique is able to suppress chaos and subharmonic oscillations for a wide range of input voltage and loads. Furthermore, a systematic methodology based on bifurcation diagrams for tuning the controller is proposed. Stability and performance analysis have been done together with a proper comparison of our technique, and the classical control strategies often used in the literature. Particularly, Vin feedforward and adaptive slope compensation controllers have been considered for the buck and boost converters, respectively. Finally, the effectiveness of the control technique is validated for the buck converter via experimental setup.

Influence of period-doubling bifurcations in the appearance of border collisions for a ZAD-strategy-controlled buck converter

The first period-doubling bifurcation of a dc–dc buck converter controlled by a zero-average dynamic strategy is studied in detail. Owing to the saturation of the duty cycle, this bifurcation is followed by a border-collision bifurcation, which is the main mechanism to introduce instability and chaos in the circuit. The multiparameter analysis presented here leads to a complete knowledge of the relatioship between these two bifurcations. The results are obtained by using a frequency-domain approach for the study of period-two oscillations in maps. Copyright

EFFECTS OF QUANTIZATION, DELAY AND INTERNAL RESISTANCES IN DIGITALLY ZAD-CONTROLLED BUCK CONVERTER

Zero Average Dynamics (ZAD) strategy has been reported in the last decade as an alternative control technique for power converters, and a lot of work has been devoted to analyze it. From a theoretical point of view, this technique has the advantage that it guarantees fixed switching frequency, low output error and robustness, however, no high correspondence between numerical and experimental results has been obtained. These differences are basically due to model assumptions; in particular, all elements in the circuit were modeled as ideal elements and simulations and conclusions about steady state stability and transitions to chaos have been carried out with this ideal model. Regarding the practical point of view and the digital implementation, we include in this paper internal resistances, quantization effects and 1-period delay to the model. This paper shows in an experimental and numerical way the effects of these elements to the model and their incidence in the results. Now, experimental and numerical analyses fully agree.