María Belén D'Amico

Hopf bifurcation for maps: a frequency-domain approach

The application of the graphical Hopf theorem (GHT) as a tool for detecting invariant cycles in maps is presented. The invariant cycle emerging from the bifurcation is approximated using an analogous version of the GHT for continuous-time systems. This technique is formulated in the so-called frequency domain and it involves the use of the Nyquist stability criterion and the harmonic balance method. Some examples are included for illustration.

STUDY OF DEGENERATE BIFURCATIONS IN MAPS: A FEEDBACK SYSTEMS APPROACH

The dynamical behavior of nonlinear maps undergoing degenerate period doubling or degenerate Hopf bifurcations is studied via a frequency-domain approach. The technique is based on a discrete-time feedback representation of the system and the application of the well-known engineering tools of harmonic balance to approximate the emerging solutions. More specifically, the results are a higher-order extension of the previous developments obtained by the authors for nondegenerate bifurcations. Two examples are included for illustration.

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

DYNAMICAL ANALYSIS OF A NETWORKED CONTROL SYSTEM

A new network data transmission strategy was proposed in [Zhang & Chen, 2005], where the resulting nonlinear system was analyzed and the effectiveness of the transmission strategy was demonstrated via simulations. In this paper, we further generalize the results of Zhang and Chen [2005] in the following ways: (1) Construct first-return maps of the nonlinear systems formulated in [Zhang & Chen, 2005] and derive several existence conditions of periodic orbits and study their properties. (2) Formulate the new system as a hybrid system, which will ease the succeeding analysis. (3) Prove that this type of hybrid systems is not structurally stable based on phase transition which can be applied to higher-dimensional cases effortlessly. (4) Simulate a higher-dimensional model with emphasis on their rich dynamics. (5) Study a class of continuous-time hybrid systems as the counterparts of the discrete-time systems discussed above. (6) Propose new controller design methods based on this network data transmission strategy to improve the performance of each individual system and the whole network. We hope that this research and the problems posed here will rouse the interest of researchers in such fields as control, dynamical systems and numerical analysis.

BIFURCATION CONTROL OF A BUCK CONVERTER IN DISCONTINUOUS CONDUCTION MODE

Abstract A nonlinear digital controller for improving the dynamical behavior of a buck converter operating in discontinuous conduction mode is presented. The aim is the extension of the operating range of the circuit, ameliorating the appearance of period-two orbits when the resistive load or the source voltage are varied. The controlled system is analyzed by using a frequency-domain technique. Numerical and experimental results are included to illustrate the performance of the system.

Performance of a Zero Average Dynamics-controlled buck converter using different pulse-width modulation schemes

The response of a digital Zero Average Dynamics ZAD-controlled buck converter under the variation of its intrinsic parameters as well as the pulse-width modulation signal is studied in detail. The multiparameter analysis presented here leads to a complete knowledge of the different dynamical scenarios exhibited by the system. Numerical results indicate that the success of the ZAD-strategy is highly dependent on the parameter and pulse-width modulation PWM combinations. Experiments are included to validate the performance inside the so-called optimum region. Copyright

Influence of PWM structure on the dynamics of a ZAD-controlled buck converter

This paper focuses on the dynamical response of the ZAD-controlled buck converter under the variation of the PWM structure. Numerical analysis shows that the system can exhibit supercritical and subcritical period-doubling bifurcations, depending on the parameter values. This indicates that the ZAD technique can be highly dependent on the PWM composition.

A small-signal averaged model of a coupled-inductor boost converter

This paper focuses on developing a small-signal model of a coupled-inductor boost converter. A circuital representation of the differential equations is also provided. The aim is to bring a tangible way of analyzing the influence of parameters like the coupling factor or the load on the behavior of the converter. Detailed numerical results complete the analytical study.

Modeling and control of a flyback converter to drive a dimmable LED array

In this paper, the modeling and control of a flyback converter used to dim a LED array is presented. Feedback is designed based on the linearized version of the true averaged state-space model of the converter. The dynamics is analyzed for all operation range and then, the worst case is chosen. Since the driver is part of an integrated circuit, there exist limitations in the type of controller to be implemented and in the desired performance. Nevertheless, commercial specifications are fulfilled for all output current values. The performance of the closed-loop system is corroborated via numerical simulations.

Reduced-order average model of a coupled-inductor dc-dc converter

This paper presents an averaged model for a coupled-inductor double-boost converter. Differential equations depend on the time intervals for which diodes are conducting simultaneously. Thus, expressions that permit to estimate those values as a function of the states of the circuit are also proposed. The response of the model is compared with that of the original converter via numerical simulations.