Bruno Robert

Secure digital communication using discrete-time chaos synchronization

Abstract In this paper we propose some secure digital communication schemes using discrete chaotic systems. In our approach a message is encrypted at the transmitter using chaotic modulation. Next, the driving signal synchronizes the receiver using discrete observer design or drive-response concept. Finally, by reverting the coding procedure the transmitted message is reconstructed. To demonstrate the efficiency of our communication schemes a modified Henon’s map is considered as an illustrative example.

Control of chaos in a PWM current-mode H-bridge inverter using time-delayed feedback

Time-delayed feedback can be used to stabilize unstable periodic orbits (UPOs) in dynamical systems. The technique involves feedback of signals delayed by the orbits period so that the feedback signals vanish on the target orbit and hence the UPO becomes a solution of the original system. An obvious advantage of this method is that it requires only the knowledge of the period of the target UPO. In this brief, a pulsewidth-modulated current-mode H-bridge inverter serves as a subject of investigation. Under certain parameter ranges, it exhibits higher periodic solutions and chaos. A simple time-delay feedback control method is applied to stabilize the UPOs. By using the time-delayed feedback control method, the stability limit and gain range of the system are increased.

Observer-based chaotic synchronization in the presence of unknown inputs

This paper deals with the problem of synchronization of chaotic dynamical systems. We consider a drive-response type of synchronization via a scalar transmitted signal. Unlike most works we consider the presence of some unknown inputs in the drive system and that no knowledge about their nature is available. A reduced-order observer-based response system is designed to synchronize with the missing states. We show that under some assumptions the synchronization is exponentially achieved. The efficiency of our method is confirmed by numerical simulations of two wellknown chaotic systems: Chuas circuit and Lure system. 2002 Elsevier Science Ltd. All rights reserved.

CONTROL OF A PWM INVERTER USING PROPORTIONAL PLUS EXTENDED TIME-DELAYED FEEDBACK

Pulse width modulation (PWM) current-mode single phase inverters are known to exhibit bifurcations and chaos when parameters vary or if the gain of the proportional controller is arbitrarily increa...

Discrete time model of a multi-cell dc/dc converter: non linear approach

By using a non linear discrete time model, this paper shows how to predict bifurcations in a two cells chopper and analyses the road to chaos. Equilibrium points and their stability are investigated in an analogical way to determine the nature of the bifurcations. The global behaviour is studied by using bifurcation diagrams showing collisions between fixed points and borderlines. The border collision bifurcations have their origin in the saturations of the PWM modulator.

Modeling and Design Rules of a Two-Cell Buck Converter Under a Digital PWM Controller

In this paper, we give a detailed analytical study of a two-cell dc-dc buck converter. We analyse the dynamics of the system by using a discrete time modelling approach and considering a digital controller. This controller includes a dynamic compensator in the form of a digital integrator for the output variable regulation. The discrete time model for the whole system is used to predict the instability of the system when some design parameters are varied. To facilitate the design, an approximated closed form discrete time model is derived in the form of a recurrence equation which accurately describes the dynamical behavior of the system. The Jury test is applied to the characteristic polynomial in order to obtain stability boundaries in the design parameter space. Some design rules to obtain optimal transient behavior are also given. Numerical simulations and experimental measurements confirm the theoretical predictions.

Adaptive time-delayed feedback for chaos control in a PWM single phase inverter

Many power converters exhibit chaotic behaviors and bifurcations when conventional feedback corrector are badly tuned or when parameters vary. Time-Delayed Feedback Control (TDFC) can be used to stabilize them using a state feedback delayed by the period of the unstable orbit (UPO) to be stabilized. An obvious advantage of this method is the robustness because it does not require the knowledge of an accurate model but only the period of the target UPO. In this paper, TDFC is applied to a PWM current-programmed single phase inverter concurrently with a proportional corrector in order to avoid bifurcations and chaos and to stabilize the fundamental UPO over a widened range of application. Moreover an improvement of the dynamical performances is realized by defining an adaptive law for the TDFC.

Stability Analysis of a Voltage Mode Controlled Two-Cells DC-DC Buck Converter

In this paper we analyze the dynamics and stability of a power electronic two cell DC-DC buck converter for high and medium voltage applications. The system is under voltage mode PWM control with dynamic controller for the output voltage loop. Numerical simulations from the exact circuit model shows that the system can undergo some nonlinear phenomena in the form of bifurcations. Different kinds of behaviors of the system are detected by varying some design parameters. These behaviors occur after losing stability of the nominal periodic behavior. In order to explain these phenomena, we derive a discrete time model in the form of a Poincare map which accurately describes the dynamical behavior of the system. The linearized small signal discrete time model is also obtained. Numerical simulations confirm the theoretical predictions

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.

Modelling and analysis of multicell converters using discrete time models

The main drawback of the discrete time models reported in the literature for predicting nonlinear phenomena in power electronic circuits is their complexity which make their use in system design very minted. The availability of approximated discrete time models that retain the accuracy of the exact model and at the same time makes the system design simple would give new perspectives in the control design of such systems. In this paper we give a detailed analytical study of a two-cell DC-DC buck converter for high voltage applications by using discrete time formulation. Different operating modes are possible and they can be modeled by a unified discrete time model. A digital controller is considered for the system. This controller includes a dynamic compensator in the form of digital integrator for the output variable regulation. An approximated discrete time model in the form of current recurrence equation which accurately describes the dynamical behavior of the system is derived. This model is use to predict instabilities when some design parameters are varied. The Jury test is applied to the characteristic polynomial in order to obtain boundary of stability in the design parameter space. Numerical simulations confirm the theoretical predictions