François Béceau Pelap

Solitonlike excitations in a one-dimensional electrical transmission line

Dynamics of modulated waves is studied in a one-dimensional discrete nonlinear electrical transmission line. Contribution of a linear dispersive capacitance is appreciated and it is shown via a reductive perturbation method that evolution of such waves in this system is governed by a higher order nonlinear Schrodinger equation. Passing through the Stokes wave analysis, a generalized criterion for the Benjamin–Feir instability in the network is presented and exact solutions of the obtained wave equation are determined by the means of the Pathria and Morris approach.

Higher Order Solitons in an Electrical Lattice

Dynamics of modulated waves in a nonlinear electrical bi-inductance line are theoretically examined by the means of a perturbation method. It has been recently established that in such lines, modul...

A novel high-frequency interpretation of a general purpose Op-Amp-based negative resistance for chaotic vibrations in a simple a priori nonchaotic circuit

A novel model of general purpose operational amplifiers is made to approximate, at best, the equivalent circuit for real model at high-frequency. With this new model, it appears that certain oscillators, usually studied under ideal considerations or using many existing real models of operational amplifiers, have hidden subtle and attractive chaotic dynamics that have previously been unknown. These can now be revealed. With the new considerations, a “two-component” circuit, consisting simply of a capacitor in parallel with a nonmodified (and usually presented as a linear, negative) resistance, tends to exhibit chaotic signals. P-Spice and laboratory experimental results are in good agreement with the theoretical predictions.

Stability of bright solitons in some physical systems

Dynamical systems described by the modified quintic complex Ginzburg Landau equation and its derivative forms are considered and the stability of their bright soliton solution is investigated numerically by means of the split-step Fourier method. Some discussions related to the way of ensuring the stability of this solution are presented.

A Modified RBF Neuro-Sliding Mode Control Technique for a Grid Connected PMSG Based Variable Speed Wind Energy Conversion System

A modified control scheme based on the combination of online trained neural network and sliding mode techniques is proposed to enhance maximum power extraction for a grid connected permanent magnet synchronous generator (PMSG) wind turbine system. The proposed control method does not need the knowledge of the uncertainty bounds nor the exact model of the nonlinear system. Since the neural network is trained online, the time to estimate good weights can affect the dynamic performance of the process during the startup phase. Therefore an appropriate way to smoothly and explicitly accelerate the neural network rate of convergence during the startup phase is proposed. Furthermore, a flexible grid side voltage source converter control structure which can handle both grid connected and standalone modes based on conventional proportional integral (PI) control method is presented. Simulations are done in Matlab/Simulink environment to verify the effectiveness and assess the performance of the proposed controller. The results analysis shows the superiority of the proposed RBF neuro-sliding mode controller compared to a nonlinear controller based on sliding mode control method when the system undergoes parameter uncertainties.

Nonlinear excitations in a continuous bi-inductance electrical line

The dynamics of nonlinear excitations in an electrical bi-inductance transmission line are examined by means of the multiple scales method. In the continuum approximation using an appropriate decoupling ansatz for the voltage of the two different cells, we consider modulated waves and show that their propagation in the network is governed by a nonlinear Schrodinger equation instead of a Korteweg–de Vries equation. We have also established the existence of two frequency modes and study separately the wave dynamics in each mode. It appears from our investigations that the continuous bi-inductance electrical line supports a dark soliton in the low frequency mode and only a bright soliton in the high frequency mode. The study of the network properties has revealed that a nonlinear bi-inductance electrical transmission line can be considered as a superposition of two independent nonlinear mono-inductance transmission lines with different inductances.