Stability analysis of periodic orbits in a class of duffing-like piecewise linear vibrators

In this paper, we study the dynamical behavior of a Duffing-like piecewise linear (PWL) springmass-damper system for vibration-based energy harvesting applications. First, we present a continuous time single degree of freedom PWL dynamical model of the system. From this PWL model, numerical simulations are carried out by computing frequency response and bifurcation diagram under a deterministic harmonic excitation for different sets of system parameter values. Stability analysis is performed using Floquet theory combined with Fillipov method.Postprint (published version

Delay effects on the limit cycling behavior in an H-bridge resonant inverter with zero current switching control strategy

Celebrado en Tarragona del 2-6 de septiembre de 2018.In this paper, bifurcations of limit cycles in a H-bridge LC resonant inverter under a zero current switching control strategy with delay in the switching action are analyzed. Mathematical analysis and numerical simulations show that the delay can degrade the quality of the oscillations and even inhibit them.Agencia Estatal de Investigación DPI2017- 84572-C2-1-RFondo Europeo de Desarrollo Regional DPI2017- 84572-C2-1-RMinisterio de Ciencia e Innovación MTM2015-65608-PJunta de Andalucía Consejería de Economía y Conocimiento P12-FQM-165

Analysis of nonlinear and non-smooth dynamics of a self-oscillating series resonant inverter

In this paper, the dynamics of a dc-ac resonant self-oscillating LC series inverter is analyzed from the point of view of piecewise smooth dynamical systems. Our system is defined by two symmetric configurations and its bifurcation analysis can be given in a one dimensional param- eter space, thus finding a non smooth transition between two strongly different dynamics. The oscillating regime, which is the one useful for applications and involves a repetitive switching action between those configurations, is given whenever their open loop equilibrium is a fo- cus. Otherwise, the only attractors are equilibrium points of node type whose stable manifolds preclude the appearance of oscillations.Postprint (author's final draft

Chaos controller for switching regulators aiming enhanced design-space towards miniaturization

This paper tackles the control of fast-scale instabilities in a buck switching power converter aiming to expand its design-space towards miniaturization. After briefly revisiting the working principle of existing chaos controllers, the paper explores an alternative approach based on amplifying the harmonic at the switching frequency. Numerical simulations show that the proposed controller can concurrently improve both fast-scale and slow-scale stability margins. Finally, the paper proposes a chaos controller combined with an output ripple reduction network and studies their interaction with the aim of achieving both low-ripple and improved stability.Preprin

Dynamical analysis of an interleaved single inductor TITO switching regulator

We study the dynamical behavior of a single inductor two inputs two outputs (SITITO) power electronics DC-DC converter under a current mode control in a PWM interleaved scheme. This system is able to regulate two, generally one positive and one negative, voltages (outputs). The regulation of the outputs is carried out by the modulation of two time intervals within a switching cycle. The value of the regulated voltages is related to both duty cycles (inputs). The stability of the whole nonlinear system is therefore studied without any decoupling. Under certain operating conditions, the dynamical behavior of the system can be modeled by a piecewise linear (PWL)map, which is used to investigate the stability in the parameter space and to detect possible subharmonic oscillations and chaotic behavior. These results are confirmed by numerical one dimensional and two-dimensional bifurcation diagrams and some experimental measurements from a laboratory prototype.Peer ReviewedPostprint (published version

Nonsmooth pitchfork bifurcation in a dc-dc converter: coexisting attractors and intermittency

In this paper we deal with the analysis of nonlinear dynamical behavior of a single inductor two inputs two outputs (SITITO) power electronics DC-DC converter. The system can be used to regulate generally two outputs (one positive and one negative). Under certain operating conditions, the switching model can be approximated by a one dimensional piecewise constant vector field and, as a consequence, the corresponding map is piecewise linear (PWL). This model is derived and then it is used to study a nonsmooth pitchfork bifurcation in the system. Coexistence of attractors are detected by using the same model. Intermittent chaotic behavior is also addressed. Analytical results are confirmed by one dimensional and twodimensional bifurcation diagrams.Peer ReviewedPostprint (published version

Limit cycle bifurcations in resonant LC power inverters under zero current switching strategy

The dynamics of a DC-AC self-oscillating LC resonant inverter with a zero current switching strategy is considered in this paper. A model that includes both the series and the parallel topologies and accounts for parasitic resistances in the energy storage components is used. It is found that only two reduced parameters are needed to unfold the bifurcation set of this extended system: one is related to the quality factor of the LC resonant tank, and the other accounts for the balance between serial and parallel losses. Through a rigorous mathematical study, a complete description of the bifurcation set is obtained and the parameter regions where the inverter can work properly is emphasized.Postprint (author's final draft

Dynamic analysis of self-oscillating H-bridge inverters with state feedback

This paper presents a comprehensive approach to analyze the dynamics of a generalized model of resonant inverters using nonsmooth dynamical system theory. The model simultaneously covers both parallel and series resonant inverters under state feedback control. The multi-parametric physical space is reduced to a plane, which is divided in several regions with different dynamical behavior. The boundaries separating these regions are located by solving their corresponding equations and it is found that they all emerge from a singular point in the parameter plane. Suitability for applications of these regions is emphasized, thus providing useful criteria for parameter selection.Postprint (author's final draft