In this paper, we present an analytical, numerical, and experimental description of the period addition phenomenon in a dynamical system arising from a boost converter controlled by ZAD strategy. The ideal model is presented, and compared with a model that includes parasitic resistances. We show the presence of chaos in the two systems, which is controlled by TDAS. In particular, numerical simulation shows the chaos control zone is greater in the system with internal resistances.
This paper shows a study, both analytical and numerical, of a continuous-time dynamical system associated with a simple model of a wastewater biorreactor. Nonsmooth phenomena and border-collision local bifurcations appear when the main parameters (dilution and biomass concentration at the inflow) are varied. We apply the Filippov methods following Kuznetsov’s work.
This article presents some results of SEPIC converter dynamics when controlled by a center pulse width modulator controller (CPWM). The duty cycle is calculated using the ZAD (Zero Average Dynamics) technique. Results obtained using this technique show a great variety of non-linear phenomena such as bifurcations and chaos, as parameters associated with the switching surface. These phenomena have been studied in the present paper in numerical form. Simulations were done in MATLAB.
The nonlinear differential equation governing the periodic motion of the one-dimensional, undamped, and unforced cubic-quintic Duffing oscillator is solved exactly, providing exact expressions for the period and the solution. The period as well as the exact analytic solution is given in terms of the famous Weierstrass elliptic function. An integrable case of a damped cubic-quintic equation is presented. Mathematica code for solving both cubic and cubic-quintic Duffing equations is given in Appendix at the end.
This paper analyzes the dynamics of a system that models the formation of biofilms in a continuous stirred-tank reactor (CSTR) when it is utilized for wastewater treatment. The growth rate of the microorganisms is modeled using two different kinetics, Monod and Haldane kinetics, with the goal of studying the influence of each in the system. The equilibrium points are identified through a stability analysis, and the bifurcations found are characterized.
In this paper, an analytical and numerical study is conducted on the dynamics of the current in the condenser of a boost converter controlled with ZAD, using a pulse PWM to the symmetric center. A stability analysis of periodic 1T-orbits was made by the analytical calculation of the eigenvalues of the Jacobian matrix of the dynamic system, where the presence of flip and Neimar-Sacker-type bifurcations was determined. The presence of chaos, which is controlled by ZAD and FPIC techniques, is shown from the analysis of Lyapunov exponents.
In high load conditions, the boost converter presents some phenomena, such as chattering, chaos, subharmonics, and nT-periodic orbits, which require studying them with the aim of reducing the effects and improving the performance of these electronic devices. In this paper, sufficient conditions for the existence of nT-periodic orbits are analytically obtained and the system stability is evaluated using eigenvalues of the Jacobian matrix of the Poincaré application. It is demonstrated numerically that 1T-periodic orbits occur for a broad range of γ parameters. The research obtains a particular class of 2T-periodic orbits in the boost converter and a formula that provides sufficient conditions for the existence of nT-periodic orbits with and without saturation in the duty cycle. In addition, an analysis of nT-periodic orbits is performed with a biparametric diagram. The system stability is computed using a variational equation that allows perturbation of the 1T-periodic orbits. Moreover, an analytical calculation of the Floquet exponents is performed to determine the stability limit of the 1T-periodic orbit. Finally, the phenomena found in this research are described according to the behavior of real applications encountered in previous literature.
This paper presents a study, both in analytical and numerical form, of a discrete dynamical system associated with a piecewise quadratic family. The orbits of periods one and two are characterized, and their stability is established. The nonsmooth phenomenon known as border collision is present when there is a period doubling. Lyapunov exponents are calculated numerically to determine the presence of chaos in the system.
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