Impact of non-linear electronic circuits and switch of chaotic dynamics

Abstract

Switch-mode power supply is an extremely non-linear system that can inevitably exhibit unpredictable behavior. These control laws may be insufficient for nonlinear systems because they are not robust when the requirements on the dynamic characteristics of the system are strict [10]. Control laws that are insensitive to parameter variations, disturbances, and nonlinearities must be used. In this paper, we have tested the method of the first harmonic, used to analyses servo controls with a nonlinear element, and to predict certain non-linear behaviors. It mainly allows predicting the limit cycles, but also the jump phenomena, the harmonics as well as the responses of non-linear systems to sinusoidal inputs. We apply this method for the prediction of limit cycles and the determination of their amplitude and frequency. We take as an example a Boost converter controlled by current [4]. This system is chaotic when the duty cycle is more significant than 0.5: we then eliminate the chaos by applying the slippery mode command (for the ripple of the output voltage, for the current ripple of the inductance and switching frequency) when the output is periodic (duty cycle less than or equal to 0.5). In this article, we assess that established approach provides the best outcomes: it appears that the preference between the classical mode and the sliding mode depends heavily on the variance domain of the parameters E, R, and I_ref.