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 Iref.
Highlights
The discovery of the chaotic dynamics of nonlinear systems dates back to Henri Poincar'e's work on the mechanical mechanics and statistical mechanics, around 1900 [3, 5]
We developed an iterative application that provides the mathematical expressions of the output voltage of the inductance current, and the switching frequency, when the output is periodic for both control methods [1, 6]
In the other case the evolution of the variables and is described by the differential equations: To see the behavior of the converter according to these parameters, we adopt modeling of the data in the form of iterative stroboscopic applications: the variables and are observing at each clock pulse
Summary
The discovery of the chaotic dynamics of nonlinear systems dates back to Henri Poincar'e's work on the mechanical mechanics and statistical mechanics, around 1900 [3, 5] They produced little interest and fell into oblivion. It was not until 1963 that Edward Lorenz, a Massachusetts Institute of Technology meteorologist, brought to light the chaotic nature of the weather conditions and, the uncontrolled movements of a fluid like the atmosphere. As he sought to determine future weather conditions from initial data on his computer, he found that a small change in the initial data (in the order of one per thousand) resulted in radically different results. This article mainly explain the control of chaos by the sliding mode command method and performs a comparative study of it with the classical method, even when the system is stable
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Periodicals of Engineering and Natural Sciences (PEN)
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
