From Modifications of Experimental Bifurcation Diagrams to Operating Process Stability Margin

Abstract

The approach to research the uncertainties and the regularities of nonlinear system behavior is developed in the paper. The peculiarity of the approach is connected with modifying the experimental bifurcation diagrams that allows to identify and to analyze certain aspects of the nonlinear dynamics evolution. The variety and the interrelation of the modified bifurcation diagrams are shown. Attention is focused on estimating the limits of the zone within which the nonlinear system behavior is characterized by the uncertainty and on making visible the particular tendencies of dynamics evolution within this zone. The results obtained on the experimental setup of PWM buck converter are used for illustrations. In particular, the uncertainty zone is assumed to be the unit of measurement to estimate the operating process stability margin. It is demonstrated that the properties corresponding to the practical experience appear as per this assumption.

Implementation of the real-time nonlinear dynamics prediction: Experimental research on location

“…1a). In addition, the trajectory of transient pro cess repeatedly intersects the complex structure of other boundary cycles [19,20]. As a result, it is not possible in phase space to unambiguously determine the direction of convergence of a transient process before its completion [11] and solution of this task demands special constructions.…”

“…Bifurcation branching resulting in a periodic process with a period of 2T (hereinafter referred to as process 2) is indicated by the white dotted line. As a consequence of the com plex correlation of nonlinear and interfering compo nents, the relief of branches has a complex form and the area of state ambiguity of a pulse energy converter (hereinafter referred to as Δα UZ zone) is observed at bifurcation point α BIF [9,10,20,24]. From the practi cal point of view, this means that either the difference between process 1 and process 2 remains comparable with the value of interference or process 1 and the pro cess 2 alternate.…”

“…1a). However, the con dition of Poincaré periodicity is not enough to study nonlinear dynamics during experiments on location and construction of modified bifurcation diagrams, it is required to identify the boundaries of Δα UZ zone [6,10,20,24]. In particular, research shows that Δα UZ zone can "round" the bifurcation point on the right at 20-30% of the range value of process 2 (Fig.…”

“…Reasoning from this statement, a sequence of production is considered in which particular solu tions of prediction tasks are synthesized in the context of the basic [11,19,20], shadow [6,17], and parallel [11,17,20] scenarios of development of nonlinear dynamics. This point of view is based on the findings of research obtained in the framework of the fractal approach.…”

“…Scientific interest in pulse energy converters is connected with the variety of nonlinear phenomena at the variation of parameters in wide ranges, which takes place in the case of service conditions becoming more difficult. At the same time, the scenario of period doubling can be distinguished as the basic development scenario that is typical for a wide spectrum of dc-dc pulse converters, for exam ple, [10,[20][21][22]. In this paper, material is arranged using the example of the dc-dc buck converter.…”