FROM MODIFICATIONS OF EXPERIMENTAL BIFURCATION DIAGRAMS TO OPERATING PROCESS STABILITY MARGIN

2013 ◽  
Vol 23 (07) ◽  
pp. 1330024 ◽  
Author(s):  
YURY KOLOKOLOV ◽  
ANNA MONOVSKAYA
Keyword(s):  
Nonlinear System ◽  
Stability Margin ◽  
Practical Experience ◽  
Buck Converter ◽  
System Behavior ◽  
Bifurcation Diagrams ◽  
Process Stability ◽  
Operating Process ◽  
Unit Of Measurement ◽  
Uncertainty Zone

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.

ESTIMATING THE UNCERTAINTY OF THE BEHAVIOR OF A PWM POWER CONVERTER BY ANALYZING A SET OF EXPERIMENTAL BIFURCATION DIAGRAMS

2013 ◽  
Vol 23 (04) ◽  
pp. 1350063 ◽  
Author(s):  
YURY KOLOKOLOV ◽  
ANNA MONOVSKAYA
Keyword(s):  
Nonlinear Dynamics ◽  
Power Converter ◽  
Engineering Practice ◽  
Bifurcation Diagrams ◽  
Process Stability ◽  
New Approach ◽  
Fundamental Properties ◽  
Operating Process ◽  
Dc Drive ◽  
Uncertainty Zone

One of the main faults of a PWM power converter is linked to losing the operating process stability because of bifurcations. A bifurcation diagram contains information on the evolution of the behavior of a PWM power converter that could be theoretically used to prevent the bifurcations. Surprisingly, applying the bifurcation analysis is not yet typical in engineering practice. One of the reasons seems to be in the fundamental properties of the PWM power converter dynamics caused by the unavoidable uncertainty of its behavior near a bifurcation point. We propose a new approach to estimating this uncertainty. By analyzing a set of experimental bifurcation diagrams, our approach allows to determine both the location of the uncertainty zone and the quantitative regularities of the behavior within this zone. The proposed approach can be applied to design and maintenance, including fault diagnosis, and also to scientific research of the nonlinear dynamics regularities. Our results are experimentally verified by using the "PWM DC drive" setup.

A Practice-Oriented Bifurcation Analysis for Pulse Energy Converters: A Stability Margin

2017 ◽  
Vol 27 (09) ◽  
pp. 1750134 ◽  
Author(s):  
Yury Kolokolov ◽  
Anna Monovskaya
Keyword(s):  
Nonlinear Dynamics ◽  
Energy Conversion ◽  
Bifurcation Analysis ◽  
Pulse Energy ◽  
Stability Margin ◽  
Variable Structure ◽  
Operating Regime ◽  
Buck Converter ◽  
Practical Applications ◽  
Operating Process

The popularity of systems of pulse energy conversion (PEC-systems) for practical applications is due to the heightened efficiency of energy conversion processes with comparatively simple realizations. Nevertheless, a PEC-system represents a nonlinear object with a variable structure, and the bifurcation analysis remains the basic tool to describe PEC dynamics evolution. The paper is devoted to the discussion on whether the scientific viewpoint on the natural nonlinear dynamics evolution can be involved in practical applications. We focus on the problems connected with stability boundaries of an operating regime. The results of both small-signal analysis and computational bifurcation analysis are considered in the parametrical space in comparison with the results of the experimental identification of the zonal heterogeneity of the operating process. This allows to propose an adapted stability margin as a sufficiently safe distance before the point after which the operating process begins to lose the stability. Such stability margin can extend the permissible operating domain in the parametrical space at the expense of using cause-and-effect relations in the context of natural regularities of nonlinear dynamics. Reasoning and discussion are based on the experimental and computational results for a synchronous buck converter with a pulse-width modulation. The presented results can be useful, first of all, for PEC-systems with significant variation of equivalent inductance and/or capacity. We believe that the discussion supports a viewpoint by which the contemporary methods of the computational and experimental bifurcation analyses possess both analytical abilities and experimental techniques for promising solutions which could be practice-oriented for PEC-systems.

FRACTAL APPROACH, BIFURCATION POKER AND SUC-LOGIC FOR NONLINEAR DYNAMICS FORECASTING

2013 ◽  
Vol 23 (12) ◽  
pp. 1350201 ◽  
Author(s):  
YURY KOLOKOLOV ◽  
ANNA MONOVSKAYA
Keyword(s):  
Nonlinear Dynamics ◽  
Physical Meaning ◽  
Risk Estimation ◽  
Stability Margin ◽  
The Novel ◽  
Computational Results ◽  
Bifurcation Diagrams ◽  
Fractal Approach ◽  
Uncertainty Zone ◽  
The Stability

The paper is devoted to the novel logic (SUC-logic) of the nonlinear dynamics forecasting. The SUC-logic is based on three main points: the special sections (S) to build the 2D projections of multidimensional spaces without the loss of useful information; the special units (U) of measurement to estimate the nonlinear dynamics evolution; the special consecutions (C) to realize the nonlinear dynamics forecasting step-by-step. The fractal approach to forecasting the nonlinear dynamics in real-time together with the approach to build the modified bifurcation diagrams to research the regularities and the uncertainties of the evolution scenarios are developed with the SUC-logic. The physical meaning of the uncertainty zone, the stability margin, the risk estimation, the farthest forecasting and the earliest forecasting are considered from the viewpoint of the nonlinear dynamics aspect. Reasonings and discussions are based on experimental and computational results.

Chaotic Threshold for Axial Loaded Beam Bridge under Moving Loads

2014 ◽  
Vol 533 ◽  
pp. 140-144
Author(s):  
Shi Zhu Yang ◽  
Xin Wei Yang
Keyword(s):  
Dynamical System ◽  
Nonlinear System ◽  
Chaotic Motion ◽  
Nonlinear Dynamical System ◽  
Pulse Excitation ◽  
Approximation Methods ◽  
Moving Loads ◽  
Bifurcation Diagrams ◽  
Nonlinear Dynamical ◽  
Beam Bridge

We studied chaotic threshold of a nonlinear dynamical system of beam bridge. The amplification and minification of integral inequality are proposed, which lead to the criteria for chaotic motion directly for the nonlinear system with a half sine pulse excitation avoiding the conventional approximation methods to retain the nature characteristics of the system. The efficiency of the criteria for chaotic motion obtained by use of the Melnikov's method is verified via the bifurcation diagrams, Lyapunov exponents and numerical simulations.

Nonlinear Analysis of a 2-DOF Piecewise Linear Aeroelastic System

2012 ◽  
Author(s):  
Tarek A. Elgohary ◽  
Tamás Kalmár-Nagy
Keyword(s):  
Linear Function ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Piecewise Linear ◽  
Piecewise Linear Function ◽  
Hopf Bifurcations ◽  
System Behavior ◽  
Bifurcation Diagrams ◽  
Aerodynamic Forces ◽  
Aeroelastic System

Aerodynamic forces for a 2-DOF aeroelastic system oscillating in pitch and plunge are modeled as a piecewise linear function. Equilibria of the piecewise linear model are obtained and their stability/bifurcations analyzed. Two of the main bifurcations are border collision and rapid/Hopf bifurcations. Continuation is used to generate the bifurcation diagrams of the system. Chaotic behavior following the intermittent route is also observed. To better understand the grazing phenomenon sets of initial conditions associated with the system behavior are defined and analyzed.

A Practice-Oriented Bifurcation Analysis for Pulse Energy Converters. Part 3: Transients

2018 ◽  
Vol 28 (06) ◽  
pp. 1850079
Author(s):  
Yury Kolokolov ◽  
Anna Monovskaya
Keyword(s):  
Energy Conversion ◽  
Bifurcation Analysis ◽  
Pulse Energy ◽  
Operating Regime ◽  
Bifurcation Diagrams ◽  
Operating Characteristics ◽  
Operating Process ◽  
Energy Conversion Systems ◽  
Basic Characteristics ◽  
And Performance

The paper continues the discussion on the bifurcation analysis conceptions for applications in practice-oriented solutions for pulse energy conversion systems (PEC-systems). This viewpoint means an attempt to resolve so-called conflict-of-units between the notions used to describe natural evolution (i.e. evolution of the operating process towards nonoperating processes and vice versa) and the notions used to describe a desirable artificial regime (i.e. the operating regime). In this connection, the correspondence between causes (degradation of the operating process stability) and effects (changes of the operating characteristics) is established in the following sequence: nonlinear dynamics output signal operating characteristics, where these characteristics include stability and performance. Two starting points follow from the previous parts. First, there are distinguishable thresholds of evolutional degradation, between which the operating process loses stability in a particular manner; and these particularities can be systematized by means of so-called uncertainty zones. Second, multi-D integrating translations of phase images with regular parametrical variation are combined with the corresponding boundaries of the operating stability and performance by means of the modified bifurcation diagrams. Then we focus on the basic characteristics of transients and first demonstrate and discuss some unified form of the modified bifurcation diagrams, to which a solution on the operating performance can be reduced. Namely, we show such solutions for an overshoot and a settling time in comparison with a control error. We believe that the practice-oriented bifurcation analysis could be interesting to pioneer research intended for the design of promising systems of pulse energy conversion.

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