scholarly journals STABILITY ANALYSIS OF PARALLEL CONNECTED DC-DC CONVERTERS

2020 ◽  
Vol 4 (2) ◽  
pp. 35-39
Author(s):  
Abdulmajed O. Elbkosh
Keyword(s):  
Poincaré Map ◽  
Monodromy Matrix ◽  
The Other ◽  
Nonlinear Behaviour ◽  
Matrix Approach ◽  
Poincare Map ◽  
Bifurcation And Chaos ◽  
The Matrix ◽  
The Stability ◽  
Map Approach

Parallel controlled DC-DC converters are nonlinear and non-smooth systems, they show various nonlinear behaviour including smooth, non-smooth bifurcation, and chaos when they work outer their design conditions. Usually, the Poincaré map approach is the most common method for studying the stability of those nonlinear systems. Stability is indicated using the eigenvalues of the Jacobian of the map computed at the fixed point. The other method is the monodromy matrix approach, where the stability can be concluded by computed the eigenvalues of the matrix. In this paper, the nonlinear dynamics of parallel connected DC-DC converters are investigated. It is shown that the concept of the monodromy matrix can be applied to determine the stability of the system as well as the Poincare map approach.

A PHYSICAL INTERPRETATION OF MELNIKOV’S METHOD

1992 ◽  
Vol 02 (01) ◽  
pp. 1-9 ◽  
Author(s):  
YOHANNES KETEMA
Keyword(s):  
Physical Interpretation ◽  
Poincaré Map ◽  
Initial Conditions ◽  
Homoclinic Orbits ◽  
Poincare Map ◽  
Stable And Unstable Manifolds ◽  
Melnikov's Method ◽  
Melnikov’S Method ◽  
Sensitive Dependence ◽  
The Stability

This paper is concerned with analyzing Melnikov’s method in terms of the flow generated by a vector field in contrast to the approach based on the Poincare map and giving a physical interpretation of the method. It is shown that the direct implication of a transverse crossing between the stable and unstable manifolds to a saddle point of the Poincare map is the existence of two distinct preserved homoclinic orbits of the continuous time system. The stability of these orbits and their role in the phenomenon of sensitive dependence on initial conditions is discussed and a physical example is given.

An Application of the Poincare´ Map to the Stability of Nonlinear Normal Modes

1980 ◽  
Vol 47 (3) ◽  
pp. 645-651 ◽  
Author(s):  
L. A. Month ◽  
R. H. Rand
Keyword(s):  
Floquet Theory ◽  
Poincaré Map ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Theory Approach ◽  
Poincare Map ◽  
Linearized Stability ◽  
Nonlinear Normal ◽  
The Stability ◽  
Two Degree Of Freedom

The stability of periodic motions (nonlinear normal modes) in a nonlinear two-degree-of-freedom Hamiltonian system is studied by deriving an approximation for the Poincare´ map via the Birkhoff-Gustavson canonical transofrmation. This method is presented as an alternative to the usual linearized stability analysis based on Floquet theory. An example is given for which the Floquet theory approach fails to predict stability but for which the Poincare´ map approach succeeds.

Precision Control Through Vibration Suppression in Piezoelectric-Stepper Response

2013 ◽  
Author(s):  
Scott Wilcox ◽  
Santosh Devasia
Keyword(s):  
Poincaré Map ◽  
Vibration Suppression ◽  
Poincare Map ◽  
Velocity Control ◽  
Precision Control ◽  
Motion Stage ◽  
Map Approach

The main contribution of this article is to show that, when compared to single actuator steppers, the response of multi-actuator steppers can be significantly less oscillatory and these reduced oscillations allow for higher precision velocity control of a motion stage. Moreover, it is shown that the resulting motion of the motion stage is stable using a Poincaré-map approach.

scholarly journals Horseshoe Chaos in a Simple Memristive Circuit

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Lei Wang ◽  
XiaoSong Yang ◽  
WenJie Hu ◽  
Quan Yuan
Keyword(s):  
Stability Analysis ◽  
Poincaré Map ◽  
Circuit Model ◽  
Computer Assisted ◽  
Poincaré Section ◽  
Poincare Map ◽  
Poincare Section ◽  
Topological Horseshoe ◽  
Memristive Circuit ◽  
The Stability

A simple memristive circuit model is revisited and the stability analysis is to be given. Furthermore, we resort to Poincaré section and Poincaré map technique and present rigorous computer-assisted verification of horseshoe chaos by virtue of topological horseshoe theory.

Analysis of a Mass-Spring-Relay System With Periodic Forcing

2021 ◽  
Author(s):  
János Lelkes ◽  
Tamás KALMÁR-NAGY
Keyword(s):  
Poincaré Map ◽  
Pitchfork Bifurcation ◽  
Global Dynamics ◽  
Poincare Map ◽  
Periodic Excitation ◽  
Periodic Forcing ◽  
Relay System ◽  
Saddle Type ◽  
The Stability ◽  
Mass Spring

Abstract The dynamics of a hysteretic relay oscillator with harmonic forcing is investigated. Periodic excitation of the system results in periodic, quasi-periodic, chaotic and unbounded behavior. A Poincare map is constructed to simplify the mathematical analysis. The stability of the xed points of the Poincare map corresponding to period-one solutions is investigated. By varying the forcing parameters, we observed a saddle-center and a pitchfork bifurcation of two centers and a saddle type xed point. The global dynamics of the system is investigated, showing discontinuity induced bifurcations of the xed points.

scholarly journals Analysis of Traffic Statics and Dynamics in Signalized Networks: A Poincaré Map Approach

2017 ◽  
Vol 51 (3) ◽  
pp. 1009-1029 ◽  
Author(s):  
Qi-Jian Gan ◽  
Wen-Long Jin ◽  
Vikash V. Gayah
Keyword(s):  
Poincaré Map ◽  
Poincare Map ◽  
Statics And Dynamics ◽  
Map Approach
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