Covariant Lyapunov analysis of chaotic Kolmogorov flows

2012 ◽  
Vol 85 (1) ◽  
Author(s):  
Masanobu Inubushi ◽  
Miki U. Kobayashi ◽  
Shin-ichi Takehiro ◽  
Michio Yamada
Keyword(s):  
Lyapunov Analysis ◽  
Kolmogorov Flows

scholarly journals Covariant Lyapunov Analysis of Chaotic Kolmogorov Flows and Time-correlation Function

2012 ◽  
Vol 5 ◽  
pp. 244-248 ◽  
Author(s):  
Masanobu Inubushi ◽  
Miki U. Kobayashi ◽  
Shin-ichi Takehiro ◽  
Michio Yamada
Keyword(s):  
Correlation Function ◽  
Time Correlation ◽  
Time Correlation Function ◽  
Lyapunov Analysis ◽  
Kolmogorov Flows

scholarly journals Refinement of a Previous Hypothesis of the Lyapunov Analysis of Isotropic Turbulence

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Nicola de Divitiis
Keyword(s):  
Structure Function ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Longitudinal Velocity ◽  
Navier Stokes ◽  
Lyapunov Analysis ◽  
Velocity Difference ◽  
Navier Stokes Equations ◽  
Previous Hypothesis ◽  
Kolmogorov Theory

The purpose of this paper is to improve a hypothesis of the previous work of N. de Divitiis (2011) dealing with the finite-scale Lyapunov analysis of isotropic turbulence. There, the analytical expression of the structure function of the longitudinal velocity differenceΔuris derived through a statistical analysis of the Fourier transformed Navier-Stokes equations and by means of considerations regarding the scales of the velocity fluctuations, which arise from the Kolmogorov theory. Due to these latter considerations, this Lyapunov analysis seems to need some of the results of the Kolmogorov theory. This work proposes a more rigorous demonstration which leads to the same structure function, without using the Kolmogorov scale. This proof assumes that pair and triple longitudinal correlations are sufficient to determine the statistics ofΔurand adopts a reasonable canonical decomposition of the velocity difference in terms of proper stochastic variables which are adequate to describe the mechanism of kinetic energy cascade.

scholarly journals Lyapunov Analysis of Two Imbalanced Power System Areas

2021 ◽  
Vol 19 (3) ◽  
Author(s):  
Gilang Nugraha Putu Pratama ◽  
Adha Imam Cahyadi
Keyword(s):  
Lyapunov Function ◽  
Transmission Lines ◽  
Transient Stability ◽  
Analytical Tool ◽  
Necessary Condition ◽  
Lyapunov Analysis ◽  
Simultaneous Solution ◽  
Region Of Attraction ◽  
Admittance Matrix ◽  
Clearing Time

The transient stability is the capability of the system to preserve synchronism while being affected by large disturbances. It is a nonlinear problem that requires a simultaneous solution for many differential equations. Therefore, a thorough analysis is needed to resolve it. In this paper, we present the transient stability for multimachine under different fault cases and to analyze using the Lyapunov function. It serves as an analytical tool to determine the necessary condition to be stable. The system is stable as long as it is contained in the region of attraction. Meanwhile, the swing equation and reduced admittance matrix are used to model the system in three conditions, pre-fault, during the fault, and post-fault. The numerical simulations are conducted to verify that the synchronism can be preserved despite under faults on the transmission lines by achieving the critical clearing time.  

scholarly journals Global Finite-Time Stabilization Problem of Affine Nonlinear Systems with Unknown Functions

2021 ◽  
Author(s):  
Fujin Jia ◽  
Junwei Lu ◽  
Yong-Min Li ◽  
Fangyuan Li
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Control Algorithm ◽  
Lyapunov Analysis ◽  
Stabilization Problem ◽  
Analysis Method ◽  
Control Approach ◽  
Affine Nonlinear Systems ◽  
Simulation Results ◽  
Finite Time Stabilization

In this paper, the global finite-time stabilization (FTS) of nonlinear systems with unknown functions (UFs) is studied. Firstly, in order to deal with UFs, a Lemma is proposed to avoid the Assumptions of UFs. Secondly, based on this Lemma, the control algorithm designed by using backstepping has no partial derivative of virtual controllers, so it avoids the “differential explosion” problem of backstepping. Thirdly, by using Lyapunov analysis method, backstepping and FTS method, a global FTS control algorithm of nonlinear systems with UFs is proposed. Finally, the feasibility of developed control approach is illustrated by the simulation results of a manipulator.

Quantifying Muscle Fatigue of the Low Back during Repetitive Load Lifting Using Lyapunov Analysis

2016 ◽  
Vol 06 (06) ◽  
Author(s):  
Elias Spyropoulos ◽  
Anastasia Kyvelidou ◽  
Nikolas Stergiou ◽  
George Athanassiou
Keyword(s):  
Muscle Fatigue ◽  
Lyapunov Analysis ◽  
Low Back

Stability of Traffic Flow: Lyapunov Analysis

1997 ◽  
Vol 30 (8) ◽  
pp. 759-764
Author(s):  
Alexander Stotsky
Keyword(s):  
Traffic Flow ◽  
Lyapunov Analysis

scholarly journals Nonlinear Synchronous Control for H-Type Gantry Stage Used in Electric VehiclesManufacturing

Energies ◽  
2019 ◽  
Vol 12 (12) ◽  
pp. 2305
Author(s):  
Ran Chen ◽  
Zongxia Jiao ◽  
Liang Yan ◽  
Yaoxing Shang ◽  
Shuai Wu
Keyword(s):  
Tracking Error ◽  
Tracking Performance ◽  
System Model ◽  
Lyapunov Analysis ◽  
End Effector ◽  
Mechanical Coupling ◽  
Synchronous Control ◽  
Linear Motors ◽  
Proposed Model ◽  
Synchronous Error

The H-type gantry stage (HGS) is widely used in electric vehicle manufacturing and other fields. However, resulting from the existence of mechanical coupling, the synchronous control problem of HGS always troubles many engineers. Most synchronization schemes were either engaged in improving each motor’s tracking performance or committed to pure motion synchronization only. However, tracking and synchronous performance are interconnected, because of the mechanical coupling. In this paper, a rigid assumed system model of HGS, concerning the effects of mid-beam rotary inertia, mid-beam stiffness, and end-effector movement, is presented. Based on the proposed model, an adaptive robust synchronous control based on a rigid assumed model (ARSCR) is proposed to improve both synchronous and tracking performance of the HGS. From the Lyapunov analysis, the proposed ARSCR can achieve the convergence of synchronous error and tracking error, simultaneously. An HGS driven by dual linear motors is built and used to perform the experimental verification. The experimental results indicate the effectiveness of the proposed method.

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