Stability of Gyroscopic Circulatory Systems

2018 ◽  
Vol 86 (2) ◽  
Author(s):  
Firdaus E. Udwadia
Keyword(s):  
Stability Analysis ◽  
Large Scale ◽  
Real Life ◽  
Central Result ◽  
The Stability ◽  
Gyroscopic Systems ◽  
Stability Results

This paper presents results related to the stability of gyroscopic systems in the presence of circulatory forces. It is shown that when the potential, gyroscopic, and circulatory matrices commute, the system is unstable. This central result is shown to be a generalization of that obtained by Lakhadanov, which was restricted to potential systems all of whose frequencies of vibration are identical. The generalization is useful in stability analysis of large scale multidegree-of-freedom real life systems, which rarely have all their frequencies identical, thereby expanding the compass of applicability of stability results for such systems. Comparisons with results in the literature on the stability of such systems are made, and the weakness of results that deal with only general statements about stability is exposed. It is shown that the commutation conditions given herein provide definitive stability results in situations where the well-known Bottema–Karapetyan–Lakhadanov result is inapplicable.

scholarly journals Impedance-Based Stability Analysis of Paralleled Grid-Connected Rectifiers: Experimental Case Study in a Data Center

Energies ◽  
2020 ◽  
Vol 13 (8) ◽  
pp. 2109 ◽  
Author(s):  
Henrik Alenius ◽  
Tomi Roinila
Keyword(s):  
Stability Analysis ◽  
Data Center ◽  
Large Scale ◽  
Real Life ◽  
System Stability ◽  
Limited Information ◽  
Impedance Measurements ◽  
Grid Connected Converters ◽  
The Stability

Grid-connected systems often consist of several feedback-controlled power-electronics converters that are connected in parallel. Consequently, a number of stability issues arise due to interactions among multiple converter subsystems. Recent studies have presented impedance-based methods to assess the stability of such large systems. However, only few real-life experiences have been previously presented, and practical implementations of impedance-based analysis are rare for large-scale systems that consist of multiple parallel-connected devices. This work presents a case study in which an unstable high-frequency operation, caused by multiple paralleled grid-connected rectifiers, of a 250 kW data center in southern Finland is reported and studied. In addition, the work presents an experimental approach for characterizing and assessing the system stability by using impedance measurements and an aggregated impedance-based analysis. Recently proposed wideband-identification techniques based on binary injection and Fourier methods are applied to obtain the experimental impedance measurements from the input terminals of a single data center rectifier unit. This work provides a practical approach to design and implement the impedance-based stability analysis for a system consisting of multiple paralleled grid-connected converters. It is shown that the applied methods effectively predict the overall system stability and the resonant modes of the system, even with very limited information on the system. The applied methods are versatile, and can be utilized in various grid-connected applications, for example, in adaptive control, system monitoring, and stability analysis.

Stability of jets in a shallow water layer

2015 ◽  
Vol 25 (2) ◽  
pp. 358-374 ◽  
Author(s):  
Zhanhong Wan ◽  
Saihua Huang ◽  
Zhilin Sun ◽  
Zhenjiang You
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Shallow Water ◽  
Large Scale ◽  
Bottom Topography ◽  
Bottom Friction ◽  
Rossby Number ◽  
Content Type ◽  
The Stability ◽  
Topographic Parameters

Purpose – The present work is devoted to the numerical study of the stability of shallow jet. The effects of important parameters on the stability behavior for large scale shallow jets are considered and investigated. Connections between the stability theory and observed features reported in the literature are emphasized. The paper aims to discuss these issues. Design/methodology/approach – A linear stability analysis of shallow jet incorporating the effects of bottom topography, bed friction and viscosity has been carried out by using the shallow water stability equation derived from the depth averaged shallow water equations in conjunction with both Chézy and Manning resistance formulae. Effects of the following main factors on the stability of shallow water jets are examined: Rossby number, bottom friction number, Reynolds number, topographic parameters, base velocity profile and resistance model. Special attention has been paid to the Coriolis effects on the jet stability by limiting the rotation number in the range of Ro∈[0, 1.0]. Findings – It is found that the Rossby number may either amplify or attenuate the growth of the flow instability depending on the values of the topographic parameters. There is a regime where the near cancellation of Coriolis effects due to other relevant parameters influences is responsible for enhancement of stability. The instability can be suppressed by the bottom friction when the bottom friction number is large enough. The amplification rate may become sensitive to the relatively small Reynolds number. The stability region using the Manning formula is larger than that using the Chézy formula. The combination of these effects may stabilize or destabilize the shallow jet flow. These results of the stability analysis are compared with those from the literature. Originality/value – Results of linear stability analysis on shallow jets along roughness bottom bed are presented. Different from the previous studies, this paper includes the effects of bottom topography, Rossby number, Reynolds number, resistance formula and bed friction. It is found that the influence of Reynolds number on the stability of the jet is notable for relative small value. Therefore, it is important to experimental investigators that the viscosity should be considered with comparison to the results from inviscid assumption. In contrast with the classical analysis, the use of multi-parameters of the base velocity and topographic profile gives an extension to the jet stability analysis. To characterize the large scale motion, besides the bottom friction as proposed in the related literature, the Reynolds number Re, Rossby number Ro, the topographic parameters and parameters controlling base velocity profile may also be important to the stability analysis of shallow jet flows.

scholarly journals A General Numerical Method for Analyzing the Linear Stability of Stratified Parallel Shear Flows

2014 ◽  
Vol 31 (12) ◽  
pp. 2795-2808 ◽  
Author(s):  
Tim Rees ◽  
Adam Monahan
Keyword(s):  
Stability Analysis ◽  
Numerical Method ◽  
Shear Flows ◽  
Numerical Solutions ◽  
Analytical Approximations ◽  
Onset Of Turbulence ◽  
Parallel Shear Flows ◽  
Critical Layers ◽  
The Stability ◽  
Stability Results

Abstract The stability analysis of stratified parallel shear flows is fundamental to investigations of the onset of turbulence in atmospheric and oceanic datasets. The stability analysis is performed by considering the behavior of small-amplitude waves, which is governed by the Taylor–Goldstein (TG) equation. The TG equation is a singular second-order eigenvalue problem, whose solutions, for all but the simplest background stratification and shear profiles, must be computed numerically. Accurate numerical solutions require that particular care be taken in the vicinity of critical layers resulting from the singular nature of the equation. Here a numerical method is presented for finding unstable modes of the TG equation, which calculates eigenvalues by combining numerical solutions with analytical approximations across critical layers. The accuracy of this method is assessed by comparison to the small number of stratification and shear profiles for which analytical solutions exist. New stability results from perturbations to some of these profiles are also obtained.

Concept Of The Decomposition And Aggregation Method With Example: Part 1

1988 ◽  
pp. 27-40
Author(s):  
Dr. Zainol Anuar Mohd. Sharif ◽  
Ng Boon Choong
Keyword(s):  
Stability Analysis ◽  
Dynamic Systems ◽  
Basic Concept ◽  
Large Scale ◽  
Direct Method ◽  
Aggregation Method ◽  
Control Engineering ◽  
Large Scale Systems ◽  
Engineering Economics ◽  
The Stability

This paper describes the basic concept of the decomposition and aggregation method. It shows the feasibility of the method and its advantages when applied, particularly to large scale systems. This method is extensively used in solving problems related to control engineering, economics, optimization and stability. This paper also illustrates specifically the application of the method of decomposition and aggregation in the analysis of dynamic systems. It is divided into two important parts, namely; the decomposition part which involves breaking up a large system into subsystems and the aggregation part which is obtained through a reformulation of the Liapunov's second method (direct method). The relation between the decomposition and the aggregation methods is also shown. The procedure for checking the stability based on this concept is also outlined.For further illustration, an example of a dynamic system has been included. It shows how the system is decomposed and aggregated to suit the requirement for stability analysis.

Efficient and Robust Approaches to the Stability Analysis of Large Multibody Systems

2007 ◽  
Vol 3 (1) ◽  
Author(s):  
Olivier A. Bauchau ◽  
Jielong Wang
Keyword(s):  
Stability Analysis ◽  
Large Scale ◽  
Equations Of Motion ◽  
Classical Stability ◽  
Linearized Stability ◽  
Signal Synthesis ◽  
Common Framework ◽  
Synthesis Procedure ◽  
The Stability ◽  
Proper Orthogonal

Linearized stability analysis methodologies that are applicable to large scale, multiphysics problems are presented in this paper. Two classes of closely related algorithms based on a partial Floquet and on an autoregressive approach, respectively, are presented in common framework that underlines their similarity and their relationship to other methods. The robustness of the proposed approach is improved by using optimized signals that are derived from the proper orthogonal modes of the system. Finally, a signal synthesis procedure based on the identified frequencies and damping rates is shown to be an important tool for assessing the accuracy of the identified parameters; furthermore, it provides a means of resolving the frequency indeterminacy associated with the eigenvalues of the transition matrix for periodic systems. The proposed approaches are computationally inexpensive and consist of purely post processing steps that can be used with any multiphysics computational tool or with experimental data. Unlike classical stability analysis methodologies, it does not require the linearization of the equations of motion of the system.

scholarly journals Simulink-Based Analysis for Coupled Metabolic Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Shinq-Jen Wu ◽  
Cheng-Tao Wu
Keyword(s):  
Stability Analysis ◽  
Dynamic Simulation ◽  
Large Scale ◽  
Dynamic Behaviour ◽  
Canonical Systems ◽  
Metabolic Systems ◽  
Good Potential ◽  
Set Up ◽  
The Stability ◽  
Interactive Behaviour

Stability analysis and dynamic simulation are important for researchers to capture the performance and the properties of underling systems. S-systems have good potential for characterizing dynamic interactive behaviour of large scale metabolic and genetic systems. It is important to develop a platform to achieve timely dynamic behaviour of S-systems to various situations. In this study, we first set up the respective block diagrams of S-systems for module-based simulation. We then derive reasonable theorems to examine the stability of S-systems and find out what kinds of environmental situations will make systems stable. Three canonical systems are used to examine the results which are carried out in the Matlab/Simulink environments.

STABILITY ANALYSIS OF A DISCRETE NONLINEAR DELAY SURVIVAL RED BLOOD CELLS MODEL

2012 ◽  
Vol 05 (04) ◽  
pp. 1250030
Author(s):  
SHUFANG MA ◽  
YUANGANG ZU
Keyword(s):  
Dynamical System ◽  
Stability Analysis ◽  
Red Blood Cells ◽  
Blood Cells ◽  
Discrete Dynamical System ◽  
Original System ◽  
Discrete Delay ◽  
The Stability ◽  
Stability Results ◽  
Nonlinear Delay

In this article we consider the kth-order discrete delay survival red blood cells model. The general form of the discrete dynamical system is rewritten as xn+1 = f(Pn, δn, xn, …, xn+1) where Pn, δn converge to the parametric values P and δ. We show that when the parameters are replaced by sequences, the stability results of the original system still hold.

scholarly journals STABILITY ANALYSIS OF FOUR TYPES OF POLE AND LINER

2010 ◽  
Vol 2 (2) ◽  
Author(s):  
St. Aisyah Farhum
Keyword(s):  
Stability Analysis ◽  
International Maritime Organization ◽  
Minimum Standard ◽  
Flat Bottom ◽  
Fishing Boat ◽  
Standard Value ◽  
Standard Values ◽  
The Stability ◽  
Stability Results ◽  
Better Than

<p>This study was purposed to compare the stability of four types of pole and liner casco (round bottom, round flat bottom, round sharp bottom and u-v bottom),. The stability value was analyzed by calculating the stability on the curve with the heeling angle of 0-90°. The stability results of each casco type were then compared with the criteria of minimum standard value derived from IMO (International Maritime Organization). Results showed that the four casco types had greater stability values than IMO standard values. This study found that the stability value of the round –sharp bottom casco was better than the others.</p><p>Keywords: Stability of fishing boat, Pole and liner, casco</p>

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