scholarly journals Stability Analysis Through the Direct Method of Lyapunov in the Oscillation of a Synchronous Machine

2018 ◽  
Vol 12 (7) ◽  
pp. 166
Author(s):  
Carlos Alberto Abello Muñoz ◽  
Pedro Pablo Cárdenas Alzate ◽  
Fernando Mesa
Keyword(s):  
Stability Analysis ◽  
Direct Method ◽  
Synchronous Generator ◽  
Scalar Function ◽  
Synchronous Machine ◽  
The Stability

This paper deals with the determination of the stability of a synchronous generator connected to an infinite bus when one of its parameters is varied. The direct method of Lyapunov is proposed for the construction of a scalar function that allows to characterize the stability of said system, this method is chosen since it has several practical advantages.

scholarly journals Stability of Fractional Differential Equations with New Generalized Hattaf Fractional Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Khalid Hattaf
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Direct Method ◽  
Lyapunov Direct Method ◽  
Science And Engineering ◽  
Fractional Differential ◽  
The Stability

This paper aims to study the stability of fractional differential equations involving the new generalized Hattaf fractional derivative which includes the most types of fractional derivatives with nonsingular kernels. The stability analysis is obtained by means of the Lyapunov direct method. First, some fundamental results and lemmas are established in order to achieve the goal of this study. Furthermore, the results related to exponential and Mittag–Leffler stability existing in recent studies are extended and generalized. Finally, illustrative examples are presented to show the applicability of our main results in some areas of science and engineering.

Stability Analysis of Multiple Time Delayed Systems Using the Direct Method

2003 ◽  
Author(s):  
Rifat Sipahi ◽  
Nejat Olgac
Keyword(s):  
Stability Analysis ◽  
Time Delays ◽  
Linear Time ◽  
Direct Method ◽  
Multiple Time ◽  
Delayed Systems ◽  
Practical Applications ◽  
Linear Time Invariant ◽  
Multiple Time Delays ◽  
The Stability

A novel treatment for the stability of a class of linear time invariant (LTI) systems with rationally independent multiple time delays using the Direct Method (DM) is studied. Since they appear in many practical applications in the systems and control community, this class of dynamics has attracted considerable interest. The stability analysis is very complex because of the infinite dimensional nature (even for single delay) of the dynamics and furthermore the multiplicity of these delays. The stability problem is much more challenging compared to the TDS with commensurate time delays (where time delays have rational relations). It is shown in an earlier publication of the authors that the DM brings a unique, exact and structured methodology for the stability analysis of commensurate time delayed cases. The transition from the commensurate time delays to multiple delay case motivates our study. It is shown that the DM reveals all possible stability regions in the space of multiple time delays. The systems that are considered do not have to possess stable behavior for zero delays. We present a numerical example on a system, which is considered “prohibitively difficult” in the literature, just to exhibit the strengths of the new procedure.

STABILITY ANALYSIS OF NONLINEAR INTERCONNECTED SYSTEMS VIA T–S FUZZY MODELS

2004 ◽  
Vol 04 (01) ◽  
pp. 41-55 ◽  
Author(s):  
WEI-LING CHIANG ◽  
CHENG-WU CHEN ◽  
FENG-HSIAG HSIAO
Keyword(s):  
Stability Analysis ◽  
Lyapunov Functions ◽  
Direct Method ◽  
Interconnected Systems ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Fuzzy Models ◽  
Fuzzy Techniques ◽  
The Stability ◽  
Takagi Sugeno

This paper is concerned with the stability problem of nonlinear interconnected systems. Each of them consists of a few interconnected subsystems which are approximated by Takagi–Sugeno (T–S) type fuzzy models. In terms of Lyapunov's direct method, a stability criterion is derived to guarantee the asymptotic stability of interconnected systems. It is shown that the stability analysis problems of nonlinear interconnected systems can be reduced to linear matrix inequality (LMI) problems via suitable Lyapunov functions and T–S fuzzy techniques. Finally, numerical examples with simulations are given to demonstrate the validity of the proposed approach.

Active Vibration Suppression With Time Delayed Feedback

2003 ◽  
Vol 125 (3) ◽  
pp. 384-388 ◽  
Author(s):  
Rifat Sipahi ◽  
Nejat Olgac
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Vibration Suppression ◽  
Linear Time ◽  
Direct Method ◽  
System Stability ◽  
Delayed Systems ◽  
Active Vibration Suppression ◽  
Active Vibration ◽  
The Stability

Various active vibration suppression techniques, which use feedback control, are implemented on the structures. In real application, time delay can not be avoided especially in the feedback line of the actively controlled systems. The effects of the delay have to be thoroughly understood from the perspective of system stability and the performance of the controlled system. Often used control laws are developed without taking the delay into account. They fulfill the design requirements when free of delay. As unavoidable delay appears, however, the performance of the control changes. This work addresses the stability analysis of such dynamics as the control law remains unchanged but carries the effect of feedback time-delay, which can be varied. For this stability analysis along the delay axis, we follow up a recent methodology of the authors, the Direct Method (DM), which offers a unique and unprecedented treatment of a general class of linear time invariant time delayed systems (LTI-TDS). We discuss the underlying features and the highlights of the method briefly. Over an example vibration suppression setting we declare the stability intervals of the dynamics in time delay space using the DM. Having assessed the stability, we then look at the frequency response characteristics of the system as performance indications.

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.

Stability of Dynamical Systems With Multiple Nonlinearities

1987 ◽  
Vol 109 (4) ◽  
pp. 410-413 ◽  
Author(s):  
Norio Miyagi ◽  
Hayao Miyagi
Keyword(s):  
Dynamical System ◽  
Stability Analysis ◽  
Dynamical Systems ◽  
Lyapunov Function ◽  
Stability Region ◽  
Direct Method ◽  
Essential Feature ◽  
Point Of View ◽  
Stability Of Dynamical Systems ◽  
The Stability

This note applies the direct method of Lyapunov to stability analysis of a dynamical system with multiple nonlinearities. The essential feature of the Lyapunov function used in this note is a non-Lure´ type Lyapunov function which surpasses the Lure´-type Lyapunov function from the point of view of the stability region guaranteed. A modified version of the multivariable Popov criterion is used to construct non-Lure´ type Lyapunov function, which allow for the dynamical sytems with multiple nonlinearities.

Dynamic Simulation Method for Hard-Rock Pillar Failure in Open-Stope Goaf

2014 ◽  
Vol 556-562 ◽  
pp. 4055-4060
Author(s):  
Hai Tao Ma ◽  
Jin An Wang
Keyword(s):  
Stability Analysis ◽  
Load Transfer ◽  
Hard Rock ◽  
Simulation Method ◽  
Collapse Load ◽  
Quantitative Criterion ◽  
The Stability ◽  
Made In ◽  
Area Data

An attempt to simulate the cascading pillar collapse is made in this paper for a quick evaluation of a large number of mined-out area data that have been collected throughout China. Pillar collapse, load transfer and load redistribution are modeled by the area-apportioned method, and this methodology is general in sense and has been implemented in the expert system developed by the authors as an independent module. The proposed method can provide a quantitative criterion for determination of the failure pattern and identification of the key pillars in the stability analysis of the mined-out area formed by a pillar-room method.

scholarly journals A Note on the Stability Analysis of Fuzzy Nonlinear Fractional Differential Equations Involving the Caputo Fractional Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Ali El Mfadel ◽  
Said Melliani ◽  
M’hamed Elomari
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Caputo Fractional Derivative ◽  
Direct Method ◽  
Stability Result ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Differential ◽  
The Stability

In this paper, we present and establish a new result on the stability analysis of solutions for fuzzy nonlinear fractional differential equations by extending Lyapunov’s direct method from the fuzzy ordinary case to the fuzzy fractional case. As an application, several examples are presented to illustrate the proposed stability result.

A Stability Algorithm for the General Milling Process: Contribution to Machine Tool Chatter Research—7

1968 ◽  
Vol 90 (2) ◽  
pp. 330-334 ◽  
Author(s):  
R. Sridhar ◽  
R. E. Hohn ◽  
G. W. Long
Keyword(s):  
Stability Analysis ◽  
Milling Process ◽  
Stability Boundaries ◽  
Machine Tool Chatter ◽  
Milling Operation ◽  
Cutting Operation ◽  
Differential Difference Equation ◽  
Linear Differential ◽  
The Stability

In this paper, a method of stability analysis for the general milling process is given. The milling operation is described by a linear differential-difference equation with periodic coefficients. An algorithm which can be used in conjunction with the digital computer is developed as a means of analytically determining the stability of this equation. This algorithm will permit the determination of the stability boundaries in the space of controllable parameters associated with a cutting operation and allows more realistic models for milling to be studied than have been attempted up to the present time. The technique is used to predict the stability in an example of a milling operation.

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