Stability Analysis of a Rotating Stepped Shaft via Lyapunov Criterion

2012 ◽  
Author(s):  
Jafar Abbaszadeh Chekan ◽  
Kaveh Merat ◽  
Hassan Zohoor
Keyword(s):  
Stability Analysis ◽  
Direct Method ◽  
Beam Theory ◽  
Point Of View ◽  
System Stability ◽  
Mode Shapes ◽  
Stability Margins ◽  
Stepped Shaft ◽  
The Stability ◽  
Adjacent Segments

In this investigation, the stability analysis of a rotating elastic stepped shaft is studied and the sufficient condition for system stability in the sense of Lyapunov is derived. The model consists of an elastic stepped shaft which is clamped rigidly to a rotary device. From the model’s point of view, the entire length of shaft is partitioned into uniform segments with different characteristics. The Lyapunov direct method is applied in this survey where the Hamilton function has been chosen as the candidate Lyapunov function. Since the dynamical mode shapes of the shaft are required for the stability analysis, the shaft has been modeled by the Euler–Bernoulli beam theory and the corresponding mode shapes have been derived based on the boundary conditions and the continuity conditions between adjacent segments. In this study, the shaft is considered to have two segments with different properties. It is notable that this model can be an appropriate model for the spindle in tool machines. Our aim in this research study is determining the area of stability for the system considering the shaft characteristics. The effects of bending stiffness and mass distribution parameters of each segment are investigated on the stability margins of the system.

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.

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.

UNIFORM APPROACH FOR STABILITY ANALYSIS OF FAST SUBSYSTEM OF TWO-TIME SCALE NONLINEAR SYSTEMS

2007 ◽  
Vol 17 (11) ◽  
pp. 4195-4203 ◽  
Author(s):  
LUÍS F. C. ALBERTO ◽  
HSIAO-DONG CHIANG
Keyword(s):  
Stability Analysis ◽  
Nonlinear Systems ◽  
Power Systems ◽  
Time Scale ◽  
Stability Region ◽  
Direct Method ◽  
System Stability ◽  
Fast Subsystem ◽  
Theoretical Support ◽  
The Stability

A new uniform methodology to study the fast subsystem stability of general two-time scale nonlinear systems is developed. It consists of a direct method that provides estimates of the stability region of the fast subsystem that are uniform with respect to the slow variables, which are treated as uncertainties. The methodology is illustrated on small power systems leading to much improved results in estimating the stability region, critical clearing times as compared to traditional methods. As a by-product, it gives the required theoretical support to justify and to correct the heuristic approaches used in power system stability analysis literature.

scholarly journals BUNDLE ADJUSTMENT-BASED STABILITY ANALYSIS METHOD WITH A CASE STUDY OF A DUAL FLUOROSCOPY IMAGING SYSTEM

2018 ◽  
Vol IV-2 ◽  
pp. 9-16 ◽  
Author(s):  
K. Al-Durgham ◽  
D. D. Lichti ◽  
I. Detchev ◽  
G. Kuntze ◽  
J. L. Ronsky
Keyword(s):  
Stability Analysis ◽  
Imaging System ◽  
Parameters Estimation ◽  
System Stability ◽  
Single Camera ◽  
Calibration Data ◽  
Analysis Method ◽  
Advantages And Disadvantages ◽  
Camera Imaging ◽  
The Stability

A fundamental task in photogrammetry is the temporal stability analysis of a camera/imaging-system’s calibration parameters. This is essential to validate the repeatability of the parameters’ estimation, to detect any behavioural changes in the camera/imaging system and to ensure precise photogrammetric products. Many stability analysis methods exist in the photogrammetric literature; each one has different methodological bases, and advantages and disadvantages. This paper presents a simple and rigorous stability analysis method that can be straightforwardly implemented for a single camera or an imaging system with multiple cameras. The basic collinearity model is used to capture differences between two calibration datasets, and to establish the stability analysis methodology. Geometric simulation is used as a tool to derive image and object space scenarios. Experiments were performed on real calibration datasets from a dual fluoroscopy (DF; X-ray-based) imaging system. The calibration data consisted of hundreds of images and thousands of image observations from six temporal points over a two-day period for a precise evaluation of the DF system stability. The stability of the DF system – for a single camera analysis – was found to be within a range of 0.01 to 0.66 mm in terms of 3D coordinates root-mean-square-error (RMSE), and 0.07 to 0.19 mm for dual cameras analysis. It is to the authors’ best knowledge that this work is the first to address the topic of DF stability analysis.

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.

scholarly journals Sliding mode learning control of uncertain nonlinear systems with Lyapunov stability analysis

2018 ◽  
Vol 41 (6) ◽  
pp. 1750-1760
Author(s):  
Erkan Kayacan
Keyword(s):  
Stability Analysis ◽  
Nonlinear Systems ◽  
Lyapunov Stability ◽  
Sliding Mode ◽  
Learning Control ◽  
System Stability ◽  
Uncertain Nonlinear Systems ◽  
System Behaviour ◽  
Lyapunov Stability Analysis ◽  
The Stability

This paper addresses the Sliding Mode Learning Control (SMLC) of uncertain nonlinear systems with Lyapunov stability analysis. In the control scheme, a conventional control term is used to provide the system stability in compact space while a type-2 neuro-fuzzy controller (T2NFC) learns system behaviour so that the T2NFC completely takes over overall control of the system in a very short time period. The stability of the sliding mode learning algorithm has been proven in the literature; however, it is restrictive for systems without overall system stability. To address this shortcoming, a novel control structure with a novel sliding surface is proposed in this paper, and the stability of the overall system is proven for nth-order uncertain nonlinear systems. To investigate the capability and effectiveness of the proposed learning and control algorithms, the simulation studies have been carried out under noisy conditions. The simulation results confirm that the developed SMLC algorithm can learn the system behaviour in the absence of any mathematical model knowledge and exhibit robust control performance against external disturbances.

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.

scholarly journals On the alternative approaches to stability analysis in decision support for damaged passenger ships

2019 ◽  
Vol 18 (3) ◽  
pp. 477-494 ◽  
Author(s):  
Pekka Ruponen ◽  
Petri Pennanen ◽  
Teemu Manderbacka
Keyword(s):  
Decision Support ◽  
Stability Analysis ◽  
Decision Support System ◽  
Support System ◽  
Point Of View ◽  
Additional Information ◽  
Damage Stability ◽  
Passenger Ships ◽  
Minimum Requirements ◽  
The Stability

Abstract A decision support system with damage stability analysis has been recognized as an important tool for passenger ships. Various software applications have been developed and taken into use over the years, without a direct link to any compelling requirement, set forth in the international regulatory framework. After the Costa Concordia accident, new regulations have been established, setting minimum requirements for a decision support system, as an extension to a loading computer. Yet, more advanced systems have been developed recently, aiming at providing valuable additional information on the predicted development of the stability of the damaged ship. This paper presents these alternative decision support systems with damage stability analysis methods for flooding emergencies on passenger ships. The technical background, usability, and usefulness of the various approaches are compared and discussed, taking into account the important statutory approval point of view. In addition, practical examples, including past accidents, are presented and discussed.

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.

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