A Graphical Stability Analysis Method for Cascade Conjugate Order Systems

2021 ◽  
Author(s):  
Gulten Cetintas ◽  
Serdar Ethem Hamamci
Keyword(s):  
Stability Analysis ◽  
Stability Criterion ◽  
Graphical Method ◽  
The Other ◽  
Complex Conjugate ◽  
Analysis Method ◽  
Control Community ◽  
Fractional Analysis ◽  
The Stability ◽  
And Control

Abstract The theory and applications of complex fractional analysis have recently become a hot topic in the fields of mathematics and engineering. Therefore, studies on the complex order systems and their subset called the complex conjugate order systems began to appear in the control community. On the other hand, the concept of stability has always been an important issue, especially in the analysis and control of dynamical systems. In this paper, a graphical method for stability analysis of the complex conjugate order systems is presented. Since the proposed method is based on the Mikhailov stability criterion known from the stability theory of integer order systems, it is named the generalized modified Mikhailov stability criterion. This method gives stability information about the higher order complex conjugate order systems, i.e. cascade conjugate order systems, according to whether it encloses the origin in the complex plane or not. Three simulation examples for the cascade conjugate order systems are given to show the effectiveness and reliability of the method presented. The results are verified by the poles on the first sheet of Riemann surface and also time responses of the systems, which are calculated analytically in a very complex way.

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.

Walking Stability Analysis of Multi-Legged Crablike Robot over Slope

2013 ◽  
Vol 572 ◽  
pp. 636-639
Author(s):  
Xi Chen ◽  
Gang Wang
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Stability Criterion ◽  
Stability Margin ◽  
Static Stability ◽  
Matlab Simulation ◽  
And Performance ◽  
The Stability ◽  
The Mathematical Model ◽  
The Relationship

This paper deals with the walking stability analysis of a multi-legged crablike robot over slope using normalized energy stability margin (NESM) method in order to develop a common stabilization description method and achieve robust locomotion for the robot over rough terrains. The robot is simplified with its static stability being described by NESM. The mathematical model of static stability margin is built so as to carry out the simulation of walking stability over slope for the crablike robot that walks in double tetrapod gait. As a consequence, the relationship between stability margin and the height of the robots centroid, as well as its inclination relative to the ground is calculated by the stability criterion. The success and performance of the stability criterion proposed is verified through MATLAB simulation and real-world experiments using multi-legged crablike robot.

Stability Analysis and Control Measures of the Kim-Yun-Mine Collapse

2012 ◽  
Vol 594-597 ◽  
pp. 358-361
Author(s):  
Shan Shan Zhang ◽  
Yu Liang Wu
Keyword(s):  
Rock Mass ◽  
Stability Analysis ◽  
Stereographic Projection ◽  
Control Measures ◽  
Collapse Characteristics ◽  
Basic Characteristics ◽  
The Stability ◽  
Mine Collapse ◽  
And Control ◽  
Dangerous Rock Mass

Collapse is one of the major geological disasters all over the world and threats to life and property safety of people. To make a better understanding of the reason it occurs and how to deal with it, the Kim-Yun-Mine collapse is researched. There are one dangerous rock mass and two collapse accumulation body. The basic characteristics of the collapse is described clearly according to the geological exploration data, and the stability of the dangerous rock mass and the collapse accumulated body is analyzed in the way of engineering geology and stereographic projection. At last, we put forward comprehensive control measures based on the results of stability analysis and collapse characteristics.

An Improved Delay-Dependent Stability Criterion for a Class of Lur’e Systems of Neutral Type

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
K. Ramakrishnan ◽  
G. Ray
Keyword(s):  
Stability Analysis ◽  
Stability Criterion ◽  
Time Derivative ◽  
Neutral Type ◽  
Linear Matrix ◽  
Lur’E Systems ◽  
The Stability ◽  
Delay Dependent ◽  
Bounded Nonlinearity ◽  
Delay Dependent Stability

In this paper, we consider the problem of delay-dependent stability of a class of Lur’e systems of neutral type with time-varying delays and sector-bounded nonlinearity using Lyapunov–Krasovskii (LK) functional approach. By using a candidate LK functional in the stability analysis, a less conservative absolute stability criterion is derived in terms of linear matrix inequalities (LMIs). In addition to the LK functional, conservatism in the proposed stability analysis is further reduced by imposing tighter bounding on the time-derivative of the functional without neglecting any useful terms using minimal number of slack matrix variables. The proposed analysis, subsequently, yields a stability criterion in convex LMI framework, and is solved nonconservatively at boundary conditions using standard LMI solvers. The effectiveness of the proposed criterion is demonstrated through a standard numerical example and Chua’s circuit.

Lattice hydrodynamic model for bidirectional pedestrian flow with the consideration of pedestrian density difference

2015 ◽  
Vol 26 (08) ◽  
pp. 1550092 ◽  
Author(s):  
Jie Zhou ◽  
Zhong-Ke Shi
Keyword(s):  
Stability Analysis ◽  
Hydrodynamic Model ◽  
Density Difference ◽  
Subway Station ◽  
Lattice Hydrodynamic Model ◽  
Analysis Method ◽  
Pedestrian Flow ◽  
Reaction Coefficient ◽  
De Vries ◽  
The Stability

Considering the effect of density difference, an extended lattice hydrodynamic model for bidirectional pedestrian flow is proposed in this paper. The stability condition is obtained by the use of linear stability analysis. It is shown that the stability of pedestrian flow varies with the reaction coefficient of density difference. Based on nonlinear analysis method, the Burgers, Korteweg–de Vries (KdV) and modified Korteweg–de Vries (MKdV) equations are derived to describe the triangular shock waves, soliton waves and kink–antikink waves in the stable, metastable and unstable regions, respectively. The results show that jams may be alleviated by considering the effect of density difference. The findings also indicate that in the process of building and subway station design, a series of auxiliary facilities should be considered in order to alleviate the possible pedestrian jams.

Causes Analysis and Control Measures of Landslide on Expressway from Yangshuo to Pingle in Guangxi

2013 ◽  
Vol 353-356 ◽  
pp. 116-119
Author(s):  
Chan Juan Yu ◽  
Yu Dong Peng
Keyword(s):  
Transfer Coefficient ◽  
Reference Value ◽  
Control Measures ◽  
The Other ◽  
Retaining Structure ◽  
Treatment Measures ◽  
Stability Of Slope ◽  
The Stability ◽  
And Control ◽  
Coefficient Method

According to the analysis on engineering geological and hydrological conditions of landslide on expressway from Yangshuo to Pingle in Guangxi, the formation mechanism of the landslide was summarized. The stability of slope was analyzed by mechanical transfer coefficient method. Then two kinds of effective preventions and treatment measures are proposed: setting retaining structure after drainage, or unloading after drainage. These measures have reference value to the management of the other landslide.

Stability of time-dependent rotational Couette flow Part 2. Stability analysis

1971 ◽  
Vol 48 (2) ◽  
pp. 365-384 ◽  
Author(s):  
C. F. Chen ◽  
R. P. Kirchner
Keyword(s):  
Growth Rate ◽  
Stability Analysis ◽  
Kinetic Energy ◽  
Initial Value Problem ◽  
Basic Flow ◽  
The Other ◽  
Time Dependent ◽  
Stability Criteria ◽  
Initial Value ◽  
The Stability

The stability of the flow induced by an impulsively started inner cylinder in a Couette flow apparatus is investigated by using a linear stability analysis. Two approaches are taken; one is the treatment as an initial-value problem in which the time evolution of the initially distributed small random perturbations of given wavelength is monitored by numerically integrating the unsteady perturbation equations. The other is the quasi-steady approach, in which the stability of the instantaneous velocity profile of the basic flow is analyzed. With the quasi-steady approach, two stability criteria are investigated; one is the standard zero perturbation growth rate definition of stability, and the other is the momentary stability criterion in which the evolution of the basic flow velocity field is partially taken into account. In the initial-value problem approach, the predicted critical wavelengths agree remarkably well with those found experimentally. The kinetic energy of the perturbations decreases initially, reaches a minimum, then grows exponentially. By comparing with the experimental results, it may be concluded that when the perturbation kinetic energy has grown a thousand-fold, the secondary flow pattern is clearly visible. The time of intrinsic instability (the time at which perturbations first tend to grow) is about ¼ of the time required for a thousandfold increase, when the instability disks are clearly observable. With the quasi-steady approach, the critical times for marginal stability are comparable to those found using the initial-value problem approach. The predicted critical wavelengths, however, are about 1½ to 2 times larger than those observed. Both of these points are in agreement with the findings of Mahler, Schechter & Wissler (1968) treating the stability of a fluid layer with time-dependent density gradients. The zero growth rate and the momentary stability criteria give approximately the same results.

scholarly journals Complex-Coefficient Frequency Domain Stability Analysis Method for a Class of Cross-Coupled Antisymmetrical Systems and Its Extension in MSR Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Yuan Ren ◽  
Jiancheng Fang
Keyword(s):  
Stability Analysis ◽  
Frequency Domain ◽  
Stability Criterion ◽  
Mimo System ◽  
Multiple Input Multiple Output ◽  
Complex Coefficient ◽  
Analysis Method ◽  
Multiple Input ◽  
Input Multiple Output ◽  
Domain Stability

This paper develops a complex-coefficient frequency domain stability analysis method for a class of cross-coupled two-dimensional antisymmetrical systems, which can greatly simplify the stability analysis of the multiple-input multiple-output (MIMO) system. Through variable reconstruction, the multiple-input multiple-output (MIMO) system is converted into a single-input single-output (SISO) system with complex coefficients. The pole locations law of the closed-loop system after the variable reconstruction has been revealed, and the controllability as well as observability of the controlled plants before and after the variable reconstruction has been studied too, and then the classical Nyquist stability criterion is extended to the complex-coefficient frequency domain. Combined with the rigid magnetically suspended rotor (MSR) system with heavy gyroscopic effects, corresponding stability criterion has been further developed. Compared with the existing methods, the developed criterion for the rigid MSR system not only accurately predicts the absolute stability of the different whirling modes, but also directly demonstrates their relative stability, which greatly simplifies the analysis, design, and debugging of the control system.

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