Time Domain Approaches to the Stability Analysis of Flexible Dynamical Systems

2015 ◽  
Vol 11 (4) ◽  
Author(s):  
Jielong Wang ◽  
Xiaowen Shan ◽  
Bin Wu ◽  
Olivier A. Bauchau
Keyword(s):  
Stability Analysis ◽  
Dynamical Systems ◽  
Time Domain ◽  
Floquet Theory ◽  
Characteristic Exponent ◽  
Periodic Coefficient ◽  
Theoretical Background ◽  
System Stability ◽  
Lyapunov Characteristic Exponent ◽  
The Stability

This paper presents two approaches to the stability analysis of flexible dynamical systems in the time domain. The first is based on the partial Floquet theory and proceeds in three steps. A preprocessing step evaluates optimized signals based on the proper orthogonal decomposition (POD) method. Next, the system stability characteristics are obtained from partial Floquet theory through singular value decomposition (SVD). Finally, a postprocessing step assesses the accuracy of the identified stability characteristics. The Lyapunov characteristic exponent (LCE) theory provides the theoretical background for the second approach. It is shown that the system stability characteristics are related to the LCE closely, for both constant and periodic coefficient systems. For the latter systems, an exponential approximation is proposed to evaluate the transition matrix. Numerical simulations show that the proposed approaches are robust enough to deal with the stability analysis of flexible dynamical systems and the predictions of the two approaches are found to be in close agreement.

Stability Analysis of Complex Multibody Systems

2005 ◽  
Vol 1 (1) ◽  
pp. 71-80 ◽  
Author(s):  
Olivier A. Bauchau ◽  
Jielong Wang
Keyword(s):  
Stability Analysis ◽  
Multibody Systems ◽  
Floquet Theory ◽  
Numerical Models ◽  
Characteristic Exponent ◽  
Prony's Method ◽  
Linearized Stability ◽  
The Stability ◽  
Curve Fitting Method ◽  
Prony’S Method

The linearized stability analysis of dynamical systems modeled using finite element-based multibody formulations is addressed in this paper. The use of classical methods for stability analysis of these systems, such as the characteristic exponent method or Floquet theory, results in computationally prohibitive costs. Since comprehensive multibody models are “virtual prototypes” of actual systems, the applicability to numerical models of the stability analysis tools that are used in experimental settings is investigated in this work. Various experimental tools for stability analysis are reviewed. It is proved that Prony’s method, generally regarded as a curve-fitting method, is equivalent, and sometimes identical, to Floquet theory and to the partial Floquet method. This observation gives Prony’s method a sound theoretical footing, and considerably improves the robustness of its predictions when applied to comprehensive models of complex multibody systems. Numerical and experimental applications are presented to demonstrate the efficiency of the proposed procedure.

Stability Analysis of Complex Multibody Systems

2005 ◽  
Author(s):  
Olivier A. Bauchau ◽  
Jielong Wang
Keyword(s):  
Stability Analysis ◽  
Floquet Theory ◽  
Numerical Models ◽  
Characteristic Exponent ◽  
Fitting Method ◽  
Prony's Method ◽  
Linearized Stability ◽  
The Stability ◽  
Curve Fitting Method ◽  
Prony’S Method

The linearized stability analysis of dynamical systems modeled using finite element based multibody formulations is addressed in this paper. The use of classical methods for stability analysis of these system, such as the characteristic exponent method or Floquet theory, results in computationally prohibitive costs. Since comprehensive multibody models are “virtual prototypes” of actual systems, the applicability to numerical models of the stability analysis tools that are used in experimental settings is investigated in this work. Various experimental tools for stability analysis are reviewed. It is proved that Prony’s method, generally regarded as a curve fitting method, is equivalent, and sometimes identical, to Floquet theory and to the partial Floquet method. This observation gives Prony’s method a sound theoretical, footing, and considerably improves the robustness of its predictions when applied to comprehensive models of complex multibody system. Numerical applications are presented to demonstrate the efficiency of the proposed procedure.

The Application of LabVIEW in Control System Stability Analysis

2012 ◽  
Vol 182-183 ◽  
pp. 788-792
Author(s):  
Xue Ning Xing
Keyword(s):  
Control System ◽  
Stability Analysis ◽  
User Interface ◽  
Control Theory ◽  
Time Domain ◽  
System Stability ◽  
Graphic User Interface ◽  
System Stability Analysis ◽  
The Stability ◽  
Classical Control

The stability of the system is the prior condition for whether the control system can operate normally, in the classical control theory, time domain analyze method, complex domain analyze method and frequency domain analyze method are often used to analyze the performance of the control system. Using LabVIEW to design graphic user interface, input parameters, then the curve can be drawn out immediately and calculate the interrelated parameters, which plays an important role in analyzing the stability of the system.

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 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.

The Analysis of the Systems Stability of Linear Differential Equations Based on the Transformation of Difference Schemes

2019 ◽  
Vol 20 (9) ◽  
pp. 542-549 ◽  
Author(s):  
S. G. Bulanov
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Computer Analysis ◽  
Linear Differential Equations ◽  
System Stability ◽  
The Difference ◽  
Linear Differential ◽  
The Stability

The approach to the analysis of Lyapunov systems stability of linear ordinary differential equations based on multiplicative transformations of difference schemes of numerical integration is presented. As a result of transformations, the stability criteria in the form of necessary and sufficient conditions are formed. The criteria are invariant with respect to the right side of the system and do not require its transformation with respect to the difference scheme, the length of the gap and the step of the solution. A distinctive feature of the criteria is that they do not use the methods of the qualitative theory of differential equations. In particular, for the case of systems with a constant matrix of the coefficients it is not necessary to construct a characteristic polynomial and estimate the values of the characteristic numbers. When analyzing the system stability with variable matrix coefficients, it is not necessary to calculate the characteristic indicators. The varieties of criteria in an additive form are obtained, the stability analysis based on them being equivalent to the stability assessment based on the criteria in a multiplicative form. Under the conditions of a linear system stability (asymptotic stability) of differential equations, the criteria of the systems stability (asymptotic stability) of linear differential equations with a nonlinear additive are obtained. For the systems of nonlinear ordinary differential equations the scheme of stability analysis based on linearization is presented, which is directly related to the solution under study. The scheme is constructed under the assumption that the solution stability of the system of a general form is equivalent to the stability of the linearized system in a sufficiently small neighborhood of the perturbation of the initial data. The matrix form of the criteria allows implementing them in the form of a cyclic program. The computer analysis is performed in real time and allows coming to an unambiguous conclusion about the nature of the system stability under study. On the basis of a numerical experiment, the acceptable range of the step variation of the difference method and the interval length of the difference solution within the boundaries of the reliability of the stability analysis is established. The approach based on the computer analysis of the systems stability of linear differential equations is rendered. Computer testing has shown the feasibility of using this approach in practice.

Modeling and Stability Analysis of Dynamic Control Through a Soft Interface

2006 ◽  
Vol 18 (3) ◽  
pp. 242-248 ◽  
Author(s):  
Mizuho Shibata ◽  
◽  
Shinichi Hirai
Keyword(s):  
Stability Analysis ◽  
Discrete Time ◽  
Feedforward Control ◽  
Dynamic Control ◽  
System Stability ◽  
Critical Stability ◽  
Runge Kutta Method ◽  
The Stability ◽  
The Relationship ◽  
Soft Interface

To analyze the stability of dynamic control through asoft interface-the viscoelastic material between a manipulating finger and a manipulated object- we model dynamic control through the soft interface in continuous-discrete time. We then formulate dynamics using a modified z-transform in continuous-discrete time for feedback and feedforward control. We show that system stability depends on the viscoelasticity of the soft interface for feedback control. The relationship between material viscosity and sampling time in critical stability is not monotonous, a phenomenon we analyze by root locus. We compare stability analysis by the modified z-transform, simulations based on the Runge-Kutta method, and a regular z-transform, demonstrating that the relationship is specific to a continuous-discrete time.

scholarly journals Floquet Theory for Discontinuously Supported Waveguides

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
A. Sorzia
Keyword(s):  
Floquet Theory ◽  
Periodic Coefficient ◽  
Fundamental Solutions ◽  
Hill Equation ◽  
Elastic Waveguide ◽  
Elastic String ◽  
Winkler Elastic Foundation ◽  
The Stability ◽  
The Hill ◽  
Band Gap Structure

We apply Floquet theory of periodic coefficient second-order ODEs to an elastic waveguide. The waveguide is modeled as a uniform elastic string periodically supported by a discontinuous Winkler elastic foundation and, as a result, a Hill equation is found. The fundamental solutions, the stability regions, and the dispersion curves are determined and then plotted. An asymptotic approximation to the dispersion curve is also given. It is further shown that the end points of the band gap structure correspond to periodic and semiperiodic solutions of the Hill equation.

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 Analysis of a Pilot Operated Counterbalance Valve for a Big Flow Rate

2014 ◽  
Author(s):  
Yeming Yao ◽  
Hua Zhou ◽  
Yinglong Chen ◽  
Huayong Yang
Keyword(s):  
Stability Analysis ◽  
Flow Rate ◽  
Numerical Optimization ◽  
Dynamic Performance ◽  
Optimization Method ◽  
System Stability ◽  
Normal Range ◽  
Alternative Approach ◽  
Linearized Stability ◽  
The Stability

Counterbalance valves are widely used in hydraulic deck machinery to balance the overrunning loads. However, as is well known, counterbalance circuit designed with poor choice of counterbalance valve tends to introduce instability to the system. This paper investigates the dynamic behavior of a pilot operated counterbalance valve which can operate at a flow rate about 2000L/min. A linearized stability analysis of such a hydraulic circuit which consists of a slip in cartridge, a pilot counterbalance valve and a hydraulic winch is presented. Pole-zero plots are employed to reveal the effect of the volume of control cavity, the hydraulic resistance on pilot line and counterbalance valve pilot area ratio on the stability of the system. The analysis results indicate that such a system will be unstable within the normal range of each parameter. An alternative approach that guarantees system stability by adding an accumulator on the pilot line is put forward. The approach stabilizes the pilot pressure by reducing the hydro-stiffness of pilot control cavity, thus the system can reach its stability condition. Finally, a numerical optimization method is putted forward, with the optimized parameters, the dynamic performance of considered system become better.

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