Frequency Domain Conditions for the Stability of Low Order Perturbed Polynomials

1988 ◽  
Author(s):  
Mohammad B. Argoun
Keyword(s):  
Frequency Domain ◽  
The Stability ◽  
Perturbed Polynomials ◽  
Low Order

scholarly journals Explicit parallel co-simulation approach: analysis and improved coupling method based on H-infinity synthesis

2021 ◽  
Author(s):  
Weitao Chen ◽  
Shenhai Ran ◽  
Canhui Wu ◽  
Bengt Jacobson
Keyword(s):  
Frequency Domain ◽  
Wide Frequency Range ◽  
Coupling Method ◽  
Sampled Data ◽  
H Infinity ◽  
First Case ◽  
Communication Step ◽  
Coupling Variables ◽  
The Stability ◽  
Stability And Accuracy

AbstractCo-simulation is widely used in the industry for the simulation of multidomain systems. Because the coupling variables cannot be communicated continuously, the co-simulation results can be unstable and inaccurate, especially when an explicit parallel approach is applied. To address this issue, new coupling methods to improve the stability and accuracy have been developed in recent years. However, the assessment of their performance is sometimes not straightforward or is even impossible owing to the case-dependent effect. The selection of the coupling method and its tuning cannot be performed before running the co-simulation, especially with a time-varying system.In this work, the co-simulation system is analyzed in the frequency domain as a sampled-data interconnection. Then a new coupling method based on the H-infinity synthesis is developed. The method intends to reconstruct the coupling variable by adding a compensator and smoother at the interface and to minimize the error from the sample-hold process. A convergence analysis in the frequency domain shows that the coupling error can be reduced in a wide frequency range, which implies good robustness. The new method is verified using two co-simulation cases. The first case is a dual mass–spring–damper system with random parameters and the second case is a co-simulation of a multibody dynamic (MBD) vehicle model and an electric power-assisted steering (EPAS) system model. Experimental results show that the method can improve the stability and accuracy, which enables a larger communication step to speed up the explicit parallel co-simulation.

Design of a Force Feedback Chatter Control System

1972 ◽  
Vol 94 (1) ◽  
pp. 5-10 ◽  
Author(s):  
C. Nachtigal
Keyword(s):  
Machine Tool ◽  
Frequency Domain ◽  
Transient Response ◽  
Force Feedback ◽  
Design Procedure ◽  
Experimental Tests ◽  
Work Piece ◽  
Regenerative Chatter ◽  
Chatter Control ◽  
The Stability

The analysis of machine tool chatter from frequency domain considerations is generally accepted as a valid representation of the regenerative chatter phenomenon. However, active control of regenerative chatter is still in its embryonic stage. It was established in reference [2] that a measurement of the cutting force could be effectively used in conjunction with a controller and a tool position servo system to increase the stability of an engine lathe and to improve its transient response. This paper presents the design basis for such a system, including both analytical and experimental considerations. The design procedure stems from a real part stability criterion based on the work by Merritt [1]. Because of the unknown variability in the dynamics of a machine tool system, the controller parameters were chosen to accomodate some mismatch between structure and tool servo dynamics. Experimental tests to determine the stability zone of the controlled machine tool system qualitatively confirmed the analytical design results. The experimental results were consistent in that the transient response tests confirmed the frequency domain stability tests. It was also demonstrated experimentally that the equivalent static stiffness of a flexible work-piece system could be substantially increased.

Frequency-domain analysis method for analyzing and improving the steady-state characteristics of microcantilever in tapping-mode atomic force microscopy

2018 ◽  
Vol 82 (1) ◽  
pp. 10701
Author(s):  
Xiaohui Gu ◽  
Lining Sun ◽  
Changhai Ru
Keyword(s):  
Steady State ◽  
Frequency Domain ◽  
Stability Margin ◽  
Domain Analysis ◽  
Frequency Domain Analysis ◽  
System Stability ◽  
Analysis Method ◽  
External Interference ◽  
Tapping Mode ◽  
The Stability

In tapping-mode AFM, the steady-state characteristics of microcantilever are extremely important to determine the AFM performance. Due to the external excitation signal and the tip-sample interactions, the solving process of microcantilever motion equation will become very complicated with the traditional time-domain analysis method. In this paper, we propose the novel frequency-domain analysis method to analyze and improve the steady-state characteristics of microcantilever. Compared with the previous methods, this new method has three prominent advantages. Firstly, the analytical expressions of amplitude and phase of cantilever system can be derived conveniently. Secondly, the stability of the cantilever system can be accurately determined and the stability margin can be obtained quantitatively in terms of the phase margin and the magnitude margin. Thirdly, on this basis, external control mechanism can be devised quickly and easily to guarantee the high stability of the cantilever system. With this novel method, we derive the frequency response curves and discuss the great influence of the intrinsic parameters on the system stability, which provides theoretical guidance for selecting samples to achieve better AFM images in the experiments. Moreover, we introduce a new external series correction method to significantly increase the stability margin. The results indicate that the cantilever system is no longer easily disturbed by external interference signals.

Stability results for an elastic–viscoelastic wave equation with localized Kelvin–Voigt damping and with an internal or boundary time delay

2020 ◽  
pp. 1-57
Author(s):  
Mouhammad Ghader ◽  
Rayan Nasser ◽  
Ali Wehbe
Keyword(s):  
Wave Equation ◽  
Time Delay ◽  
Frequency Domain ◽  
Viscoelastic Damping ◽  
One Dimensional ◽  
Viscoelastic Wave ◽  
Smooth Coefficients ◽  
The Stability ◽  
Stability Results ◽  
Dimensional Wave

We investigate the stability of a one-dimensional wave equation with non smooth localized internal viscoelastic damping of Kelvin–Voigt type and with boundary or localized internal delay feedback. The main novelty in this paper is that the Kelvin–Voigt and the delay damping are both localized via non smooth coefficients. Under sufficient assumptions, in the case that the Kelvin–Voigt damping is localized faraway from the tip and the wave is subjected to a boundary delay feedback, we prove that the energy of the system decays polynomially of type t − 4 . However, an exponential decay of the energy of the system is established provided that the Kelvin–Voigt damping is localized near a part of the boundary and a time delay damping acts on the second boundary. While, when the Kelvin–Voigt and the internal delay damping are both localized via non smooth coefficients near the boundary, under sufficient assumptions, using frequency domain arguments combined with piecewise multiplier techniques, we prove that the energy of the system decays polynomially of type t − 4 . Otherwise, if the above assumptions are not true, we establish instability results.

Identification of highly accurate low order state space models in the frequency domain

1996 ◽  
Vol 52 (2) ◽  
pp. 195-207 ◽  
Author(s):  
Robert N. Jacques ◽  
Ketao Liu ◽  
David W. Miller
Keyword(s):  
State Space ◽  
Frequency Domain ◽  
State Space Models ◽  
Order State ◽  
Low Order

Data Processing in Bifurcation Analysis of Maps with Time-Delays in the Frequency Domain

2014 ◽  
Vol 685 ◽  
pp. 634-637
Author(s):  
Li Zeng ◽  
Jun Wei Wang
Keyword(s):  
Data Processing ◽  
Frequency Domain ◽  
Time Delays ◽  
Period Doubling ◽  
Feedback Systems ◽  
Bifurcation Solution ◽  
Nonlinear Maps ◽  
The Stability ◽  
Frequency Domain Approach ◽  
Period Doubling Bifurcations

A unified frequency-domain approach to analyze the NS (Neimark-Sacker) bifurcations and the period-doubling bifurcations of nonlinear maps with time-delays in the linear feed-forward term is presented. The technique relies on the HBA (harmonic balance approximation, a very important method in data processing ) and feedback systems theory. The expressions of the bifurcation solution and the stability are derived.

STABILITY AND HOPF BIFURCATION ON A TWO-NEURON SYSTEM WITH TIME DELAY IN THE FREQUENCY DOMAIN

2007 ◽  
Vol 17 (04) ◽  
pp. 1355-1366 ◽  
Author(s):  
WENWU YU ◽  
JINDE CAO
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Frequency Domain ◽  
Harmonic Balance ◽  
Neuron System ◽  
Bifurcation Theorem ◽  
Nyquist Criterion ◽  
The Stability ◽  
Frequency Domain Approach ◽  
System With Time Delay

In this paper, a general two-neuron model with time delay is considered, where the time delay is regarded as a parameter. It is found that Hopf bifurcation occurs when this delay passes through a sequence of critical value. By analyzing the characteristic equation and using the frequency domain approach, the existence of Hopf bifurcation is determined. The stability of bifurcating periodic solutions are determined by the harmonic balance approach, Nyquist criterion and the graphic Hopf bifurcation theorem. Numerical results are given to justify the theoretical analysis.

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