On the stability of low-order perturbed polynomials

1990 ◽  
Vol 35 (2) ◽  
pp. 180-182 ◽  
Author(s):  
M.B. Argoun
Keyword(s):  
The Stability ◽  
Perturbed Polynomials ◽  
Low Order

scholarly journals How Climate Model Complexity Influences Sea Ice Stability

2015 ◽  
Vol 28 (10) ◽  
pp. 3998-4014 ◽  
Author(s):  
Till J. W. Wagner ◽  
Ian Eisenman
Keyword(s):  
Sea Ice ◽  
Climate Models ◽  
Ice Cover ◽  
Arctic Sea Ice ◽  
Global Climate Models ◽  
Model Complexity ◽  
The Arctic ◽  
Arctic Sea ◽  
The Stability ◽  
Low Order

Abstract Record lows in Arctic sea ice extent have been making frequent headlines in recent years. The change in albedo when sea ice is replaced by open water introduces a nonlinearity that has sparked an ongoing debate about the stability of the Arctic sea ice cover and the possibility of Arctic “tipping points.” Previous studies identified instabilities for a shrinking ice cover in two types of idealized climate models: (i) annual-mean latitudinally varying diffusive energy balance models (EBMs) and (ii) seasonally varying single-column models (SCMs). The instabilities in these low-order models stand in contrast with results from comprehensive global climate models (GCMs), which typically do not simulate any such instability. To help bridge the gap between low-order models and GCMs, an idealized model is developed that includes both latitudinal and seasonal variations. The model reduces to a standard EBM or SCM as limiting cases in the parameter space, thus reconciling the two previous lines of research. It is found that the stability of the ice cover vastly increases with the inclusion of spatial communication via meridional heat transport or a seasonal cycle in solar forcing, being most stable when both are included. If the associated parameters are set to values that correspond to the current climate, the ice retreat is reversible and there is no instability when the climate is warmed. The two parameters have to be reduced by at least a factor of 3 for instability to occur. This implies that the sea ice cover may be substantially more stable than has been suggested in previous idealized modeling studies.

scholarly journals Design of a Low-Order Harmonic Disturbance Observer with Application to a DC Motor Position Control

Energies ◽  
2020 ◽  
Vol 13 (5) ◽  
pp. 1020
Author(s):  
In Hyuk Kim ◽  
Young Ik Son
Keyword(s):  
Disturbance Observer ◽  
Position Control ◽  
Uncertain System ◽  
Dc Motor ◽  
Singular Perturbation Theory ◽  
Layer System ◽  
Unknown Amplitude ◽  
Nominal Performance ◽  
The Stability ◽  
Low Order

Among various tools implemented to counteract undesired effects of time-varying uncertainties, disturbance observer (DOB)-based controller has gained wide popularity as a result of its flexibility and efficacy. In this paper, a low-order DOB that is capable of compensating for the effects of a biased harmonic disturbance, as well as plant uncertainties is presented. The proposed low-order DOB can asymptotically estimate a harmonic disturbance of known frequency but unknown amplitude and phase, by using measurable output variables. An analysis carried out by using the singular perturbation theory shows that the nominal performance of the system can be recovered from a real uncertain system when the observer gain is sufficiently large. The observer gains that result in the performance recovery of the real uncertain system are obtained from the stability condition of the boundary-layer system. To test the performance of the proposed observer, computer simulations with a numerical example and laboratory experiments using a DC motor system have been carried out. The experimental results show that the proposed low-order DOB-based control scheme can provide enhanced performance.

The Effect of Modeling Errors on Linear State Reconstructors and Regulators

1974 ◽  
Vol 96 (4) ◽  
pp. 454-459 ◽  
Author(s):  
F. E. Thau ◽  
A. Kestenbaum
Keyword(s):  
Dynamic Systems ◽  
Upper Bound ◽  
Reconstruction Error ◽  
Order Model ◽  
Modeling Errors ◽  
Parameter Variations ◽  
Linear State ◽  
The Stability ◽  
Linear Regulators ◽  
Low Order

The effect of imprecise knowledge of system parameters on the reconstruction error of linear observers and on the stability of a class of linear regulators is examined. An upper bound on the reconstruction error for linear unforced systems is obtained. It is shown that in the regulator problem consideration of parameter uncertainty leads to the inclusion of step disturbances. An upper bound on allowed parameter variations that guarantees stability of a class of closed-loop regulators is obtained. It is also shown that by properly choosing parameters of a low-order observer, the output of this low-order model can be made to follow closely the output of a higher-order dynamic systems. The effect of modeling errors on randomly perturbed systems is also examined.

Thermoacoustic Stability Analysis of an Annular Combustion Chamber With Acoustic Low Order Modeling and Validation Against Experiment

2005 ◽  
Author(s):  
Jan Kopitz ◽  
Andreas Huber ◽  
Thomas Sattelmayer ◽  
Wolfgang Polifke
Keyword(s):  
Transfer Function ◽  
Network Model ◽  
Transfer Functions ◽  
Model Simulation ◽  
Scaling Methods ◽  
Annular Combustor ◽  
The Stability ◽  
Operating Points ◽  
Low Order

A low order acoustic network model is used to examine the stability of an annular combustor for different operating points. The results obtained by this approach are compared against experimental data from a full annular combustor. This annular combustor, in contrast to commonly used single burners or sector rigs, was used to include also 2-dimensional effects like the influence of circumferential modes, which can occur in practical gas turbine applications. The influence of the flame enters the network model simulation through an experimentally measured flame transfer function in terms of the response of heat release to acoustic velocity fluctuations. This flame transfer function, which has been measured at a stable operating point, is then used as a basis for the determination of flame transfer functions at other operating points by means of scaling methods. The transition to instability is thereby simulated by determination of the complex eigen modes, applying methods from control theory. The analytically determined stability behavior is compared to the experimentally measured one, with the aim to enhance and validate the network model approach as a means of predicting combustion instabilities in early design stages.

Characteristic stabilized finite element method for non-stationary conduction-convection problems

2019 ◽  
Vol 30 (2) ◽  
pp. 625-658
Author(s):  
Yongshuai Wang ◽  
Md. Abdullah Al Mahbub ◽  
Haibiao Zheng
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Time Derivative ◽  
Content Type ◽  
Stabilized Finite Element ◽  
Stabilized Finite Element Method ◽  
Advection Term ◽  
The Stability ◽  
Element Method ◽  
Low Order

Purpose This paper aims to propose a characteristic stabilized finite element method for non-stationary conduction-convection problems. Design/methodology/approach To avoid difficulty caused by the trilinear term, the authors use the characteristic method to deal with the time derivative term and the advection term. The space discretization adopts the low-order triples (i.e. P1-P1-P1 and P1-P0-P1 triples). As low-order triples do not satisfy inf-sup condition, the authors use the stability technique to overcome this flaw. Findings The stability and the convergence analysis shows that the method is stable and has optimal-order error estimates. Originality/value Numerical experiments confirm the theoretical analysis and illustrate that the authors’ method is highly effective and reliable, and consumes less CPU time.

Delay Identification in Thermoacoustics

2021 ◽  
Author(s):  
F. Gant ◽  
G. Ghirardo ◽  
A. Cuquel ◽  
M. R. Bothien
Keyword(s):  
Time Series ◽  
Time Delay ◽  
Additive White Gaussian Noise ◽  
A Priori ◽  
Accurate Estimate ◽  
Combustion Noise ◽  
Unknown Parameters ◽  
Acoustic Damping ◽  
The Stability ◽  
Low Order

Abstract The stability of thermoacoustic systems is often regulated by the time delay between acoustic perturbations and corresponding heat release fluctuations. An accurate estimate of this value is of great importance in applications, since even small modifications can introduce significant changes in the system behavior Different studies show that the nonlinear delayed dynamics typical of these systems can be well captured with low-order models. In the present work, a method is introduced to estimate the most likely value of the time delay of a single thermoacoustic mode from a measured acoustic pressure signal. The mode of interest is modeled by an oscillator equation, with a nonlinear delayed forcing term modeling the deterministic flame contribution and an additive white Gaussian noise to embed the stochastic combustion noise. Additionally, other thermoacoustic relevant parameters are estimated. The model accounts for a flame gain, for a flame saturation coefficient, for a linear acoustic damping and for the background combustion noise intensity. The pressure data time series is statistically analyzed and the set of unknown parameters is identified. Validation is performed with respect to synthetically generated time series and low order model simulations, for which the underlying delay is known a priori. A discussion follows about the accuracy of the method, in particular a comparison with existing methods is drawn.

ANALYSIS OF THE STABILITY OF LINEAR SYSTEMS

2020 ◽  
pp. 12-18
Author(s):  
Filier Zalmen ◽  
Keyword(s):  
Linear Systems ◽  
Complex Plane ◽  
Autonomous Systems ◽  
Entire Complex ◽  
The Stability ◽  
Low Order

Various criteria of stability of linear autonomous systems are considered. It is stated that the method of A.V. Mikhailov makes it possible to visually establish the stability of equations of a low order. The methods of criterion finityzation proposed by the author make it possible to use it to analyze the stability of equations with delays. An interesting way of finding the hodograph with the entire complex plane. Keywords: criterion of stability, finityzation, hodograph, delay

scholarly journals An improving control strategy for grid -connected current in weak grid

2021 ◽  
Vol 252 ◽  
pp. 01010
Author(s):  
Deng Songyuan ◽  
Zhao Xia
Keyword(s):  
Control Strategy ◽  
Feedforward Control ◽  
Power Grid ◽  
Impedance Analysis ◽  
System Stability ◽  
Grid Impedance ◽  
Grid Connected Inverter ◽  
The Stability ◽  
Proportional Controller ◽  
Low Order

The traditional proportional feedforward control strategy can suppress the low order harmonics in the strong power grid, but in the weak power grid environment, the grid impedance will have an adverse impact on the stability of the system, resulting in the proportional feedforward control can not suppress the low order harmonics well. In order to solve this problem, a control strategy combining resonant feedforward and new repetitive proportional controller is proposed. Firstly, the stability of traditional proportional feedforward and resonant feedforward systems is analyzed and compared by impedance analysis method. Then, a new repetitive controller is added to suppress low order harmonics based on resonant feedforward control, and the stability of single-phase LCL grid connected inverter system is analyzed Matlab / Simulink is used to simulate and verify the system. The results show that the system stability and the ability to suppress low order harmonics are significantly improved.

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