OFF-CENTER COMPRESSION OF THE ROD BY POTENTIAL AND NONCONSERVATIVE FORCES

2020 ◽  
pp. 9-16
Author(s):  
V. P. Radin ◽  
V. P. Chirkov ◽  
A. V. Shchugorev ◽  
V. N. Shchugorev
Keyword(s):  
Equilibrium Position ◽  
Stability Region ◽  
Dynamic Method ◽  
Classical Problem ◽  
Flutter Boundary ◽  
Cantilever Rod ◽  
The Stability

The paper studies the stability of the rectilinear form of equilibrium with the construction of the boundaries of the stability region for a rod with uniformly distributed mass. The stability of the cantilever rod is considered for the off-center application of potential and tracking forces. In case of non-conservative loads, when it is possible to lose the stability of the equilibrium position, a dynamic method of research is used. it is shown that the influence of the eccentric application of loads does not affect the location of the flutter boundary, but in contrast to the classical problem, the rod oscillations do not occur in the vicinity of the rectilinear form of equilibrium, but in the vicinity of the curved shape determined by the eccentricity value.

The influence of the Stokes and Archimedes forces on the stability of a two-phase flow

2003 ◽  
Vol 3 ◽  
pp. 266-270
Author(s):  
B.H. Khudjuyerov ◽  
I.A. Chuliev
Keyword(s):  
Spectral Method ◽  
Stability Region ◽  
Gas Flow ◽  
Two Phase Flow ◽  
Solid Phase ◽  
Stability Characteristic ◽  
Phase Flow ◽  
Two Phase ◽  
The Stability

The problem of the stability of a two-phase flow is considered. The solution of the stability equations is performed by the spectral method using polynomials of Chebyshev. A decrease in the stability region gas flow with the addition of particles of the solid phase. The analysis influence on the stability characteristic of Stokes and Archimedes forces.

Enlarging the region of stability in robust model predictive controller based on dual-mode control

2021 ◽  
pp. 014233122110123
Author(s):  
Fatemeh Khani ◽  
Mohammad Haeri
Keyword(s):  
Stability Region ◽  
Linear Matrix ◽  
Input State ◽  
Dual Mode ◽  
Model Predictive Controller ◽  
Mode Control ◽  
Robust Model ◽  
Output Constraints ◽  
Predictive Controller ◽  
The Stability

Industrial processes are inherently nonlinear with input, state, and output constraints. A proper control system should handle these challenging control problems over a large operating region. The robust model predictive controller (RMPC) could be an linear matrix inequality (LMI)-based method that estimates stability region of the closed-loop system as an ellipsoid. This presentation, however, restricts confident application of the controller on systems with large operating regions. In this paper, a dual-mode control strategy is employed to enlarge the stability region in first place and then, trajectory reversing method (TRM) is employed to approximate the stability region more accurately. Finally, the effectiveness of the proposed scheme is illustrated on a continuous stirred tank reactor (CSTR) process.

Global stability result for parabolic Cauchy problems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Mourad Choulli ◽  
Masahiro Yamamoto
Keyword(s):  
New York ◽  
Partial Differential Equations ◽  
Global Stability ◽  
Classical Problem ◽  
Stability Result ◽  
Cauchy Problems ◽  
Smooth Solutions ◽  
Linear Partial Differential Equations ◽  
Ill Posed ◽  
The Stability

AbstractUniqueness of parabolic Cauchy problems is nowadays a classical problem and since Hadamard [Lectures on Cauchy’s Problem in Linear Partial Differential Equations, Dover, New York, 1953], these kind of problems are known to be ill-posed and even severely ill-posed. Until now, there are only few partial results concerning the quantification of the stability of parabolic Cauchy problems. We bring in the present work an answer to this issue for smooth solutions under the minimal condition that the domain is Lipschitz.

Stability of a Rigid Body With an Oscillating Particle: An Application of MACSYMA

1985 ◽  
Vol 52 (3) ◽  
pp. 686-692 ◽  
Author(s):  
L. A. Month ◽  
R. H. Rand
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Classical Problem ◽  
Moment Of Inertia ◽  
Model Parameters ◽  
Stability Chart ◽  
The Stability ◽  
Transition Curves ◽  
Minimum Moment ◽  
Small Angular Velocity

This problem is a generalization of the classical problem of the stability of a spinning rigid body. We obtain the stability chart by using: (i) the computer algebra system MACSYMA in conjunction with a perturbation method, and (ii) numerical integration based on Floquet theory. We show that the form of the stability chart is different for each of the three cases in which the spin axis is the minimum, maximum, or middle principal moment of inertia axis. In particular, a rotation with arbitrarily small angular velocity about the maximum moment of inertia axis can be made unstable by appropriately choosing the model parameters. In contrast, a rotation about the minimum moment of inertia axis is always stable for a sufficiently small angular velocity. The MACSYMA program, which we used to obtain the transition curves, is included in the Appendix.

DRY TURBULENCE FROM A TIME-DELAYED CHUA'S CIRCUIT

1993 ◽  
Vol 03 (02) ◽  
pp. 645-668 ◽  
Author(s):  
A. N. SHARKOVSKY ◽  
YU. MAISTRENKO ◽  
PH. DEREGEL ◽  
L. O. CHUA
Keyword(s):  
Difference Equation ◽  
Stability Region ◽  
Nonlinear Difference Equation ◽  
Chua’S Circuit ◽  
Stability Boundaries ◽  
Chua's Circuit ◽  
Infinite Dimensional ◽  
Chaotic Region ◽  
The Stability ◽  
Left Portion

In this paper, we consider an infinite-dimensional extension of Chua's circuit (Fig. 1) obtained by replacing the left portion of the circuit composed of the capacitance C2 and the inductance L by a lossless transmission line as shown in Fig. 2. As we shall see, if the remaining capacitance C1 is equal to zero, the dynamics of this so-called time-delayed Chua's circuit can be reduced to that of a scalar nonlinear difference equation. After deriving the corresponding 1-D map, it will be possible to determine without any approximation the analytical equation of the stability boundaries of cycles of every period n. Since the stability region is nonempty for each n, this proves rigorously that the time-delayed Chua's circuit exhibits the "period-adding" phenomenon where every two consecutive cycles are separated by a chaotic region.

Vehicle Lateral Motion Control Based on Estimated Stability Regions

2017 ◽  
Author(s):  
Yiwen Huang ◽  
Yan Chen
Keyword(s):  
Measurement Errors ◽  
Local Stability ◽  
Stability Region ◽  
Control Method ◽  
Linearization Method ◽  
Stability Control ◽  
Lateral Stability ◽  
Shortest Distance ◽  
The Stability ◽  
Yaw Moment

This paper presents a novel vehicle lateral stability control method based on an estimated lateral stability region on the phase plane of vehicle yaw rate and lateral speed, which is obtained through a local linearization method. Since the estimated stability region does not only describe vehicle local stability, but also define the oversteering and understeering characteristics, the proposed control method can achieve both local stability and vehicle handling stability. Considering the irregular geometric shape of the estimated stability region, a stability analysis algorithm is designed to determine the distance between vehicle states and stability region boundaries. State estimation or measurement errors are also incorporated in the distance calculation. Based on the calculated shortest distance between vehicle states and stability boundaries, a direct yaw moment controller is designed to maintain vehicle states stay within the stability region. CarSim® and Simulink® co-simulation is applied to verify the control design through a cornering maneuver. The simulation results show that the proposed control method can make the vehicle stay within the stability region successfully and thus always operate in a safe manner.

Approximate calculation of the Caputo-type fractional derivative from inaccurate data. Dynamical approach

2021 ◽  
Vol 24 (3) ◽  
pp. 895-922
Author(s):  
Platon G. Surkov
Keyword(s):  
Control Theory ◽  
Fractional Derivative ◽  
Approximate Calculation ◽  
Classical Problem ◽  
Tikhonov Regularization Method ◽  
Inaccurate Data ◽  
Local Modification ◽  
Ill Posed ◽  
Computational Errors ◽  
The Stability

Abstract A specific formulation of the “classical” problem of mathematical analysis is considered. This is the problem of calculating the derivative of a function. The purpose of this work is to construct an algorithm for the approximate calculation of the Caputo-type fractional derivative based on the methods of control theory. The input data of the algorithm is represented by inaccurate measured function values at discrete, frequently enough, times. The proposed algorithm is based on two aspects: a local modification of the Tikhonov regularization method from the theory of ill-posed problems and the Krasovskii extremal shift method from the guaranteed control theory, both of which ensure the stability to informational noises and computational errors. Numerical experiments were carried out to illustrate the operation of the algorithm.

scholarly journals On the saturation rule for the stability of queues

1995 ◽  
Vol 32 (02) ◽  
pp. 494-507 ◽  
Author(s):  
François Baccelli ◽  
Serguei Foss
Keyword(s):  
Queueing Networks ◽  
Stability Region ◽  
Queueing Systems ◽  
Main Tool ◽  
Stationary Regime ◽  
Arrival Process ◽  
State Variables ◽  
Arrival Times ◽  
Harris Recurrence ◽  
The Stability

This paper focuses on the stability of open queueing systems under stationary ergodic assumptions. It defines a set of conditions, the monotone separable framework, ensuring that the stability region is given by the following saturation rule: ‘saturate' the queues which are fed by the external arrival stream; look at the ‘intensity' μ of the departure stream in this saturated system; then stability holds whenever the intensity of the arrival process, say λ satisfies the condition λ < μ, whereas the network is unstable if λ > μ. Whenever the stability condition is satisfied, it is also shown that certain state variables associated with the network admit a finite stationary regime which is constructed pathwise using a Loynes-type backward argument. This framework involves two main pathwise properties, external monotonicity and separability, which are satisfied by several classical queueing networks. The main tool for the proof of this rule is subadditive ergodic theory. It is shown that, for various problems, the proposed method provides an alternative to the methods based on Harris recurrence and regeneration; this is particularly true in the Markov case, where we show that the distributional assumptions commonly made on service or arrival times so as to ensure Harris recurrence can in fact be relaxed.

Stability Prediction in Turning of Flexible Components

2010 ◽  
Vol 112 ◽  
pp. 149-157 ◽  
Author(s):  
Gorka Urbicain ◽  
David Olvera ◽  
Luis Norberto López de Lacalle ◽  
Francisco Javier Campa
Keyword(s):  
Machine Tool ◽  
Surface Quality ◽  
Classical Problem ◽  
Cutting Conditions ◽  
Stability Prediction ◽  
Nose Radius ◽  
The Stability ◽  
Tool Nose Radius ◽  
Flexible Components

Chatter is the most classical problem in machining. It is prone to occur in low rigidity structures generating poor surface quality and harmful vibrations which could damage any part of the machine-tool system. In finishing operations, the effect of the tool nose radius should be taken into account in order to obtain safe and reliable cutting conditions. The present paper uses a simple SDOF model to study the stability during finishing operations.

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