Absolute stability of a stochastic integrodifferential system. II

1986 ◽  
Vol 34 (2) ◽  
pp. 1535-1541
Author(s):  
B. L. S. Prakasa Rao
Keyword(s):  
Absolute Stability ◽  
Integrodifferential System

The Condition for Absolute Stability of an Electroelastic Actuator Control System for Nanomechatronics

2020 ◽  
Vol 10 (10) ◽  
pp. 52-58
Author(s):  
Sergey M. AFONIN ◽  
Keyword(s):  
Control System ◽  
Adaptive Optics ◽  
Absolute Stability ◽  
Deformation Characteristic ◽  
Straight Line Segment ◽  
Control Mechanisms ◽  
Relative Width ◽  
Random Inputs ◽  
Deformation Control ◽  
Actuator Control

An electroelastic actuator for nanomechatronics is used in nanotechnology, adaptive optics, microsurgery, microelectronics, and biomedicine to actuate or control mechanisms, systems based on the electroelastic effect, and to convert electrical signals into mechanical displacements and forces. In nanomechatronic systems, a piezoactuator is used in scanning microscopy, laser systems, in astronomy for precision alignment, for compensation of temperature, gravitational deformations and atmospheric turbulence, focusing, and stabilizing the image. In this study, a condition for absolute stability of an electroelastic actuator control system for nanomechatronics under deterministic and random inputs is obtained. A number of equilibrium positions in an electroelastic actuator mechatronic control system are found, the totality of which is represented by a straight line segment. The electroelastic actuator’s deformation control system dead band relative width is determined for the actuator’s symmetric and asymmetric hysteresis characteristics. Under deterministic inputs and with fulfilling the condition for the derivative of the nonlinear hysteresis actuator deformation characteristic, the set of equilibrium positions of the electroelastic actuator control system for nanomechatronics is absolutely stable. Under random inputs, the system absolute stability with respect to the mathematical expectations of the electroelastic actuator mechatronic control system equilibrium positions has been determined subject to fulfilling the condition on the derivative of the actuator hysteresis characteristic.

scholarly journals Controllability of a damped nonlinear fractional order integrodifferential system with input delay

2021 ◽  
Author(s):  
Irshad Ahmad ◽  
Ghaus Ur Rahman ◽  
Saeed Ahmad ◽  
Nawal A. Alshehri ◽  
S.K. Alagan
Keyword(s):  
Fractional Order ◽  
Input Delay ◽  
Integrodifferential System

On the convergence of difference schemes for the generalized BBM–Burgers equation

2019 ◽  
Vol 26 (3) ◽  
pp. 341-349 ◽  
Author(s):  
Givi Berikelashvili ◽  
Manana Mirianashvili
Keyword(s):  
Exact Solution ◽  
Sobolev Space ◽  
Difference Scheme ◽  
Absolute Stability ◽  
Burgers Equation ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Algebraic Equations ◽  
The Difference ◽  
Initial Boundary Value

Abstract A three-level finite difference scheme is studied for the initial-boundary value problem of the generalized Benjamin–Bona–Mahony–Burgers equation. The obtained algebraic equations are linear with respect to the values of the desired function for each new level. The unique solvability and absolute stability of the difference scheme are shown. It is proved that the scheme is convergent with the rate of order {k-1} when the exact solution belongs to the Sobolev space {W_{2}^{k}(Q)} , {1<k\leq 3} .

scholarly journals Effects of Ambient Pressure on the Instability of a Liquid Boiling Explosively at the Superheat Limit

1986 ◽  
Vol 108 (2) ◽  
pp. 418-424 ◽  
Author(s):  
D. Frost ◽  
B. Sturtevant
Keyword(s):  
Atmospheric Pressure ◽  
Bubble Growth ◽  
Absolute Stability ◽  
Pressure Field ◽  
Ambient Pressure ◽  
Small Temperature ◽  
Instability Theory ◽  
Two Stages ◽  
Single Droplets ◽  
Superheat Limit

The effect of ambient pressure on the intrinsic instability of rapid vaporization in single droplets boiling explosively at the limit of superheat has been studied experimentally and theoretically. The instability that distorts the evaporating interface and substantially enhances the mass flux at atmospheric pressure is suppressed at high pressure. The radiated pressure field is two orders of magnitude smaller from stabilized bubbles than from unstable. At intermediate pressures bubble growth occurs in two stages, first stable, then unstable. The Landau–Darrieus instability theory predicts absolute stability at atmospheric pressure for a spherical bubble, whereas the theory for planar interfaces yields results in general agreement with observation. The sensitivity of the instability to temperature suggests that small temperature nonuniformities may be responsible for quantitative departures of the behavior from predictions.

scholarly journals Absolute stability and integral control

2006 ◽  
Vol 79 (4) ◽  
pp. 311-326 ◽  
Author(s):  
T. Fliegner ◽  
H. Logemann ◽  
E. P. Ryan
Keyword(s):  
Absolute Stability ◽  
Integral Control
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