Set Of Equilibrium Positions Research Articles

Absolute stability of system with nano piezoengine for biomechanics

The nano piezoengine is used for biomechanics and nano sciences in dosing device, scanning microscopy, nano manipulator, nano pump. For the nano piezoengine with hysteresis in control system its set of equilibrium positions is the segment of line. The frequency method for studying the stability of system is used. By applying Yakubovich criterion for system with the nano piezoengine the absolute stability of system is calculated for biomechanics. The ratio of the piezomodules of the nano piezoengine with transverse, longitudinal, shear piezoelectric effects is proportional the ratio of its tangents of the angle of inclination to the hysteresis.

Condition absolute stability of system with nano piezoactuator for astrophysics research

For the nano piezoactuator with hysteresis in control system its set of equilibrium positions is the segment of line. By applying Yakubovich criterion for system with the nano piezoactuator the condition absolute stability of system is evaluated.

Absolute Stability of System with Nanopiezoactuator for Nanomedicine Sciences

For the nanopiezoactuator with hysteresis in control system its set of equilibrium positions is the segment of line. By applying Yakubovich criterion for system with the nanopiezoactuator the absolute stability of system is calculated for nanomedicine sciences.

Условие абсолютной устойчивости системы управления электроупругим актюатором для наномехатроники

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.

The equilibrium positions of a satellite carrying a three-degree-of-freedom powered gyroscope in a central gravitational field

For a satellite, carrying an arbitrary number of three-degree-of-freedom powered gyroscopes, the whole set of equilibrium positions in a central gravitational field in a circular orbit is determined and a detailed analysis of their secular stability is presented. The asymptotic properties of the satellite motions when there is dissipation in the axes of the gyroscope frames are investigated.

Absolute stability of the control system for piezoconverter deformation in a nanodrive

The conditions ensuring absolute stability of the control system for the deformation of an electroelastic converter are established, in the case of determinate and random perturbations. The set of equilibrium positions in this control system is determined.

A self-adaptative oscillator

The dynamics of a system where a mass is free to slide on a vibrating string is investigated as the excitation frequency is varied. One degree of freedom is thus added to the system studied by Helmholtz in which a mass was fixed on a vibrating string. This new system exhibits a specific dynamics characterized by the existence of a self- adaptative behaviour. When the driving frequency falls into wide and well defined frequency bands, a long transient is observed by which the mass adjusts its position so that the whole system becomes resonant. In the gaps between these bands, bifurcations give other equilibrium positions. A theoretical model is proposed. It accounts for all the experimental results. In the case where two masses are present on the string, two degrees of freedom are added and the set of equilibrium positions would be expected to be infinite. However, in the experiment, the two masses are observed to go to positions where they are symmetrical with respect to the middle of the string. A selection mechanism due to the string stretching is pointed out.

Nonlinear equations

We consider a Cauchy problem in a Hilbert space H for the equation given A, linear operator; G, Gateaux derivative of a functional; real β, α>0,δgt;0, constants. We prove that if the equilibrium positions are isolated and if a(u(t))=(Au(t),u(t)) remains bounded for t≥0, then u(t) tends, as t goes to infinity, to an equilibrium position, in the energy norm. The proof relies on properties of the weakly continuous dynamical system defined by the equation. This technique was devejopped by Ball [1] , using the methods of Lions [4]. Application is given. In particular, a generalization of the damped extensible beam equation is considered, if G(u)= M(a(u))Au, for M a real function. Then it is quite simple to see that a(u(t)) remains bounded and, if all eigenvalues of αA2−λAu=0 are simple, the set of equilibrium positions is finite. For other applications, we refer to methods in Chow and Hale [3].