Experimental study of digital force control

A one degree of freedom experimental rig was designed and manufactured to test the stability properties of digital force control and to compare the theoretical and measured stability charts. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hertzian contact in the presence of a Mindlin force

The smooth axisymmetric contact between a rigid spherical punch and an isotropic elastic halfspace is perturbed by an internally applied Mindlin force which is located along the axis of symmetry. The paper presents certain closed form solutions to this unilateral contact problem.     

Stability in the presence of degeneracy and error estimation

Received February 10, 1997 / Revised version received June 6, 1998 Published online October 9, 1998     

Stability of recursive digital filters

If B(z) is an absolutely convergent power series on the unit disk, the requirements for the reciprocal of B to also be absolutely convergent on the unit disc are well known. These requirements are that B does not vanish on the unit disc. This paper gives an alternate characterization of the corresponding theorem in two-variables along with a new proof.     

The damping force on a body oscillating in an elastico-viscous fluid

Résumé On calcule la force d'amortissement agissant sur un corps de forme arbitraire auquel on fait subir de petites oscillations latérales dans une expansion infinie de liquide élastique et visqueux. On montre que l'élasticité a pour effet de réduire la résistance à des fréquences hautes et de l'augmenter à des fréquences basses.     

Micro-chaos in digital control

Summary In this paper we analyze a model for the effect of digital control on one-dimensional, linearly unstable dynamical systems. Our goal is to explain the existence of small, irregular oscillations that are frequently observed near the desired equilibrium. We derive a one-dimensional map that captures exactly the dynamics of the continuous system. Using thismicro-chaos map, we prove the existence of a hyperbolic strange attractor for a large set of parameter values. We also construct an “instability chart” on the parameter plane to describe how the size and structure of the chaotic attractor changes as the parameters are varied. The applications of our results include the stick-and-slip motion of machine tools and other mechanical problems with locally negative dissipation.     

Thermoelastic damping effect analysis in micro flexural resonator of atomic force microscopy

In the design of high-Q micro/nano-resonators, dissipation mechanisms may have damaging effects on the quality factor (Q). One of the major dissipation mechanisms is thermoelastic damping (TED) that needs an accurate consideration for prediction. Aim of this paper is to evaluate the effect of TED on the vibrations of thin beam resonators. In particular, we will focus on cantilever beam resonator used in atomic force microscopy (AFM). AFM resonator is actually a cantilever with a spring attached to its free end. The end spring is considered to capture the effect of surface stiffness between tip and sample surface. The coupled governing equations of motion of thin beam with consideration of TED effects are derived. In general, there are four elastic equations that are coupled with thermal conduction equation. Based on accurate assumptions, these equations are simplified and the various boundary conditions have been used in order to validate the computational procedure. In order to accurately determine TED effects, the coupled thermal conduction equation is solved for the temperature field by considering three-dimensional (3-D) heat conduction along the length, width and thickness of the beam. Weighted residual Galerkin technique is used to obtain frequency shift and the quality factor of the thin beam resonator. The obtained results for quality factor, frequency shift and sensitivity change due to thermo-elastic coupling are presented graphically. Furthermore, the effects of beam aspect ratio, stress-free temperature on the quality factor and the influence of the surface stiffness on the frequencies and modal sensitivity of the AFM cantilever with and without considering thermo-elastic damping effects are discussed.     

Guideway based damping control of vehicle suspensions

The information on the routing of a road provided by a navigation system can be used by the driver of a vehicle with adaptive shock absorber to decide either for optimal comfort or optimal safety depending on the course of the guideway. However, the assessment criteria comfort and safety are with respect to the shock absorber in conflict with each other. In particular, maximal safety on a curvaceous road results in lower comfort. Thus, deciding on high safety means low comfort conveying a warning to the driver to reduce the speed. The methods applied in this paper originate from multibody dynamics, and they are extended by the stochastic road unevenness and the guideway curvature available to the driver from a navigation system using GPS data. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimal damping control and nonlinear parabolic systemes

An optimal control problem for a parabolic equation when the control parameter is the zero order coefficient of the differential operator is considered. An optimality system is derived. Under a certain sign condition, the problem is solved completely, by proving uniqueness and providing a constructive existence proof for the nonlinear parabolic optimality system.     

Stability of planar diffusion wave for the quasilinear wave equation with nonlinear damping

In this paper, we will show that under some smallness conditions, the planar diffusion wave v(√x11+) is stable for a quasilinear wave equation with nonlinear damping: vttt-f(v) + vt + g(vt) = 0, x =(xn1, x2,, xn)∈ R, where v(√x11+) is the unique similar solution to the one dimensional nonlinear heat equattion: vt-f(v)x1x1= 0, f ′(v) > 0, v(±∞, t) = v±, v+ = v-. We also obtain the L∞ time decay rate which rreads v-v L∞= O(1)(1 + t)-4, where r = min{3, n}. To get the main result, the energy method and a new inequality have been used.     

Stability analysis of an open cracked rotor with the anisotropic rotational damping in rotating operation

The damping effects with the distinction of stationary damping and the anisotropic rotating damping on the dynamic stability of the rotating rotor with an open crack on the surface of the shaft is studied. The motion equations of the cracked rotor system are formed by Lagranges principal. Different from previous studies, the anisotropic system with the multi periodical varied coefficients is simplified by the moving frame method such that the stability analysis based on the root locus method can be applied. The corresponding Campbell diagram, decay rate plot and roots locus plot are derived to prove the destabilizing influence of both the rotational damping and the varied anisotropy ratio of the rotating damping. The effects of anisotropy of stiffness on the decisions of the critical range are also presented. The result with theoretical precision would not only generally provide practical applicability to crack detection and instability control of the heavy loading turbo-machinery system, but also give the suggestion that, the increased proportion and the aggravated anisotropy of the rotational damping due to the crack of the fatigue rotor should been taken into consideration on the modeling of cracked rotor system.     

Geometric control in the presence of a black box

We apply the ``black box scattering' point of view to problems in control theory for the Schrödinger equation and in high energy eigenvalue scarring. We show how resolvent bounds with origins in scattering theory, combined with semi-classical propagation, give quantitative control estimates. We also show how they imply control for time dependent problems.

     

Inventory control in the presence of an electronic marketplace

This paper studies a periodic review inventory model in the presence of an electronic marketplace (EM). Emergency orders can be placed in the EM for additional cost, and excess inventory can be sold to the EM. When the order leadtime from the supplier is one period, the optimal inventory control policy is developed from a dynamic programming model of the problem. The policy is characterized by three critical inventory levels. When the order leadtime from the supplier is longer than one period, an EM policy is developed to determine the quantities of inventory to purchase from and sell to the EM in each period. Based on this EM policy, three ordering policies are proposed to determine the order quantity from the supplier. Numerical results show that significant cost reductions can be obtained by using the EM to adjust the inventory level in each period. The amount of cost reduction is greatly affected by system parameters, especially the order leadtime from the supplier and the costs for transactions in the EM.     

Stability theory of solitary waves in the presence of symmetry,I

Consider an abstract Hamiltonian system which is invariant under a one-parameter unitary group of operators. By a “solitary wave” we mean a solution the time development of which is given exactly by the one-parameter group. We find sharp conditions for the stability and instability of solitary waves. Applications are given to bound states and traveling waves of nonlinear PDEs such Klein-Gordon and Schrödinger equations.     

Stability of models with four-fermion interaction in the presence of vector fields

On the basis of an effective potential for quarks and gluons, for models with fourfermion interaction, stability is examined both with and without vector fields (gluons). The stability conditions relate the main characteristics of four-quark models with quark and gluon condensates.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 189, pp. 3–9, 1991.     

THE FEEDBACK DELAY IN DIGITAL CONTROL

It is a fact that the feedback delay actually ariese in digital control systems.It is necessary to modify the structure of digital control systems and develop new control algorithms,which is done in this paper.A great number of digital computer simulation experiments have shown the obvious advantage of the new algorithms.     

Chaos control using small-amplitude damping signals of the extended Duffing equation

This paper examines the application of a simple feedback controller to eliminate the chaotic behavior in a controlled extended Duffing system. The main idea is to regulate the chaotic motion of an extended Duffing system around less complex attractors, such as equilibrium points and periodic orbits. The proposed feedback controller is composed by a high-pass filter and a saturator, so its implementation is quite simple and can be made on the basis of measured signals. The affectivity of the proposed feedback control strategy is illustrated by means of numerical simulations.