Stabilization of the rotating disk-beam system with a delay term in boundary feedback

In this article, the stabilization problem of a rotating disk-beam system is addressed. It is assumed that the flexible beam is free at one end, whereas the other end is attached to the center of the rotating disk whose angular velocity is time-varying. The proposed feedback law consists of a torque control which acts on the disk, whereas a delayed boundary force control is exerted at the free end of the beam. Thereafter, it is proved that the presence of such controls in the system guarantees the exponential stability of the system under a realistic smallness condition on the angular velocity of the disk as well as the feedback gain in the delay term. This result is illustrated by numerical examples.     

Global dynamic output feedback for high-order nonlinear systems with uncertain output function

Nonlinear Dynamics - In this article, a dynamic output feedback controller is proposed for a family of high-order nonlinear systems with uncertain output function. First, the nominal system is...     

Contact problems for elastic solids with initial stresses (elastic dies) (review)

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Khmel'nitsk Technological Institute. Translated from Prikladnaya Mekhanika, Vol. 27, No. 9, pp. 3–26, September, 1991.     

Dynamic output feedback control for nonlinear networked control systems with a two-terminal event-triggered mechanism

Nonlinear Dynamics - This paper is mainly concerned with the stabilization problem for nonlinear networked control systems (NCSs) with a two-terminal event-triggered mechanism. Firstly,...     

Stabilization meshless method for convection-dominated problems

It is weN-known that the standard Galerkin is not ideally suited to deal with the spatial discretization of convection-dominated problems. In this paper, several techniques are proposed to overcome the instabilitY issues in convection-dominated problems in the simulation with a meshless method. These stable techniques included nodal refinement, enlargement of the nodal influence domain, full upwind meshless technique and adaptive upwind meshless technique. Numerical results for sample problems show that these techniques are effective in solving convection-dominated problems, and the adaptive upwind meshless technique is the most effective method of all.     

Recent investigations on dynamic problems for an elastic body with initial (residual) stresses (review)

Recent investigations of dynamic problems for bodies with initial stresses are reviewed. These are investigations carried out over the last six years using the piecewise-homogeneous body model and the three-dimensional linearized theory of elastic waves in initially stressed bodies. Emphasis is on the investigations performed by the author and his students. The research studies on the wave propagation and dynamic time-harmonic stress-state problems are reviewed separately. The areas for further investigations are pointed out Published in Prikladnaya Mekhanika, Vol. 43, No. 12, pp. 3–27, December 2007.     

Stabilization of parabolic systems via a degenerate nonnegative feedback

A degenerate nonnegative linear operatorB is added to an unbounded self-adjoint linear operatorL in a Hilbert space. The perturbed operator is of the formL + kB, k being a positive parameter. A sufficient condition is sought so that we can choose the minimum eigenvalue ofL + kB arbitrarily large. It is also studied from the numerical analytic viewpoint how the minimum eigenvalue behaves ask increases in relation to an approximation ofB. Modifications of the classical theory of spectrum perturvations are required, since a new type of information is relevant concerning bounds on the multiplicative constant in the familiar formulations of exponential decay. The result is then applied to a new stabilization problem for a class of linear and/or semilinear parabolic differential equations so that their evolutions can be stabilized and at the same time not deviate very much from the initial states for everyt>0, wherekB is considered as a feedback operator.     

Event-triggered output feedback control for feedforward nonlinear systems with unknown measurement sensitivity

Nonlinear Dynamics - This paper investigates the event-triggered output feedback control problem for feedforward nonlinear systems with unknown measurement sensitivity. The nonlinear terms are...     

Positive position feedback (PPF) controller for suppression of nonlinear system vibration

In this paper, a study for positive position feedback controller is presented that is used to suppress the vibration amplitude of a nonlinear dynamic model at primary resonance and the presence of 1:1 internal resonance. We obtained an approximate solution by applying the multiple scales method. Then we conducted bifurcation analyses for open and closed loop systems. The stability of the system is investigated by applying the frequency-response equations. The effects of the different controller parameters on the behavior of the main system have been studied. Optimum working conditions of the system were extracted to be used in the design of such systems. Finally, numerical simulations are performed to demonstrate and validate the control law. We found that all predictions from analytical solutions are in good agreement with the numerical simulation. A comparison with the available published work is included at the end of the work.     

Robust output feedback control of time-delay nonlinear systems with dead-zone input and application to chemical reactor system

Nonlinear Dynamics - This paper investigates the problem of robust output feedback control for a class of time-delay nonlinear systems with unknown continuous time varying output function. Unlike...     

Neural network-based adaptive output feedback formation control for multi-agent systems

This paper investigates the problem of output feedback formation tracking control for second-order multi-agent systems under an undirected connected graph and in the presence of dynamic uncertainties and bounded external disturbances. Two state tracking error measures (i.e., absolute and relative state tracking errors) are considered for each individual agent in the formation, and linear reduced-order observers are constructed based on the lumped state tracking errors which include absolute and relative state tracking errors. Chebyshev neural networks are used to approximate unknown nonlinear function in the agent dynamics on-line, and the implementation of the basis functions of Chebyshev neural networks depends only on the desired signals. The smooth projection algorithm is applied to guarantee that the estimated parameters remain in some known bounded sets. Numerical simulations are presented to illustrate the performance of the proposed controller.     

Stabilization of wave segments under a delayed feedback in the parameter space

Nonlinear Dynamics - We investigate the effects of delayed feedback on the stabilization of a propagating wave segment by introducing a dynamical subsystem in the parameter space. This method aims...     

Local problems for vibrating systems with concentrated masses: a review

In this review we collect certain results obtained in the last decades on vibrating systems with concentrated masses. In particular, we show the connection of the eigenvalues and eigenfunctions of the local problem with the low and high frequency vibrations of the original problem. To cite this article: M. Lobo, E. Pérez, C. R. Mecanique 331 (2003).     

Variational formula for a body with a crack and its applications (review)

A review is made of studies on the variational formula for a body with a crack, asymptotic expansions, weight functions, and displacements of crack faces __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 8, pp. 30–46, August 2007.