Rhb Rob Fey

Application of a dynamic vibration absorber to a piecewise linear beam system

This paper deals with the application of a linear dynamic vibration absorber (DVA) to a piecewise linear beam system to suppress its first harmonic resonance. Both the undamped and the damped DVAs are considered. Results of experiments and simulations are presented and show good resemblance. It appears that the undamped DVA is able to suppress the harmonic resonance, while simultaneously many subharmonics appear. The damped DVA suppresses the first harmonic resonance as well as its super- and subharmonics.

Phase Feedback for Nonlinear MEM Resonators in Oscillator Circuits

In this paper, a phase feedback approach for using nonlinear microelectromechanical (MEM) resonators in oscillator circuits is investigated. Phase feedback makes use of the oscillation phase condition for oscillator circuits and enables fine-tuning of the frequency at which the resonator oscillates by means of setting the phase in the feedback amplifier. The principle of the approach is illustrated for a nonlinear Duffing resonator, which is representative of many types of MEM resonators. Next, the approach is applied to an electrostatically actuated nonlinear clamped-clamped beam MEM resonator, on simulation level. Phase feedback allows for operation of the resonator in its nonlinear regime. The closed-loop technique enables control of both the frequency of oscillation and the output power of the signal. Additionally, optimal operation points for oscillator circuits incorporating a nonlinear resonator can be defined. Application of phase feedback results in more robustness with respect to dynamic pull in than in open-loop case, however, at the cost of a deteriorated phase noise response.

Steady-State Behaviour of Flexible Rotordynamic Systems with Oil Journal Bearings

This paper deals with the long term behaviour of flexible rotor systems, which are supported by nonlinear bearings. A system consisting of a rotor and a shaft which is supported by one oil journal bearing is investigated numerically. The shaft is modelled using finite elements and reduced using a component mode synthesis method. The bearings are modelled using the finite-length bearing theory. Branches of periodic solutions are calculated for three models of the system with an unbalance at the rotor. Also self-excited oscillations are calculated for the three models if no mass unbalance is present. The results show that a mass unbalance can stabilize rotor oscillations.

Network synchronization using invariant-manifold-based diffusive dynamic couplings with time-delay

We address the problem of controlled synchronization in networks of nonlinear systems interconnected through diffusive time-delayed dynamic couplings. These couplings can be realized as dynamic output feedback controllers constructed by combining nonlinear observers and time-delayed feedback interconnection terms. Using Immersion and Invariance techniques, we present a general tool for constructing the dynamics of the couplings. Sufficient conditions on the systems to be interconnected, the network topology, the couplings, and the time-delay that guarantee (global) state synchronization are derived. The asymptotic stability of the synchronization manifold is proved using Lyapunov-Razumikhin methods. Moreover, using Lyapunov-Krasovskii functionals and the notion of semipassivity, we prove that under some mild conditions, the solutions of the interconnected systems are ultimately bounded. Simulation results using FitzHugh-Nagumo neural oscillators illustrate the performance of the control scheme.

Experimental verification of the steady-state behavior of a beam system with discontinuous support

This article deals with the experimental verification of the long-term behavior of a periodically excited linear beam supported by a one-sided spring. Numerical analysis of the beam showed subharmonic, quasi-periodic, and chaotic behavior. Further, three different routes leading to chaos were found. Because of the relative simplicity of the beam system and the variety of calculated nonlinear phenomena, an experimental setup is made of this beam system to verify the numerical results. The experimental results correspond very well with the numerical results as far as the subharmonic behavior is concerned. Measured chaotic behavior is proved to be chaotic by calculating Lyapunov exponents of experimental data.

Vibration Control of Periodically Excited Nonlinear Dynamic Multi-dof Systems

For nonlinear mechanical systems, which have stable subharmonic resonance peaks and one or more coexisting unstable harmonic solutions, a large reduction of maximum subharmonic, quasi-periodic, or chaotic displacement can be established if the coexisting unstable harmonic solution could be made stable. The control effort to obtain this goal can be very small in that case. In this article, a method for controlling nonlinear multi-degree-of-freedom (multi-dof) systems to unstable periodic solutions is developed. This is established by putting a single control force somewhere on the system. Because the selected control method uses the full state of the system and because only measured displacements and accelerations of a very limited number of dofs are assumed to be available, a reconstruction method has to be used for estimating the full state on-line. Simulations are done using a beam system supported by a one-sided spring that is control led to the unstable harmonic solution. The robustness of the method with respect to model errors, system disturbance, and measurement errors is examined. Further, the performance of the method in case of a varying excitation frequency during the control is investigated.

Synchronization of Identical Linear Systems and Diffusive Time-Delayed Couplings

We study the problem of controlled network synchronization for a class of identical linear systems. The systems are interconnected through static and dynamic diffusive couplings with time-delays. In particular, we derive conditions on the systems, on the couplings, on the time-delay, and on the network topology that guarantee global synchronization of the systems. Diffusive time-delayed dynamic couplings are constructed by combining linear observers and output feedback controllers. Using passivity properties, sufficient conditions for boundedness of the interconnected systems are derived. Moreover, predictor-based dynamic couplings are proposed in order to enhance robustness against time-delays in the network. The results are illustrated by numerical simulations.

Network synchronization of time-delayed coupled nonlinear systems using predictor-based diffusive dynamic couplings

We study the problem of controlled network synchronization of coupled semipassive systems in the case when the outputs (the coupling variables) and the inputs are subject to constant time-delay (as it is often the case in a networked context). Predictor-based dynamic output feedback controllers are proposed to interconnect the systems on a given network. Using Lyapunov-Krasovskii functional and the notion of semipassivity, we prove that under some mild assumptions, the solutions of the interconnected systems are globally ultimately bounded. Sufficient conditions on the systems to be interconnected, on the network topology, on the coupling dynamics, and on the time-delays that guarantee global state synchronization are derived. A local analysis is provided in which we compare the performance of our predictor-based control scheme against the existing static diffusive couplings available in the literature. We show (locally) that the time-delay that can be induced to the network may be increased by including the predictors in the loop. The results are illustrated by computer simulations of coupled Hindmarsh-Rose neurons.

Steady-state behaviour of a solar array system with elastic stops

In recent years a method was developed by the authors for efficient analysis of the long term behaviour of mechanical systems with local nonlinearities under periodic excitation. In this method the linear parts of the system are modelled using the finite element method. In order to keep the cpu-time for the nonlinear analyses acceptable, the number of degrees of freedom (dof) of the linear part of the system is reduced using a component mode synthesis (cms) technique. The cms technique used is based on free-interface eigenmodes and residual flexibility modes. Eigenmodes are kept up to a user-defined cut-off frequency. Subsequently, the reduced linear model is coupled to local nonlinearities, such as nonlinear springs and dampers, dry friction elements, backlash etc. The model obtained in this way is analysed using a nonlinear dynamics toolbox, which among others contains solvers for the calculation of periodic solutions and their stability and a path following method. The approach outlined above is described in Fey (1992) and Fey et al. (1996) and was integrated in the finite element package DIANA (1997). Until now, this approach was applied to rather academic, archetypal problems in order to verify its value. The approach turned out to be very successful: numerical results were compared with experimental results and a good correspondence was achieved (van de Vorst, 1996, van de Vorst et al., 1996a, van de Vorst et al., 1996b).

Finite Element Model Reduction and Model Updating of structures for Control

Estimation and control of unmeasurable performance variables in complex large-scale systems is an important issue in systems and control. The preferred solution to this problem is to have a relatively low-order and accurate standard plant model which can be used for control purposes. For this purpose, a two-step procedure is proposed. The first step is to generate a reduced Finite Element (FE) model based on the selection of desired Degrees Of Freedom (DOFs), resulting in reduced-order mass, damping, and stiffness matrices. The second step is updating of the reduced-order FE model that is carried out to minimize the differences between the model and the measurements from the structure with the focus on input-output behavior. The presented approach helps to create sufficiently accurate reduced-order dynamic models which can be used for control purposes. The approach will be examined on a planar plate FE model.