Dj David Rijlaarsdam

Brief paper: Spectral analysis of block structured nonlinear systems and higher order sinusoidal input describing functions

When analyzing and modeling dynamical systems in the frequency domain, the effects of nonlinearities need to be taken into account. This paper contributes to the analysis of the effects of nonlinearities in the frequency domain by supplying new analytical tools and results that allow spectral analysis of the output of a class of nonlinear systems. A mapping from the parameters defining the nonlinear and LTI dynamics to the output spectrum is derived, which allows analytic description and analysis of the corresponding higher order sinusoidal input describing functions. The theoretical results are illustrated by examples that show both the use and efficiency of the proposed algorithms.

Technical communique: Uniquely connecting frequency domain representations of given order polynomial Wiener-Hammerstein systems

The notion of frequency response functions has been generalized to nonlinear systems in several ways. However, a relation between different approaches has not yet been established. In this paper, frequency domain representations for nonlinear systems are uniquely connected for a class of nonlinear systems. Specifically, by means of novel analytical results, the generalized frequency response function (GFRF) and the higher order sinusoidal input describing function (HOSIDF) for polynomial Wiener-Hammerstein systems are explicitly related, assuming the linear dynamics are known. Necessary and sufficient conditions for this relation to exist and results on the uniqueness and equivalence of the HOSIDF and GFRF are provided. Finally, this yields an efficient computational procedure for computing the GFRF from the HOSIDF and vice versa.

Synchronization of Chaotic Cellular Neural Networks based on Rössler Cells

Using and extending the approach in previous studies we demonstrate synchronization of two hyper chaotic cellular neural networks consisting of 25 cells governed by chaotic Rossler dynamics. We guarantee global asymptotic stability of the synchronization manifold by designing a nonlinear observer in such a way that the resulting error system is linear and time invariant. This linear error system is evaluated and a state feedback is designed to accomplish full state synchronization. Analytical as well as numerical simulation results are presented

Experimental Huygens Synchronization of Oscillators

We present an experimental set-up that allows to study both controlled and uncontrolled synchronization between a variety of different type of oscillators. The setup consists of two fully actuated mass-damper-spring oscillators mounted on an actuated platform. By means of different types of feedback realized through computer controlled actuation it is possible to demonstrate different synchronization phenomena, i.e. synchronization of pendula, synchronization of Duffing oscillators, synchronization of rotating bodies, etc. Two experiments are presented where uncontrolled synchronization between two types of identical oscillators is investigated. First, uncontrolled synchronization between two Duffing oscillators is investigated and second, uncontrolled synchronization between two coupled rotating disks is discussed.

New Connections Between Frequency Response Functions for a Class of Nonlinear Systems

The notion of frequency response functions has been generalized to nonlinear systems in several ways. However, a relation between different approaches has not yet been established. In this paper, frequency domain representations for nonlinear systems are uniquely connected. Specifically, by means of novel analytical results, the generalized frequency response function (GFRF) and the higher order sinusoidal input describing function (HOSIDF) for polynomial Wiener-Hammerstein systems are explicitly related. Necessary and sufficient conditions for this relation to exist and results on uniqueness and equivalence of the HOSIDF and GFRF are provided. Finally, a numerically efficient computational procedure is presented that allows to compute the GFRF from the HOSIDF and vice versa.

Frequency domain based friction compensation - Industrial application to transmission electron microscopes -

Friction is a performance limiting factor in many industrial motion systems. Correct compensation or control of friction and other nonlinearities is generally difficult. Apart from the complex nature of friction, compensation of even the most basic type of friction, Coulomb friction, is non trivial. Most available tuning methods rely on time domain data and are often unable to distinguish between nonlinear effects of friction and that of for example linear viscous damping. Furthermore, the sensitivity of time domain data to the influence of friction is too low for correct tuning in many of the high precision motion applications currently used in industry. In this paper a frequency domain method is introduced that allows fast and high accuracy tuning of controller parameters when the closed loop system is subject to nonlinear influences. This methodology is applied to optimally compensate friction in a high precision motion stage of a transmission electron microscope. Theoretical and experimental results are presented and related to time domain performance to illustrate the advantage of frequency domain tuning over time domain tuning.