Pwjm Pieter Nuij

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.

Optical boundary reconstruction of tokamak plasmas for feedback control of plasma position and shape

A new diagnostic is developed to reconstruct the plasma boundary using visible wavelength images. Exploiting the plasmas edge localized and toroidally symmetric emission profile, a new coordinate transform is presented to reconstruct the plasma boundary from a poloidal view image. The plasma boundary reconstruction is implemented in MATLAB and applied to camera images of Mega-Ampere Spherical Tokamak discharges. The optically reconstructed plasma boundaries are compared to magnetic reconstructions from the offline reconstruction code EFIT, showing very good qualitative and quantitative agreement. Average errors are within 2 cm and correlation is high. In the current software implementation, plasma boundary reconstruction from a single image takes 3 ms. The applicability and system requirements of the new optical boundary reconstruction, called OFIT, for use in both feedback control of plasma position and shape and in offline reconstruction tools are discussed.

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.

Systematic design and simulation of a tearing mode suppression feedback control system for the TEXTOR tokamak

Suppression of tearing modes is essential for the operation of tokamaks. This paper describes the design and simulation of a tearing mode suppression feedback control system for the TEXTOR tokamak. The two main control tasks of this feedback control system are the radial alignment of electron cyclotron resonance heating and current drive (ECRH/ECCD) with a tearing mode and the stabilization of a mode at a specific width. In order to simulate these control tasks, the time evolution of a tearing mode subject to suppression by ECRH/ECCD and destabilization by a magnetic perturbation field is modelled using the generalized Rutherford equation. The model includes an equilibrium model and an ECRH/ECCD launcher model. The dynamics and static equilibria of this model are analysed. The model is linearized and based on the linearized model, linear feedback controllers are designed and simulated, demonstrating both alignment and width control of tearing modes in TEXTOR.

Identification of non-linear dynamics using higher order frequency response functions

An experiment is designed to identify input-output relations of a mechanical positioning system with excitation amplitude dependent mechanical behavior. When evaluated in the frequency domain, these relations constitute a fingerprint of the dynamical behavior of the system. Since the commonly used FFT based techniques for Frequency Response Function (FRF) estimations require stationary signals, an alternative technique is introduced. With a digital filtering based technique fixed frequency higher order can be estimated as function of time dependent excitation levels. The paper describes the data processing techniques and shows measurement results of the higher order FRFs of a system with strong amplitude dependent mechanical behavior caused by a friction induced resonance.

Real-time period determination for relaxation oscillators using wavelets

In this article an algorithm for optimized realtime sensing of crashes for control purposes is presented. The algorithm is based on time-scale wavelet theory and edge-detection. It is designed for the control of the sawtooth instability, a relaxation oscillator, in fusion plasmas. However, in principle, it can be applied to any periodic crash, measured with any temporally resolved data. It is argued that the detection of crashes has considerably less delay and detects crashes with higher temporal accuracy than other linear methods; this holds especially for very noisy measurements.

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.