H∞ design procedure using robust stabilization of normalized coprime factors

A two-stage H∞-based design procedure is described which uses a normalized coprime factor approach to robust stabilization of linear systems. A loop-shaping procedure is incroporated to allow the specification of performance characteristics. Theoretical justification of this technique and an outline of the design methodology are given.

On the applicability of the lognormal distribution in random dynamical systems

This paper is concerned with the probability density function of the energy of a random dynamical system subjected to harmonic excitation. It is shown that if the natural frequencies and mode shapes of the system conform to the Gaussian Orthogonal Ensemble, then under common types of loading the distribution of the energy of the response is approximately lognormal, providing the modal overlap factor is high (typically greater than two). In contrast, it is shown that the response of a system with Poisson natural frequencies is not approximately lognormal. Numerical simulations are conducted on a plate system to validate the theoretical findings and good agreement is obtained. Simulations are also conducted on a system made from two plates connected with rotational springs to demonstrate that the theoretical findings can be extended to a built-up system. The work provides a theoretical justification of the commonly used empirical practice of assuming that the energy response of a random system is lognormal.

The interaction of riblets with wall-bounded turbulence

The purpose of this thesis is to give answer to the question: why do riblets stop working for a certain size? Riblets are small surface grooves aligned in the mean direction of an overlying turbulent flow, designed specifically to reduce the friction between the flow and the surface. They were inspired by biological surfaces, like the oriented denticles in the skin of fastswimming sharks, and were the focus of a significant amount of research in the late eighties and nineties. Although it was found that the drag reduction depends on the riblet size scaled in wall units, the physical mechanisms implicated have not been completely understood up to now. It has been explained how riblets of vanishing size interact with the turbulent flow, producing a change in the drag proportional to their size, but that is not the regime of practical interest. The optimum performance is achieved for larger sizes, once that linear behavior has broken down, but before riblets begin adopting the character of regular roughness and increasing drag. This regime, which is the most relevant from a technological perspective, was precisely the less understood, so we have focused on it. Our efforts have followed three basic directions. First, we have re-assessed the available experimental data, seeking to identify common characteristics in the optimum regime across the different existing riblet geometries. This study has led to the proposal of a new length scale, the square root of the groove crosssection, to substitute the traditional peak-to-peak spacing. Scaling the riblet dimension with this length, the size of breakdown of the linear behavior becomes roughly universal. This suggests that the onset of the breakdown is related to a certain, fixed value of the cross-section of the groove. Second, we have conducted a set of direct numerical simulations of the turbulent flow over riblets, for sizes spanning the full drag reduction range. We have thus been able to reproduce the gradual transition between the different regimes. The spectral analysis of the flows has proven particularly fruitful, since it has made possible to identify spanwise rollers immediately above the riblets, which begin to appear when the riblet size is close to the optimum. This is a quite surprising feature of the flow, not because of the uniqueness of the phenomenon, which had been reported before for other types of complex and porous surfaces, but because most previous studies had focused on the detail of the flow above each riblet as a unit. Our novel approach has provided the adequate tools to capture coherent structures with an extended spanwise support, which interact with the riblets not individually, but collectively. We have also proven that those spanwise structures are responsible for the increase in drag past the viscous breakdown. Finally, we have analyzed the stability of the flow with a simplified model that connects the appearance of rollers to a Kelvin–Helmholtz-like instability, as is the case also for the flow over plant canopies and porous surfaces. In spite of the model emulating the presence of riblets only in an averaged, general fashion, it succeeds to capture the essential attributes of the breakdown, and provides a theoretical justification for the scaling with the groove cross-section.

Theoretical simulation studies of pulsed field magnetisation of (RE)BCO bulk superconductors

The magnetisation of bulk high temperature superconductors (HTS), such as RE-Ba-Cu-O [(RE)BCO, where RE is a rare earth element or Y], by a practical technique is essential for their application in high field, permanent magnet-like devices. Research to-date into the pulsed field magnetisation (PFM) of these materials, however, has been limited generally to experimental techniques, with relatively little progress in the development of theoretical models. This is because not only is a multi-physics approach needed to take account of the heating of the samples but also the high electric fields generated are well above the regime in which there are reliable experimental results. This paper describes a framework of theoretical simulation using the finite element method (FEM) that is applicable to both single- and multi-pulse magnetisation processes of (RE)BCO bulk superconductors. The model incorporates the heat equation and provides a convenient way of determining the distribution of trapped field, current density and temperature change within a bulk superconductor at each stage of the magnetisation process. An example of the single-pulse magnetisation of a (RE)BCO bulk is described. Potentially, the model may serve as a cost-effective tool for the optimisation of the bulk geometry and the magnetisation profile in multi-pulse magnetisation processes. © 2010 IOP Publishing Ltd.