The Grad-Shafranov Reconstruction of Toroidal Magnetic Flux Ropes: Method Development and Benchmark Studies

We develop an approach of Grad-Shafranov (GS) reconstruction for toroidal structures in space plasmas, based on in-situ spacecraft measurements. The underlying theory is the GS equation that describes two-dimensional magnetohydrostatic equilibrium as widely applied in fusion plasmas. The geometry is such that the arbitrary cross section of the torus has rotational symmetry about the rotation axis $Z$, with a major radius $r_0$. The magnetic field configuration is thus determined by a scalar flux function $\Psi$ and a functional $F$ that is a single-variable function of $\Psi$. The algorithm is implemented through a two-step approach: i) a trial-and-error process by minimizing the residue of the functional $F(\Psi)$ to determine an optimal $Z$ axis orientation, and ii) for the chosen $Z$, a $\chi^2$ minimization process resulting in the range of $r_0$. Benchmark studies of known analytic solutions to the toroidal GS equation with noise additions are presented to illustrate the two-step procedures and to demonstrate the performance of the numerical GS solver, separately. For the cases presented, the errors in $Z$ and $r_0$ are 9$^\circ$ and 22\%, respectively, and the relative percent error in the numerical GS solutions is less than 10\%. We also make public the computer codes for these implementations and benchmark studies.Comment: submitted to Sol. Phys. late Dec 2016; under review; code will be made public once review is ove

Sliding mode and shaped input vibration control of flexible systems

Copyright [2008] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, the vibration reduction problem is investigated for a flexible spacecraft during attitude maneuvering. A new control strategy is proposed, which integrates both the command input shaping and the sliding mode output feedback control (SMOFC) techniques. Specifically, the input shaper is designed for the reference model and implemented outside of the feedback loop in order to achieve the exact elimination of the residual vibration by modifying the existing command. The feedback controller, on the other hand, is designed based on the SMOFC such that the closed-loop system behaves like the reference model with input shaper, where the residual vibrations are eliminated in the presence of parametric uncertainties and external disturbances. An attractive feature of this SMOFC algorithm is that the parametric uncertainties or external disturbances of the system do not need to satisfy the so-called matching conditions or invariance conditions provided that certain bounds are known. In addition, a smoothed hyperbolic tangent function is introduced to eliminate the chattering phenomenon. Compared with the conventional methods, the proposed scheme guarantees not only the stability of the closed-loop system, but also the good performance as well as the robustness. Simulation results for the spacecraft model show that the precise attitudes control and vibration suppression are successfully achieved

Development of a novel virtual coordinate measuring machine

Existing VCMMs (virtual coordinate measuring machine) have been mainly developed to either simulate the measurement process hence enabling the off-line programming, or to perform error analysis and uncertainty evaluation. Their capability and performance could be greatly improved if there is a complete solution to cover the whole process and provide an integrated environment. The aim of this study is to develop such a VCMM that not only supports measurement process simulation, but also performs uncertainty evaluation. It makes use of virtual reality techniques to provide an accurate model of a physical CMM, together with uncertainty evaluation. An interface is also provided to communicate with CMM controller, allowing the measuring programs generated and simulated in the VCMM to be executed or tested on the physical CMM afterwards. This paper discusses the proposal of a novel VCMM design and the preliminary results

New Darboux Transformation for Hirota-Satsuma coupled KdV System

A new Darboux transformation is presented for the Hirota-Satsuma coupled KdV system. It is shown that this Darboux transformation can be constructed by means of two methods: Painlev\'{e} analysis and reduction of a binary Darboux transformation. By iteration of the Darboux transformation, the Grammian type solutions are found for the coupled KdV system.Comment: LaTeX 2.09, 10 page

Design, implementation, and testing of advanced virtual coordinate-measuring machines

Copyright @ 2011 IEEE. This article has been made available through the Brunel Open Access Publishing Fund.Advanced virtual coordinate-measuring machines (CMMs) (AVCMMs) have recently been developed at Brunel University, which provide vivid graphical representation and powerful simulation of CMM operations, together with Monte-Carlo-based uncertainty evaluation. In an integrated virtual environment, the user can plan an inspection strategy for a given task, carry out virtual measurements, and evaluate the uncertainty associated with the measurement results, all without the need of using a physical machine. The obtained estimate of uncertainty can serve as a rapid feedback for the user to optimize the inspection plan in the AVCMM before actual measurements or as an evaluation of the measurement results performed. This paper details the methodology, design, and implementation of the AVCMM system, including CMM modeling, probe contact and collision detection, error modeling and simulation, and uncertainty evaluation. This paper further reports experimental results for the testing of the AVCMM

Correlation-induced suppression of decoherence in capacitively coupled Cooper-pair boxes

Charge fluctuations from gate bias and background traps severely limit the performance of a charge qubit in a Cooper-pair box (CPB). Here we present an experimentally realizable method to control the decoherence effects of these charge fluctuations using two strongly capacitively coupled CPBs. This coupled-box system has a low-decoherence subspace of two states. Our results show that the inter-box Coulomb correlation can help significantly suppress decoherence of this two-level system, making it a promising candidate as a logical qubit, encoded using two CPBs.Comment: 5 pages, 2 figures. Phys. Rev. B, in pres