Delay compensated control of the Stefan problem and robustness to delay mismatch

This paper presents a control design for the one‐phase Stefan problem under actuator delay via a backstepping method. The Stefan problem represents a liquid‐solid phase change phenomenon which describes the time evolution of a material's temperature profile and the interface position. The actuator delay is modeled by a first‐order hyperbolic partial differential equation (PDE), resulting in a cascaded transport‐diffusion PDE system defined on a time‐varying spatial domain described by an ordinary differential equation (ODE). Two nonlinear backstepping transformations are utilized for the control design. The setpoint restriction is given to guarantee a physical constraint on the proposed controller for the melting process. This constraint ensures the exponential convergence of the moving interface to a setpoint and the exponential stability of the temperature equilibrium profile and the delayed controller in the norm. Furthermore, robustness analysis with respect to the delay mismatch between the plant and the controller is studied, which provides analogous results to the exact compensation by restricting the control gain.     

Predictor‐based tracking for neuromuscular electrical stimulation

We present a new tracking controller for neuromuscular electrical stimulation (NMES), which is an emerging technology that artificially stimulates skeletal muscles to help restore functionality to human limbs. The novelty of our work is that we prove that the tracking error globally asymptotically and locally exponentially converges to zero for any positive input delay, coupled with our ability to satisfy a state constraint imposed by the physical system. Also, our controller only requires sampled measurements of the states instead of continuous measurements and allows perturbed sampling schedules, which can be important for practical purposes. Our work is based on a new method for constructing predictor maps for a large class of time‐varying systems, which is of independent interest. Copyright © 2014 John Wiley & Sons, Ltd.     

Boundary control and estimation of reaction–diffusion equations on the sphere under revolution symmetry conditions

ABSTRACT

Recently, the problem of designing boundary controllers and observers for unstable linear constant-coefficient reaction–diffusion equation on N-balls has been solved by means of the backstepping method. However, the extension of these results to spatially varying coefficients is far from trivial. This work deals with radially varying reaction coefficients under revolution symmetry conditions on a sphere (the three-dimensional case). Under these conditions, the equations become singular in the radius. When applying the backstepping method, a similar type of singularity appears in the backstepping control and observer kernel equations. However, with a simple scaling transformation, we are able to reduce the singular equation to a regular equation, which turns out to be the same kernel equations appearing when using the one-dimensional backstepping method. In addition, the scaling transformation allows us to prove stability in the H ¹ space.     

Spectroscopic evaluation of the colour play effect of thermochromic liquid crystal printing inks

Colour changes of a thermochromic liquid crystal (TLC) ink printed on a black substrate are clearly observed by the naked eye, and therefore it is reasonable to expect that every approach recommended for colour measurements of samples with solid colour would be appropriate. In addition, the published spectroscopic analyses of TLC inks do not provide any guidance or limitations for the measurement geometry. On the other hand, our study demonstrates that spectroscopic measurements of such samples are not so straightforward. When using the most simple and commonly used measurement equipment with a directional illumination and viewing approach, the temperature-dependent spectral features resolve in a narrow spectral region that gives only a small part of the colour play effect. Detection of the entire effect requires the use of integrating spheres, which spatially integrate the radiant flux reflected on a sample in any direction; better results are obtained by spheres of larger diameter. The comparision of spectroscopic and colorimetric results obtained when different measurement geometries are applied on the same sample may demonstrate certain properties of the liquid crystal material inside microcapsules and help in understanding some details of the optical properties of the ink layer.     

Assessment of potential for natural gas-based cogeneration in Thailand

Using the results of a comprehensive data analysis of final energy consumption in industry and commercial buildings, the assessment has been made of the potential for gradual implementation of cogeneration plants in these facilities. In doing so, plans for the expansion of the natural gas pipeline distribution network in Thailand are taken into consideration. The sample comprises of 2540 factories and 1651 commercial buildings from which it was found that 817 factories and 966 commercial buildings were suitable for the implementation of natural gas-based cogeneration technologies until 2020. By the implementation of cogeneration in these facilities, it is possible to save 3.2% of the total primary energy consumption in Thailand in 2003.     

Chemical sputtering of deuterated carbon surfaces at various surface temperatures

The chemical sputtering of deuterated amorphous carbon (a-C:D) surfaces irradiated by 1-50 eV deuterium atoms at surface temperatures between 300 and 1000 K was studied using classical molecular dynamics. A quasi-stationary state was reached by cumulative bombardment for each energy and temperature. Results were compared with available experimental data and previous modeling results and the applicability of molecular dynamics for thermally generated processes was discussed. An attempt is made to correct the absence of the thermally stimulated desorption/degassing of hydrogen from the MD simulations, which evolve at the longer time scales.     

Fuzzy ε-subgroups

The aim of the paper is to investigate the known classical problem of a partition of a semigroup into a family of groups in the lattice-valued (fuzzy) framework. For that purpose, a fuzzy subgroup of a fuzzy subsemigroup is introduced and characterized by cuts, using the cutworthy approach. As a main result it is proved that a fuzzy subsemigroup can be partitioned (using special type of fuzzy partitions) into a family of fuzzy ε-subgroups if and only if it is fuzzy completely regular.     

Mechanochemical and Low‐Temperature Synthesis of Nanocrystalline Fluorohydroxyapatite/Fluorapatite

Low‐temperature synthesis of fluorapatite/fluorohydroxyapatite with precursor mixture previously mechanochemically treated is described in this article. Ethylene vinylacetate/versatate copolymer as a surface active substance was mechanically treated to obtain a core‐shell system with strongly controlled grain size. Despite usual behavior of mechanically activated systems, only an amorphous phase formed from precursor ions present in the mixture composed of β‐Ca₂P₂O₇, CaCO₃, CaF₂, and unreacted Ca(OH)₂ was obtained during milling for 5 min to 8 h. The mixture contained depots of labile F^? ions conserved in micelles cages, which are useful for teeth protection from carries. For transformation of these amorphous phases into fluorapatite, an additional low thermal treatment was necessary. The mechanism of the precursor mixture transformation into fluorapatite during milling and thermal treatment was investigated using FTIR spectroscopy and X‐ray diffraction. The morphology and size distribution of the obtained powders was studied using SEM and TEM.