Observer-based stabilisation of linear systems with parameter uncertainties by using enhanced LMI conditions

International audienceThis paper deals with the problem of observer-based stabilisation for linear systems with structured norm-bounded parameter uncertainties. A new design methodology is established thanks to a judicious use of some mathematical artefacts such as the well-known Young inequality and various matrix decompositions. The proposed method allows one to compute simultaneously the observer and controller gains by solving a single bilinear matrix inequality (BMI), which becomes a linear matrix inequality (LMI) by freezing some scalars. Furthermore, we show that some existing and elegant results reported in the literature can be regarded as particular cases of the stability conditions presented here. Numerical examples and evaluations of the conservatism are provided to show the effectiveness of the proposed design methodology

Optimization of Quartz Sand Leaching Process Using Design Experiments Method (DOE)

The present study aims at investigating the Algerian quartz sand from Djelfa deposit as a potential source to produce silicon. The sand from the Djelfa deposit has a high concentration but not enough to be used as raw material for pyrometallurgy (97%) of SiO2. Therefore, the quartz was treated using acid leaching process to increase the silica concentration up to 98.5%. Otherwise, we employ Design of Experiments Method Software (DOE) as numerical model to optimize the parameters of leaching and also to predict the etching behavior of sand grains during the primary step of the process. The results show that the effect of acid concentration has more influence than the grains particle sizes and leaching time to obtain the required silica purity. Using DOE numerical method in the first step of leaching, optimal response of purity (ΔP)(ΔP)\\left (\\mathrm \\\\Delta \ P\ \\right ) about 98.48% is obtained. In this context, the optimal grain sizes of sand and the optimal acid concentration are respectively, 276.9 \textmum and 21.15%, for 6 hours leaching time. The obtained response is very close to the experimental values and can be used for the next stage of the silicon production chain

Sand Dune Characterization for Preparing Metallurgical Grade Silicon

Dune sand, from Biskra, Algeria which is in the Great Algerian huge desert attracts tourists from all over the world. Dune sand composes around 80% of the total area of the desert. To date only a few studies have been conducted on this sand. The purpose of the present study is to shed light on the textural and physico-chemical characteristics of this sand using several characterization methods, and to understand the potential for using for photovoltaic applications. The chemical composition of Biskra sand indicated a high purity quartz with 97.6% silica, and a presence of others oxides. Granular analysis enabled the determination of the size of the sand grains which was found to be fine to medium. On the other hand, a Scanning Electron Microscopy and optical observations were carried out, the micrographs observations indicated the presence of different shapes of sand grain, some rounded whereas others are angular edged or elongated. X-ray diffraction indicates the highly crystalline nature of the Biskra sand