A kind of generalized proportional-integral(GPI) observer for descriptor linear systems is introduced. We first propose two complete parametric solutions to generalized Sylvester matrix equation corresponding to the left eigenvector matrices in the case of Jordan form. Then a parametric design approach for the observer is presented. The proposed method provides all parametric expression of the gain matrices and the corresponding finite left eigenvector matrix and guarantees the regularity and impulse-freeness of the expanded error system. Two numerical examples are given to explain the design procedure and illustrate the effectiveness of the proposed method.

The chemical composition of alloys plays an important role at their crystallization and influences the solid phase formation, and thus, microstructure and properties. The present paper studies the release of the heat of crystallization of alloyed wear-resistant cast irons in order to determine the quantitative patterns of the chemical composition influence to the kinetics of crystallization. The differential thermal analysis was applied to get the data of heat release, its rate at cast iron temperature decrease. The normalized dependence of the amount of crystallization heat over time was obtained. The main temperature parameters were analyzed and four stages at irons crystallization were established and characterized with their duration and released heat. The multiple correlation analysis allowed considering a numerous physical and chemical factors and distinguishing their role at crystallization of irons. As a result, the quantitative regularities are determined of influencing the content of alloying elements, impurities and carbides on a heat and time of crystallization at the different stages of solidification, which are of great importance in developing alloyed irons with required quality and properties.

We derive exact and approximate controllability conditions for the linear one-dimensional heat equation in an infinite and a semi-infinite domains. The control is carried out by means of the time-dependent intensity of a point heat source localized at an internal (finite) point of the domain. By the Green’s function approach and the method of heuristic determination of resolving controls, exact controllability analysis is reduced to an infinite system of linear algebraic equations, the regularity of which is sufficient for the existence of exactly resolvable controls. In the case of a semi-infinite domain, as the source approaches the boundary, a lack of L2-null-controllability occurs, which is observed earlier by Micu and Zuazua. On the other hand, in the case of infinite domain, sufficient conditions for the regularity of the reduced infinite system of equations are derived in terms of control time, initial and terminal temperatures. A sufficient condition on the control time, heat source concentration point and initial and terminal temperatures is derived for the existence of approximately resolving controls. In the particular case of a semi-infinite domain when the heat source approaches the boundary, a sufficient condition on the control time and initial temperature providing approximate controllability with required precision is derived.

The entropy production per unit time is calculated for the regular lamellae -, and for the regular rods formation, respectively. The entropy production is a function of some parameters which define the eutectic phase diagram, coefficient of the diffusion in the liquid, and some capillary parameters connected with the mechanical equilibrium located at the triple point of the solid/liquid interface. Minimization of the entropy production allowed to formulate mathematically the so-called Growth Law for both envisaged eutectic morphologies.

Installation and operation of rail vehicles powered by multiple system voltages forces the construction of multi-system traction substation. The article describes a traction substation power supply with 15 kV output voltage and frequency Hz and 25 kV at 50 Hz. The topology of the power electronics system and the control structure of the power supply enables parallel connection of several power supplies. The selected topology and control structure ensures minimizing the rms value of the LCRL filter capacitor current used at the output of the inverters. The article analyses the influence of harmonics consumed by the active front end (AFE) rectifier used in traction vehicles on the rms current of the LCRL filter capacitor.

New ways of calculating narrow microparticle size distributions based on using the Tikhonov and the modified Twomey methods for the laser diffraction technique are presented. These allow to have reduced the broadening (over-smoothing) of the result occurring in these methods for narrow distributions both singular and their sum. The calculated singular distributions and their distribution sum were then approximated by a Gaussian function and a bimodal Gaussian function, respectively, using the Levenberg-Marquardt method. The angular distribution of scattering power was measured for polystyrene particles with radii of 0.676 µm and 1.573 µm, and for their sum. The tests were carried out for linearly polarized He-Ne laser light scattered by a dilute aqueous suspension of these particles. The results obtained were compared with those obtained with the nanoDS instrument (CILAS). It turned out that using the way based on the Twomey method, the parameters of the narrow distribution sought could be determined quite well.