Design, parametrization, and pole placement of stabilizing output feedback compensators via injective cogenerator quotient signal modules

Control design belongs to the most important and difficult tasks of control engineering and has therefore been treated by many prominent researchers and in many textbooks, the systems being generally described by their transfer matrices or by Rosenbrock equations and more recently also as behaviors. Our approach to controller design uses, in addition to the ideas of our predecessors on coprime factorizations of transfer matrices and on the parametrization of stabilizing compensators, a new mathematical technique which enables simpler design and also new theorems in spite of the many outstanding results of the literature: (1) We use an injective cogenerator signal module ? over the polynomial algebra [Formula: see text] (F an infinite field), a saturated multiplicatively closed set T of stable polynomials and its quotient ring [Formula: see text] of stable rational functions. This enables the simultaneous treatment of continuous and discrete systems and of all notions of stability, called T-stability. We investigate stabilizing control design by output feedback of input/output (IO) behaviors and study the full feedback IO behavior, especially its autonomous part and not only its transfer matrix. (2) The new technique is characterized by the permanent application of the injective cogenerator quotient signal module [Formula: see text] and of quotient behaviors [Formula: see text] of [Formula: see text]-behaviors B. (3) For the control tasks of tracking, disturbance rejection, model matching, and decoupling and not necessarily proper plants we derive necessary and sufficient conditions for the existence of proper stabilizing compensators with proper and stable closed loop behaviors, parametrize all such compensators as IO behaviors and not only their transfer matrices and give new algorithms for their construction. Moreover we solve the problem of pole placement or spectral assignability for the complete feedback behavior. The properness of the full feedback behavior ensures the absence of impulsive solutions in the continuous case, and that of the compensator enables its realization by Kalman state space equations or elementary building blocks. We note that every behavior admits an IO decomposition with proper transfer matrix, but that most of these decompositions do not have this property, and therefore we do not assume the properness of the plant. (4) The new technique can also be applied to more general control interconnections according to Willems, in particular to two-parameter feedback compensators and to the recent tracking framework of Fiaz/Takaba/Trentelman. In contrast to these authors, however, we pay special attention to the properness of all constructed transfer matrices which requires more subtle algorithms.     

Development and optimization of ultra-high performance supercritical fluid chromatography mass spectrometry method for high-throughput determination of tocopherols and tocotrienols in human serum

The goal of this study was to develop an effective supercritical fluid chromatography method using single quadrupole MS for analysis of all isomeric forms of vitamin E. Finally, two fast and effective methods, the high resolution one and the high speed one, for the determination of 8 vitamin E isomers in human serum were developed.     

Three-Stage Extraction of Gelatines from Tendons of Abattoir Cattle: 2—Properties of Gelatines

The subject of our previous paper (part 1) was three-stage extraction of gelatines from short cattle tendons. In this paper, we studied influence of extraction conditions on quality of produced gelatines??protein content, ash content, rigidity of gelatine gels, viscosity, and distribution of molecular weights. Ash content of gelatines ranged in limits 3.5?C10.5?%. Rigidity of the gels was influenced by extraction conditions and by elastin content in gelatines; highest-quality gels display rigidity of 213 Bloom. Viscosity of gelatines ranged from 2.47 to 12.11?mPa?s. Molecular weights of gelatines display a proportion of fractions from 20 to 36?kDa, a quite high proportion of fractions from approximately 50 to 100?kDa, in some cases even fractions above 200?kDa appear. It was found that transition temperature and melting temperature of gelatines extracted from tendons are in accord with data on gelatines obtained by traditional extraction techniques from skins and bones. With respect to efficiency of the whole extraction process and to quality of extracted gelatine, we may recommend extraction conditions as follows: in the 1st processing stage, shaking degreased starting material with water in ratio 1:10 at 25?°C for 5?h; in the 2nd stage, treating the swelled material with 5?% (w/w) added proteolytic enzyme at 40?°C for 25?h; in 3rd stage, extracting gelatine while boiling for 16?min.     

Controlling 6-endo-selectivity in oxidation/bromocyclization cascades for synthesis of aplysiapyranoids and other 2,2,6,6-substituted tetrahydropyrans

A cascade, composed of (i) oxovanadium(V)-catalyzed oxidation of bromide by tert-butyl hydroperoxide and (ii) stereoselective 6-endo-bromocyclization, affords 3-bromo-2-aryl-2,6,6-trimethyltetrahydropyrans from styrene-type tertiary alkenols in synthetically useful yields. (E)-Alkenols add the bromo- and the alkoxy substituent anti-selectively across the double bond, indicating a bromonium ion-mechanism for the ring closure. 6-endo-control of the alkenol cyclization thereby arises from the polar effect of the aryl substituent. Two methyl substituents bound to the alkene terminus are not similarly able to favor 6-endo-cyclization, because strain arising from methyl group repulsion, as the bromonium-activated π-bond and the hydroxyl oxygen approach, directs bromocyclization of tertiary prenyl-type substrates toward tetrahydrofuran formation. A hexasubstituted bromotetrahydropyran prepared from the oxidation/bromocyclization cascade served as starting material for synthesis of racemic aplysiapyranoid A, in a sequence of free radical and polar functional group interconversion.     

Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool

The EMD algorithm is a technique that aims to decompose into their building blocks functions that are the superposition of a (reasonably) small number of components, well separated in the time–frequency plane, each of which can be viewed as approximately harmonic locally, with slowly varying amplitudes and frequencies. The EMD has already shown its usefulness in a wide range of applications including meteorology, structural stability analysis, medical studies. On the other hand, the EMD algorithm contains heuristic and ad hoc elements that make it hard to analyze mathematically.In this paper we describe a method that captures the flavor and philosophy of the EMD approach, albeit using a different approach in constructing the components. The proposed method is a combination of wavelet analysis and reallocation method. We introduce a precise mathematical definition for a class of functions that can be viewed as a superposition of a reasonably small number of approximately harmonic components, and we prove that our method does indeed succeed in decomposing arbitrary functions in this class. We provide several examples, for simulated as well as real data.     

Interaction Products of 12·5 Deuterons with Molybdenum and their Isolation Possibilities from Worn-out Cyclotron Parts

Using chemical separations and radiometric measurements medium-half-life irradiation products of molybdenum with 12.5 MeV deuterons were determined (⁹⁰Nb, ⁹²Nb, ^95mNb, ⁹⁵Nb, ⁹⁶Nb, ⁹⁹Mo, ^95mTc, ⁹⁶Tc, ^99mTc) as well as thick target yields for some of them: ⁹²Nb (0.22 μCi/μAh), ⁹⁵Nb(0.05 μCi/μAh), ⁹⁹Mo (64 μCi/μAh), ^95mTc(0.76 μCi/μAh), ⁹⁶Tc((62.5 μCi/μAh). Moreover isolation possibiities of radioactive preparations from removed worn-cut molybdenum parts of the U-120 cycletron are discussed.     

Polylactones. 13. Transesterification of Poly(L-Lactide) with Poly(Glycoude), Poly(β-Propio-Lactone), and Poly[ε -Caprolactone)

Homogeneous blends of poly(L-lactide) (M _n = 30 000 to 40 000) and poly(β-propiolactone) or poly(ε-caprolactone) were prepared in solution. The solvent-free blends were subjected to transesterification catalyzed by means of methyl triflate, triflic acid, boron trifluoride, or tributyltin methoxide at 100 or 150°C. At 100°C, transesterification was barely detectable even after 96 h. When poly(β-propiolactone) was used as the reactant at 150°C, degradation was faster than transesterification regardless of the catalyst. The same negative result was obtained for heterogeneous blends of poly(L-lactide) and poly(glycolide). In the case of poly(ε-caprolactone), copolyesters with slightly blocky sequences were obtained with tributyltin methoxide as catalyst, whereas the acidic catalysts caused rapid degradation. The copolyesters were characterized by means of ¹H-NMR spectroscopy with regard to their molar composition, by means of ¹³C-NMR spectroscopy with regard to their sequences, and by means of differential scanning calorimetry with regard to crystallinity.     

The effect of crystal structure on the thermal reactivity of CL-20 and its C4-bonded explosives

The critical temperature and mechanism functions for thermal decomposition of ε-CL-20, RS-ε-CL-20, α-CL-20, ε-CL-20/C4, and RS-ε-CL-20/C4 were evaluated based on non-isothermal TG data. A two-step mechanism has been found for thermal decomposition of α-CL-20, ε-CL-20/C4, and RS-ε-CL-20/C4, where the initial step is partly controlled by crystal structure of CL-20. The more reasonable mean activation energies could be obtained after peak separation for each individual steps. In fact, the activation energy for the post integrated process is almost equivalent with that of the second step, indicating that the total activation energy at the main decomposition process is dominated by thermolysis of CL-20 molecular. Besides, it has been found that the decomposition of C4 matrix does not affect the decomposition of normal ε-CL-20, resulting in identical activation energy and reaction model. However, the interaction between the C4 matrix and RS-ε-CL-20 is significant especially at the initial stage, where the activation energy of RS-ε-CL-20/C4 was overestimated before peak separation, while the activation energy for the second step due to thermolysis of CL-20 molecular is underestimated. The first decomposition step for α-CL-20, ε-CL-20/C4, and RS-ε-CL-20/C4 could be considered as autocatalytic process (AC model), whereas the second as JMA model, which is also applicable to that of pure ε-CL-20 and RS-ε-CL-20. Moreover, The critical temperatures of thermal explosion (T _b) are obtained as 205.6, 205.5, 209.4, 214.4, and 227.5 °C for α-CL-20, ε-CL-20, RS-ε-CL-20, ε-CL-20/C4, and RS-ε-CL-20/C4, respectively. It proves that the C4 matrix could stabilize ε-CL-20 while the crystal form of CL-20 has little effect on its thermal stability.