The LQ controller problem: an example

We provide an example of LQ controller synthesis for a distributedplant, namely an RLCG transimssion line without distortion. The characteristic feature of our example is that both controland observation are of houndary form, and thus this exampleis beyond the scope of the existing theory for the LQ problem.The formal spectral-factorization method is used to get an explicitanalytic form of the optimal controller. It is shown that thiscontrol law has an extremely simple physical realization. Theformally derived optimal controller is then confirmed by theWiener-Hopf technique. Our example shows the need for some generalization of the existingLQ-problem theory as well as the spectral-factorization method.     

Quantum cluster equilibrium theory treatment of hydrogen-bonded liquids: water,methanol and ethanol

The quantum cluster equilibrium (QCE) theory was used in order to predict the composition of the hydrogen bonded liquids: water, methanol and ethanol. The calculations were based on high accuracy theoretical data obtained at the DFT/B3LYP/6-311 G(d,p) level of theory. All investigated liquids are predicted to be composed of big clusters: hexamers in the case of water, tetramers, pentamers, hexamers and heptamers in the case of methanol and pentamers in the case of ethanol. The content of big clusters in a liquid phase as predicted by QCE is overestimated. We have found two confirmations of this. First of all, the behaviour of the liquid water isobar clearly demonstrates that there should be a substantial amount of small clusters in order to obtain the correct temperature dependence of the molar volume. Indeed, the theoretical molar volume close to the boiling point is by about 0.6cm³ lower than the experimental one. The molar volume is too low due to the overestimated population of big clusters resulting in too high a liquid density. Second, the temperature dependence of the chemical shift of the hydroxyl protons in liquid methanol and ethanol, obtained as the population weighted average of the chemical shift of individual clusters, is shifted down field as compared to experiment by as much as 2ppm. This is because big clusters with strongly deshielded hydroxyl protons contribute too much to the weighted average. Possible shortcomings of the QCE approach are discussed.     

On the Spectral-Lyapunov Approach to Parametric Optimization of Distributed-Parameter Systems

The paper is devoted to the discussion of the Riesz-bases applicationin the analysis of distributed-parameter systems controlledby a finite-dimensional or conventional controller. Both boundarycontrol and boundary observation are allowed. The Riesz basesare constructed from a system of eigenfunctions of the closed-loopsystem operator. On the basis of the results obtained, theyare expected to be an effective tool in proving that the closed-loopsystem is well-posed; i.e. they give rise to a C₀-semigroup.These bases also enable us to construct Lyapunov functionalsin the form of series expansions. The analysis is illustratedby a completely worked-out example where the proportional controllersetting is optimized with respect to the ISE criterion. Thecontroller is applied to a parabolic plant modelling a resistive—capacitative(noninductive) direct-current transmission line.     

Approximate parametric optimization of infinite-dimensional systems

We consider the problem of finding g M_n such that where M_n is the n-dimensional subspace of the complexHilbert space L²(0, ) spanned by an n-tuple of normalized eigenvectoesof the operator , corresponding to eigenvalues. The solution is g = P_nf and P_n denotesthe orthoprojector onto M_n. From Grabowski (1991) we know thatP_n can be expressed in terms of the Malmquist functions. Wegive an alternative approach, more convenient for applicationof the standard mathematical software. The problem of convergenceas n is discussed from both theoretical and numerical viewpoint.The reslts are illustrated by the problems of finding the optimaladjustment of the proportional controller stabilizing a distributedplant. Email: pgrab{at}ia.agh.edu.pl     

Kinetics of Degradation of Biapenem

The kinetic and thermodynamic analysis of biapenem degradation was conducted during acid–base hydrolysis, under the influence of buffer components and in the solid state at increased temperature (dry air) and relative air humidity (RH > 50%). The effects of the initial concentration of biapenem and the formation of degradation products on its stability were investigated.     

Are HBO− and BOH− electronically stable?

The binding of an excess electron to HBO and BOH was studied at the coupled cluster level of theory with single, double and non-iterative triple excitations and with extended basis sets to accommodate the loosely bound excess electron. The bent BOH molecule, with a dipole moment of 2.803 D, binds an electron by 39cm^?1, whereas the linear HBO tautomer possesses a similar dipole moment (2.796 D) yet binds the electron by less than 1 cm^?1. It is therefore likely that HBO^? is not stable when rotational energies are included whereas BOH^? is for low rotational quantum numbers.