An intrinsic observer for a class of Lagrangian systems

We propose a new design method of asymptotic observers for a class of nonlinear mechanical systems: Lagrangian systems with configuration (position) measurements. Our main contribution is to introduce a state (position and velocity) observer that is invariant under any changes of the configuration coordinates. The observer dynamics equations, as the Euler-Lagrange equations, are intrinsic. The design method uses the Riemannian structure defined by the kinetic energy on the configuration manifold. The local convergence is proved by showing that the Jacobian of the observer dynamics is negative definite (contraction) for a particular metric defined on the state-space, a metric derived from the kinetic energy and the observer gains. From a practical point of view, such intrinsic observers can be approximated, when the estimated configuration is close to the true one, by an explicit set of differential equations involving the Riemannian curvature tensor. These equations can be automatically generated via symbolic differentiations of the metric and potential up to order two. Numerical simulations for the ball and beam system, an example where the scalar curvature is always negative, show the effectiveness of such approximation when the measured positions are noisy or include high frequency neglected dynamics.     

Mechanism of the skeletal isomerisation of linear butenes over ferrierite: analysis of side reactions

An investigation of the effect of reaction conditions on product distribution in the skeletal isomerisation reaction of linear butenes has been carried out. The main reaction routes over ferrierite have been identified. Beside the main product isobutene, major by-product formation occurs. The unwanted reactions include dimerisation of butene to form octenes, hydrogen transfer yielding small amounts of saturated C₃ and C₄ hydrocarbons and disproportionation producing propene and pentenes. The most abundant by-products were pentene and propene, though these were not formed in equimolar amounts as could be expected. Oligomerisation experiments of propene over ferrierite produced large amounts of butene and pentene, revealing the presence of adsorbed nonene. The cracking of this surface species to hexene and propene is the most likely reaction route for the excess propene formation. This additional path to propene formation operates mainly at temperatures above 623 K.     

Analysis and synthesis of on-chip spiral inductors

This paper presents a physically based compact model for estimating high-frequency performance of spiral inductors. The model accurately accounts for skin and proximity effects in the metal conductors as well as eddy current losses in the substrate. The model shows excellent agreement with measured data mostly within 10% across a variety of inductor geometries and substrate dopings up to 20 GHz. A web-based spiral inductor synthesis and analysis tool COILS, which makes use of the compact models, is presented. An optimization algorithm using binary searches speeds up the synthesis of inductor designs.     

Calculation of the molar volume of liquid hydrocarbons

Equations are proposed for calculating the molar volume of liquid hydrocarbons used in production of surfactants. With such data, it will be possible to calculate most of the physicochemical properties of these hydrocarbons to solve many process problems. __________ Translated from Khimiya i Tekhnologiya Topliv i Masel, No. 6, pp. 39–41, Novemmber–December, 2006.