On Fractional Adaptive Control

Introducing fractional operators in the adaptive control loop, and especially in Model Reference Adaptive Control (MRAC), has proven to be a good mean for improving the plant dynamics with respect to response time and disturbance rejection. The idea of introducing fractional operators in adaptation algorithms is very recent and needs to be more established, that is why many research teams are working on the subject. Previously, some authors have introduced a fractional model reference in the adaptation scheme, and then fractional integration has been used to deal directly with the control rule. Our original contribution in this paper is the use of a fractional derivative feedback of the plant output, showing that this scheme is equivalent to the fractional integration, one with a certain benefit action on the system dynamical behaviour and a good robustness effect. Numerical simulations are presented to show the effectiveness of the proposed fractional adaptive schemes.     

Clôture Intégrale D'idéaux et la Propriété (Z k )

Dans cet article nous donnons quelques applications du théoréme de valuations de Rees à l’étude de la clôture intégrale des idéaux. En particulier, nous étudions la question de Hübl et Swanson (Cf. [2 Hübl , R. , Swanson , I. ( 2001 ). Discrete valuations centered on local domains . J. Pure Appl. Algebra 161 ( 1–2 ): 145 – 166 .[Crossref], [Web of Science ®] , [Google Scholar]], Question 2.9). Ensuite, nous introduisons une nouvelle propriété des idéaux, que nous l'appelons (Z _k ). Cette propriété nous permettra de majorer le nombre de valuations de Rees associées à un idéal I.     

A note on the commutativity of groups

In this article, we show that a group is abelian if and only if every two elements of the same order commute.     

The effective conductivity equation for a highly heterogeneous periodic medium

We consider the homogenization of a conductivity equation for a medium made up of a set ${F_\varepsilon}$ ( ${\varepsilon}$ being the size of the period of the medium) of highly conductive vertical fibers surrounded by another material (the matrix) assumed to be a poor conductor. The conductivity coefficients in the fibers behave as ${\frac{1}{\varepsilon^2}}$ while whose of the matrix behave as ${\varepsilon^2}$ . We show that the homogenized problem consists of an equality of the kind u(x) = m(x) f (x) where u denotes the macroscopic temperature, f the source term and m(x) a coefficient given by solving some cell equation.     

Quantitative measurements of ammonium, hydrogenophosphate and Cu(II) by diffuse reflectance spectrometry

Diffuse reflectance spectrometry is shown to be useful for the quantitative determination of small amounts of pollutants. The relation between sample concentration and reflectance is described by the Kubelka-Munk equation. The experiments were performed with a laboratory constructed diode array spectrophotometer. We can obtain the quantitative reflectance values of different precipitates like ammonium with Nessler's reagent, hydrogenophosphate with silver nitrate and a complex such as Cu(II) with dithiooxamide 'rubeanic acid' by forming a spot colour on filter paper. We have obtained for each reagent a calibration curve by plotting the relative intensity of reflectance versus the log of the mol (dm(3))(-1) concentration. The linearity was obtained for Cu(II) from 8x10(-4) to 2.5x10(-2) mol l(-1) with r(2)=0.9838 and from 10(-3) to 10(-1) mol l(-1) for polyphosphate with r(2)=0.9975 and from 5x10(-4) to 5x10(-2) mol l(-1) for ammonium with r(2)=0.9889. We can consider that for a direct measurement of the intensity of reflectance, it is possible to perform quantitative spot-test analysis.     

Synthesis and Chelating Properties of Polystyrene Supported Schiff Base (N,N′-disalicylidenepropylenetriamine) Resin Toward Some Divalent Metal Ions

A new polystyrene-supported Schiff base resin, N,N-bis(salicylidenepropylenetriamine)- aminomethyl polystyrene, has been synthesized through a reaction between the commercially available 4-chloromethyl polystyrene polymer and the Schiff base, N,N′-disalicylidenepropylenetriamine. The chelation behavior of this resin toward the divalent metal ions Cu^{2 +}, Ni^{2 +}, Zn^{2 +}, and Pb^{2 +} in aqueous solutions was investigated. Batch equilibration experiments were carried out as a function of contact time, pH, amount of metal-ion, polymer mass, and temperature. The amount of metal-ion uptake of the polymers was determined by using atomic absorption spectrometry (AAS). Results of the study revealed that the resin exhibited higher capacities and a more pronounced adsorption toward Cu^{2 +} and that the metal-ion uptake follows the order: Cu^{2 +} > Zn ^{2 +} > Ni^{2 +} > Pb²⁺. The adsorption and binding capacity of the resin toward the various metal ions investigated are discussed.     

On the fundamental linear fractional order differential equation

This paper deals with the rational function approximation of the irrational transfer function G(s) = \fracX(s)E(s) = \frac1[(t₀s)^2m + 2z(t₀s)^m + 1]G(s) = \frac{X(s)}{E(s)} = \frac{1}{[(\tau _{0}s)^{2m} + 2\zeta (\tau _{0}s)^{m} + 1]} of the fundamental linear fractional order differential equation (t₀)^2m\fracd^2mx(t)dt^2m + 2z(t₀)^m\fracd^mx(t)dt^m + x(t) = e(t)(\tau_{0})^{2m}\frac{d^{2m}x(t)}{dt^{2m}} + 2\zeta(\tau_{0})^{m}\frac{d^{m}x(t)}{dt^{m}} + x(t) = e(t), for 0<m<1 and 0<ζ<1. An approximation method by a rational function, in a given frequency band, is presented and the impulse and the step responses of this fractional order system are derived. Illustrative examples are also presented to show the exactitude and the usefulness of the approximation method.     

Features,Questions and Future Challenges in Layered Silicates Clay Nanocomposites with Semicrystalline Polymer Matrices

The present features review article discusses the crystallisation of the polymer matrix when containing silicate layers. The accent is put on nylons (polyamides) and poly(ethylene oxide) as typical hydrophilic polymers and, poly(propylene) from the hydrophobic group. The effects of the clay, either intercalated or exfoliated, on the crystallisation behaviour of the matrix are highlighted. In addition, the crucial aspects of the semicrystalline morphology of the matrix in the presence of the clay platelets are also debated. The overall crystallisation rate is reported to slow down for most of the crystallisable polymer matrices on account of a retarding growth effect exerted by the clay platelets. As far as the location of the exfoliated clay platelets in the polymer matrix is concerned, they are assumed to be rejected from the crystalline phase in the interspherulitic space.