Effect of fractional orders in the velocity control of a servo system

The application of fractional-order PID controllers is now an active field of research. This article investigates the effect of fractional (derivative and integral) orders upon system's performance in the velocity control of a servo system. The servo system consists of a digital servomechanism and an open-architecture software environment for real-time control experiments using MATLAB/Simulink tools. Experimental responses are presented and analyzed, showing the effectiveness of fractional controllers. Comparison with classical PID controllers is also investigated.

Comments on ‘‘Modeling fractional stochastic systems as non-random fractional dynamics driven Brownian motions

Applied Mathematical Modelling, Vol.33

Fractional central differences and derivatives

Journal of Vibration and Control, Vol. 14, Nº 9-10

Fractional derivatives: probability interpretation and frequency response of rational approximations

The theory of fractional calculus (FC) is a useful mathematical tool in many applied sciences. Nevertheless, only in the last decades researchers were motivated for the adoption of the FC concepts. There are several reasons for this state of affairs, namely the co-existence of different definitions and interpretations, and the necessity of approximation methods for the real time calculation of fractional derivatives (FDs). In a first part, this paper introduces a probabilistic interpretation of the fractional derivative based on the Grünwald-Letnikov definition. In a second part, the calculation of fractional derivatives through Padé fraction approximations is analyzed. It is observed that the probabilistic interpretation and the frequency response of fraction approximations of FDs reveal a clear correlation between both concepts.

On the relation between the fractional Brownian motion and the fractional derivatives

Physics Letters A, vol. 372; Issue 7

Baeyer-Villiger oxidation of Keotones catalysed by rhenium complexes bearing N- Or Oxo-Ligands

Rhenium (I, III-V or VII) complexes bearing N-donor or oxo-ligands catalyse the Baeyer-Villiger oxidation of cyclic and linear ketones (e.g. 2-methylcyclohexanone, 2-methylcyclopentanone, cyclohexanone, cyclopentanone, cyclobutanone and 3,3-dimethyl-2-butanone) into the corresponding lactones or esters, in the presence of aqueous H2O2 (30%). The effects of various reaction parameters are studied allowing to achieve yields up to 54%.

Pt/Carbon materials as Bi-Functional catalysts for N-decane hydroisomerization

The activity and selectivity of bi-functional carbon-supported platinum catalysts for the hydroisomerization of n-alkanes have been studied. The influence of the properties of the carbon support on the performance of the catalysts were investigated by incorporating the metallic function on a series of carbons with varied porosity (microporous: GL-50 from Norit, and mesoporous: CMK-3) and surface chemistry (modified by wet oxidation). The characterization results achieved with H-2 chemisorption and TEM showed differences in surface metal concentrations and metal-support interactions depending on the support composition. The highest metal dispersion was achieved after oxidation of the carbon matrix in concentrated nitric acid, suggesting that the presence of surface functional sites distributed in inner and outer surface favors a homogeneous metal distribution. On the other hand, the higher hydrogenating activity of the catalysts prepared with the mesoporous carbon pointed out that a fast molecular traffic inside the pores plays an important role in the catalysts performance. For n-decane hydroisomerization of long chain n-alkanes, higher activities were obtained for the catalysts with an optimized acidity and metal dispersion along with adequate porosity, pointing out the importance of the support properties in the performance of the catalysts.

Synthesis of organometallic Ruthenium(II) complexes with strong activity against several human canceer cell lines

A new family of "RuCp" (Cp=eta(5)-C5H5) derivatives with bidentate N,O and N,N'-heteroaromatic ligands revealed outstanding cytotoxic properties against several human cell lines namely, A2780, A2780CisR, HT29, MCF7, MDAMB231, and PD. IC50 values were much lower than those found for cisplatin. Crystal structure of compound 4 was determined by X-ray diffraction studies. Density functional theory (DFT) calculations performed for compound 1 showed electronic flow from the ruthenium center to the coordinated bidentate ligand, in agreement with the electrochemical studies and the existence of a metal-to-ligand charge-transfer (MLCT) band evidenced by spectroscopic data.

A coherent approach to non-integer order derivatives

Signal Processing, vol. 86, nº 10

A new least-squares approach to differintegration modeling

Signal Processing, Vol. 86, nº 10

Riesz potential operators and inverses via fractional centred derivatives

International Journal of Mathematics and Mathematical Sciences, Vol.2006

On the initial conditions in continuous-time fractional linear systems

Signal Processing, Vol. 83, nº 11

Introduction to fractional linear systems. Part 1 : continuous-time case

IEE Proceedings - Vision, Image, and Signal Processing, Vol. 147, nº 1

A signal processing view of differintegration

Proceedings of the European Control Conference, ECC’01, Porto, Portugal, September 2001

Factorization by invariant embedding of elliptic problems: circular and star-shaped domains

Dissertação apresentada para obtenção do grau de Doutor em Matemática na especialidade de Equações Diferenciais, pela Universidade Nova de Lisboa,Faculdade de Ciências e Tecnologia