Annular‐ring slot antenna designs with circular polarization radiation

The design of a microstrip‐fed annular‐ring slot antenna (ARSA) with circular polarization (CP) radiation is initially studied. To obtain CP radiation with broad 3‐dB axial ratio (AR) bandwidth that can cover the WiMAX 2.3 GHz (2305–2320 MHz, 2345–2360 MHz) and WLAN 2.4 GHz (2400–2480 MHz) bands, a novel technique of extending an inverted L‐shaped slot from the bottom section of the annular‐ring is proposed. To suppress the harmonic modes induced by the CP ARSA, the technique of integrating a defected ground structure into the annular‐ring slot is further introduced. From the measured results, 10‐dB impedance bandwidth and 3‐dB AR bandwidth of 44.86 and 9.68% were achieved by the proposed harmonic suppressed CP ARSA. Furthermore, average gain and radiation efficiency of ～4.7 dBic and 71%, respectively, were also exhibited across the bands of interest. © 2014 Wiley Periodicals, Inc. Int J RF and Microwave CAE 25:337–345, 2015.     

Quasi-Chun-Ching Shih''''s Fractional Fourier Transform with Periodicity of 2,3 and M

Based on Chun-Ching Shih's idea, the basic transform was substituted and the quasi-ChunChing Shih's fractional Fourier transform with periodicity of 2, 3 and M was deduced. The two former transforms and the Chun-Ching Shih's fractional Fourier transform were only the particular cases of quasiChun-Ching Shih's fractional Fourier transform with periodicity of M.     

A new method for the determination of wax precipitation from non-diluted crude oils by fractional precipitation

Wax precipitation is one of the most important flow assurance problems. Unfortunately, experimental data are very scarce to confirm existing models for prediction of such precipitation problem. This work reports a new experimental method. Multistage fractional wax precipitation was carried out by decreasing the temperature of crude oil. No solvent dilution was used, so the effect of solvent on temperature wax precipitation was avoided. The reproducibility of the method was tested with comparable results. The precipitation curve and the wax appearance temperature were obtained for two crude oils with different chemical nature using the reported method.     

Design of internal model control based fractional order PID controller

This article presents a design of the internal model control(IMC)based single degree of freedom(SDF) fractional order(FO)PID controller with a desired bandwidth specification for a class of fractional order system(FOS). The drawbacks of the SDF FO-IMC are eliminated with the help of the two-degree of freedom(TDF)FO PID controller. The robust stability and robust performance of the designed controller are analyzed using an example.     

FracSym: Automated symbolic computation of Lie symmetries of fractional differential equations

In this paper, we present an algorithm for the systematic calculation of Lie point symmetries for fractional order differential equations (FDEs) using the method as described by Buckwar & Luchko (1998) and Gazizov, Kasatkin & Lukashchuk (2007, 2009, 2011). The method has been generalised here to allow for the determination of symmetries for FDEs with n$n$ independent variables and for systems of partial FDEs. The algorithm has been implemented in the new MAPLE package FracSym (Jefferson and Carminati 2013) which uses routines from the MAPLE symmetry packages DESOLVII (Vu, Jefferson and Carminati, 2012) and ASP (Jefferson and Carminati, 2013). We introduce FracSym by investigating the symmetries of a number of FDEs; specific forms of any arbitrary functions, which may extend the symmetry algebras, are also determined. For each of the FDEs discussed, selected invariant solutions are then presented.     

On the robust control of stable minimum phase plants with large uncertainty in a time constant. A fractional-order control approach

This paper addresses the problem of designing controllers that are robust to a great uncertainty in a time constant of the plant. Plants must be represented by minimum phase rational transfer functions of an arbitrary order. The design specifications are: (1) a phase margin for the nominal plant, (2) a gain crossover frequency for the nominal plant, (3) zero steady state error to step commands, and (4) a constant phase margin for all the possible values of the time constant (T$T$): 0<T<∞$0<T<\infty$. We propose a theorem that defines the structure of the set of controllers that fulfil these specifications and show that it is necessary for these robust controllers to include a fractional-order PI$PI$ term. Examples are developed for both stable and unstable plants, and the results are compared with a standard PI$PI$ controller and a robust controller designed using the QFT$QFT$ methodology.     

LAG WINDOW ESTIMATION OF THE DEGREE OF DIFFERENCING IN FRACTIONALLY INTEGRATED TIME SERIES MODELS

Abstract. In this paper we consider the estimation of the degree of differencing d in the fractionally integrated autoregressive moving-average time series model ARFIMA ( p, d, q ). Using lag window spectral density estimators we develop a regression type estimator of d which is easy to calculate and does not require prior knowledge of p and q. Some large sample properties of the estimator are studied and the performance of the estimator for small samples is investigated using the simulation method for a range of commonly used lag windows. Some practical recommendations on the choice of lag windows and the choice of the window parameters are provided.