Vol. 2, No. 3 (2013): Regular Issue

This paper is a review paper on CRONE control, a frequency-domain robust control design methodology based on fractional differentiation. Principles of CRONE control are presented. The recent extension of this design methodology to multi-input, multi-output systems and to time varying systems are described. Major applications done during industrial collaborations are briefly described.

Here we consider the univariate fuzzy fractional quantitative approximation of fuzzy real valued functions on a compact interval by quasi-interpolation sigmoidal and hyperbolic tangent fuzzy neural network operators. These approximations are derived by establishing fuzzy Jackson type inequalities involving the fuzzy moduli of continuity of the right and left Caputo fuzzy frac-tional derivatives of the engaged function. The approximations are fuzzy pointwise and fuzzy uniform. The related feed- forward fuzzy neural networks are with one hidden layer. Our fuzzy frac- tional approximation results into higher order converges better than the fuzzy ordinary ones.

The nonlinear sloshing of two superposed fluids in a rectangular tank is studied. The equations governing the nonlinear motion of the interface and the free surface have been resolved at first and second order. The shape of these surfaces depends on the perturbation parameter ε and density ratio ρ of the fluids. The analysis of nonlinear effects shows new aspects that are not pre-viously observed. Linear theory is still valid for very small sloshing amplitude. When the amplitude increases, nonlinear effects can not be neglected. Superposed fluids with neighbors densities are more sensitive to nonlinear effects. they occurs in this case, by sub harmonic instabilities in space and beats phenomena in time. The first non-linear effects are observed at the interface. when ε increases, the influence of terms related to the first order eigenfrequency ω11 decreases and the influence of terms related to the eigenfrequency 2ω11 increases faster than those relating to the second order eigenfrequency ω21. At the free surface, the influence of terms related to the second order eigenfrequency ω21 is more pronounced when they appear as the influence of those relating to the eigenfrequency 2ω11.

The time series obtained by numerical simulations of the model of the Bray-Liebhafsky oscillatory reaction is analyzed under the continuously fed well stirred tank reactor (CSTR) conditions, with the aim to find bifurcation points in which system of Bray-Liebhafsky oscillatory reaction transforms from stable to unsta- ble state and vice versa. Types of bifurcation points, supercrit- ical and subcritical Andronov-Hopf bifurcation and saddle-loop bifurcation are determined from characteristic scaling laws.

This papers considers an electromechanical butterfly valve and discusses the conditions for appearance of bistability and bursting oscillations. The critical nonlinear stiffness coefficient and inlet velocities leading to such dynamics are obtained as a function of the system parameters, and the effects of external perturbation on the bursting response of the system are illustrated. It is observed that the driving parameters and the direct current voltage strongly affect the sharpness, the number of strikes, the amplitude of the strikes and the time interval between the strikes. Combinations of large-amplitude oscillations and small- amplitude oscillations are obtained for the electric circuit, while combination of fast-slow dynamics is obtained for the mechani- cal part. The results of the paper provide potential criteria for evaluating and optimizing system performance.