Control Method Results Research Articles

Fractional-Order sliding mode control of a 4D memristive chaotic system

Chaotic systems depict complex dynamics, thanks to their nonlinear behaviors. With recent studies on fractional-order nonlinear systems, it is deduced that fractional-order analysis of a chaotic system enriches its dynamic behavior. Therefore, the investigation of the chaotic behavior of a 4D memristive Chen system is aimed in this study by taking the order of the system as fractional. The nonlinear behavior of the system is observed numerically by comparing the fractional-order bifurcation diagrams and Lyapunov Exponents Spectra with 2D phase portraits. Based on these analyses, two different fractional orders (i.e., q = 0.948 and q = 0.97) are determined where the 4D memristive system shows chaotic behavior. Furthermore, a single state fractional-order sliding mode controller (FOSMC) is designed to maintain the states of the fractional-order memristive chaotic system on the equilibrium points. Then, control method results are obtained by both numerical simulations and different illustrative experiments of microcontroller-based realization. As expected, voltage outputs of the microcontroller-based realization are in good agreement with the time series of numerical simulations.

Cadmium and lead ions can be removed simultaneously from a binary aqueous solution by the sono-sorption method

This paper presents the effect of ultrasound on the simultaneous removal of Cd 2+ and Pb 2+ ions from a binary aqueous solution in the presence of natural sorbent (sono-sorption method). The obtained results compare with the results of control method which was achieved in the absence of ultrasound. The experiments under sonication were carried out by 20 kHz apparatus. The effect of different parameters such as the amount of sorbent, contact time, temperature, and specially the competitive sorption of ions were considered for both methods. It is found that the sorption efficiency of Cd 2+ was decreased in the presence of Pb 2+. But, the presence of Cd 2+ had a negligible effect on the removal of Pb 2+. The results show that in the binary solution, the removal efficiency was higher in the presence of ultrasound than the control method. Both ions in binary solution can be removed to near completion with ultrasound . Two different multi-component isotherm equations based on the Langmuir isotherm were applied on the studied system to predict the sorption behavior of the components.