RESONANCES OF A NON-LINEAR s.d.o.f. SYSTEM WITH TWO TIME-DELAYS IN LINEAR FEEDBACK CONTROL

2002 ◽  
Vol 253 (5) ◽  
pp. 985-1000 ◽  
Author(s):  
J.C. JI ◽  
A.Y.T. LEUNG
Keyword(s):  
Feedback Control ◽  
Time Delays ◽  
Linear Feedback ◽  
Linear Feedback Control ◽  
Non Linear

Composite non-linear feedback control using Mittag-Leffler function

2019 ◽  
Vol 7 (2) ◽  
pp. 785-794 ◽  
Author(s):  
Ujjwala Thakar ◽  
Vrunda Joshi ◽  
Vishwesh A. Vyawahare
Keyword(s):  
Feedback Control ◽  
Linear Feedback ◽  
Linear Feedback Control ◽  
Non Linear

scholarly journals Longitudinal Modulation of Marangoni Wave Patterns in Thin Film Heated From Below: Instabilities and Control

2021 ◽  
Vol 7 ◽  
Author(s):  
Anna Samoilova ◽  
Alexander Nepomnyashchy
Keyword(s):  
Feedback Control ◽  
Modulational Instability ◽  
Landau Equation ◽  
Thin Liquid Film ◽  
Additional Term ◽  
Amplitude Equation ◽  
Linear Feedback ◽  
Linear Feedback Control ◽  
Linear Interaction ◽  
Non Linear

Non-linear Marangoni waves, which are generated by the long-wave oscillatory instability of the conductive state in a thin liquid film heated from below in the case of a deformable free surface and a substrate of very low conductivity, are considered. Previously, the investigation of traveling Marangoni waves was restricted to the analysis of the bifurcation and stability with respect to disturbances with strongly different wave vectors. In the present article, for the first time, the modulational instability of traveling waves is investigated. We derive the amplitude equation for the modulated traveling wave, which describes non-linear interaction of the main convective pattern with the perturbations with slightly different wavenumbers. The amplitude equation differs from the conventional complex Ginzburg–Landau equation as it contains an additional term of the local liquid level rise. Linear stability analysis reveals two modulational instability modes: the amplitude modulational and the phase modulational (Benjamin–Feir) ones. It is shown that traveling rolls are stable against the longitudinal modulation for the uncontrolled convection. We also investigate the influence of the non-linear feedback control, which was applied previously to eliminate subcritical excitation of traveling rolls. Computations reveal both the modulational modes under the non-linear feedback control. The obtained results show that the modulational instabilities significantly influence the region of parameters where the non-linear feedback control is efficient for stabilization of waves.

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