Delay-induced oscillations in a thermal convection loop under negative feedback control with noise

Abstract

We study both experimentally and theoretically the problem of active control of the mechanical equilibrium of a fluid in a convection loop heated from below and cooled from above. In order to easily obtain and maintain the mechanical equilibrium of fluid we have designed a rectangular-shaped loop with long vertical channels and short crosspieces between them. The control is performed by using a negative feedback subsystem which inhibits the convection by introducing small discrete changes in the spatial orientation of the loop with respect to gravity. In this paper, we focus on effects that arise when the feedback controller operates with time delays and/or is subjected to random fluctuations. Both these intrinsic features of the controller could be tuned in experiments to explore their effects together and separately. When the noise is absent, the excess feedback was found to lead to the excitation of delay-related oscillations. In addition, we show that time delay coupled with noise can cause a system to be oscillatory even when its deterministic counterpart exhibits no oscillations. So, we give an example of a hydrodynamic system having, generally, a large number degrees of freedom, which behaves like a small-sized stochastic system heavily dependent on fluctuations, even far from the point of bifurcation. The experimental data and theory is shown to be in good agreement.