Dynamics of a Surge Tank Under Delayed Feedback Control

In some previous manuscripts [1,2], we showed that when a general class of systems with a resonant frequency is coupled to a delay element, the composite system can have two cross-over frequencies at some critical delays. This implies that the composite system under feedback control will destabilize at high gain with two frequencies. This constitutes a torus attractor in dynamical systems theory. When nonlinearities are introduced, this torus can evolve into a chaotic attractor according to several postulated paths to chaos. In this paper, we show, both experimentally and by simulation, that such a transition to chaos does exist when a simple liquid level control system is placed under cascaded control.