Affiliation:
1. Setpoint Inc., Houston, TX 77057, USA
2. Department of Chemical Engineering, University of Notre Dame, IN 46556, USA
Abstract
By using the center manifold and normal form theories of dynamical systems, we were able to show that when a "resonant" system, with a maximum in its amplitude Bode plot, is placed under delayed negative feedback, two-torus attractors appear near specific values of delay and feedback gain [Boe & Chang, 1989]. The two-torus attractors of a classical liquid-level control experiment with cascaded feedback are studied both numerically and experimentally here to complete the local analysis of the previous paper. Like other two-torus systems, we observe a Devil's staircase of frequency-locked tori with a fractal dimension 0.87. A torus-wrinkling mechanism for the transition to chaos, as proposed by Ostlund et al. [1983], is supported by our experiments.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)
Cited by
24 articles.
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