The Damped, Driven Pendulum as a Test Case for Algorithms to Control Low Dimensional Chaos

Previously, we have employed the Recursive Proportional Feedback algorithm\footnote{Rollins \textit{et al}, Phys. Rev. E \textbf{47}, R780 (1993).} to achieve control of the chaotic formation of Taylor-Vortex pairs in Modified Taylor-Couette flow with hourglass geometry\footnote{Wiener \textit{et al}, Phys. Rev. Lett. \textbf{83}, 2340 (1999).}. We have developed analogous algorithms and seek to test them in a more easily accessible system to test them prior to implementation in the Taylor-Couette system. To this end we have implemented a damped driven mechanical pendulum\footnote{J. A. Blackburn \textit{et al}, Rev. Sci. Instr. \textbf{60}, 422 (1989).}. We report on the measures of chaos and the application of control algorithms.