Ref: M. A. Rhode and R. W. Rollins, A. J. Markworth, K. D. Edwards and K. Nguyen, C. S. Daw and J. F. Thomas, J. Appl. Phys. 78, 2224-2232 (1995).

Controlling Chaos in a Model of Thermal Pulse Combustion

M. A. Rhode and R. W. Rollins
Condensed Matter and Surface Science Program,
Department of Physics and Astronomy,Ohio University, Athens, Ohio 45701-2979

A. J. Markworth
Engineering Mechanics Department,
Battelle Memorial Institute, Columbus, Ohio 43201-2693

K. D. Edwards and K. Nguyen
Mechanical and Aerospace Engineering Department,
University of Tennessee, Knoxville, TN 37996

C. S. Daw and J. F. Thomas
Oak Ridge National Laboratory,
Oak Ridge, TN 37831

Abstract

We describe methods for automating the control and tracking of states within or near a chaotic attractor. The methods are applied in a simulation using a recently developed model of thermal pulse combustion at the dynamical system. The controlled state is automatically tracked while a parameter is slowly changed well beyond the usual flame- out point where the chaotic attractor ceases to exist because of boundary crisis. A learning strategy based on simple neural networks is applied to map-based proportional feedback control algorithms both with and without a recursive term. Adaptive recursive proportional feedback is found to track farther beyond the crisis (flame-out) boundary than does the adaptive non-recursive map-based control. We also found that a continuous-time feedback proportional to the derivative of a system variable will stabilize and track an unstable fixed point near the chaotic attractor. The positive results suggest that a pulse combustor, and other nonlinear systems, may be suitably controlled to reduce undesierable cyclic variablility and extend their useful range.

PACS numbers: 05.45.+b, 87.10.+e


Ref: M. A. Rhode and R. W. Rollins, A. J. Markworth, K. D. Edwards and K. Nguyen, C. S. Daw and J. F. Thomas, J. Appl. Phys. 78, 2224-2232 (1995).


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