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Two-dimensional simple proportional feedback control of a chaotic reaction system

Lookup NU author(s): Dr Ankur Mukherjee, Dr Dominic Searson, Dr Mark Willis

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Abstract

The simple proportional feedback (SPF) control algorithm may, in principle, be used to attain periodic oscillations in dynamic systems exhibiting low-dimensional chaos. However, if implemented within a discrete control framework with sampling frequency limitations, controller performance may deteriorate. This phenomenon is illustrated using simulations of a chaotic autocatalytic reaction system. A two-dimensional (2D) SPF controller that explicitly takes into account some of the problems caused by limited sampling rates is then derived by introducing suitable modifications to the original SPF method. Using simulations, the performance of the 2D-SPF controller is compared to that of a conventional SPF control law when implemented as a sampled data controller. Two versions of the 2D-SPF controller are described: linear (L2D-SPF) and quadratic (Q2D-SPF). The performance of both the L2D-SPF and Q2D-SPF controllers is shown to be superior to the SPF when controller sampling frequencies are decreased. Furthermore, it is demonstrated that the Q2D-SPF controller provides better fixed point stabilization compared to both the L2D-SPF and the conventional SPF when concentration measurements are corrupted by noise. © 2008 The American Physical Society.


Publication metadata

Author(s): Mukherjee A, Searson DP, Willis MJ, Scott SK

Publication type: Article

Publication status: Published

Journal: Physical Review E: Statistical, Nonlinear, and Soft Matter Physics

Year: 2008

Volume: 77

Issue: 4

ISSN (print): 1539-3755

ISSN (electronic): 1550-2376

Publisher: American Physical Society

URL: http://dx.doi.org/10.1103/PhysRevE.77.046215

DOI: 10.1103/PhysRevE.77.046215


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