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Journal of Control Science and Engineering
Volume 2011 (2011), Article ID 169848, 11 pages
Research Article

Limit Cycle Predictions of Nonlinear Multivariable Feedback Control Systems with Large Transportation Lags

Department of Aeronautical Engineering, National Formosa University, 64, Wen Hua Road, Huwei, Yunlin 63208, Taiwan

Received 4 September 2010; Revised 1 February 2011; Accepted 6 April 2011

Academic Editor: Peilin Fu

Copyright © 2011 Tain-Sou Tsay. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A practical method is developed for limit-cycle predictions in the nonlinear multivariable feedback control systems with large transportation lags. All nonlinear elements considered are linear independent. It needs only to check maximal or minimal frequency points of root loci of equivalent gains for finding a stable limit-cycle. This reduces the computation effort dramatically. The information for stable limit-cycle checking can be shown in the parameter plane also. Sinusoidal input describing functions with fundamental components are used to find equivalent gains of nonlinearities. The proposed method is illustrated by a simple numerical example and applied to one 2 × 2 and two 3 × 3 complicated nonlinear multivariable feedback control systems. Considered systems have large transportation lags. Digital simulation verifications give calculated results provide accurate limit cycle predictions of considered systems. Comparisons are made also with other methods in the current literature.