A practical numerical procedure is introduced for determining the stability robustness map of a general class of higher order linear time invariant systems with three independent delays, against uncertainties in the delays. The procedure is based on an efficient and exhaustive frequency-sweeping technique within a single loop. This operation results in determination of the complete description of the kernel and the offspring hypersurfaces, which constitute exhaustively the potential stability switching loci in the space of the delays. The new numerical procedure corresponds to the first step in the overarching framework, called the cluster treatment of characteristic roots. The results of this treatment can also be represented in another domain (called the spectral delay space) within a finite dimensional cube called the building block, which is much simpler to view and analyze. The paper also offers several case studies to demonstrate the practicality of the new numerical methodology.
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e-mail: rifat@coe.neu.edu
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September 2009
Research Papers
Stability Analysis of LTI Systems With Three Independent Delays—A Computationally Efficient Procedure
Rifat Sipahi,
Rifat Sipahi
Department of Mechanical and Industrial Engineering,
e-mail: rifat@coe.neu.edu
Northeastern University
, Boston, MA 02115
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Hassan Fazelinia,
Hassan Fazelinia
Department of Mechanical Engineering,
University of Connecticut
, Storrs, CT 06269-3139
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Nejat Olgac
Nejat Olgac
Department of Mechanical Engineering,
University of Connecticut
, Storrs, CT 06269-3139
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Rifat Sipahi
Department of Mechanical and Industrial Engineering,
Northeastern University
, Boston, MA 02115e-mail: rifat@coe.neu.edu
Hassan Fazelinia
Department of Mechanical Engineering,
University of Connecticut
, Storrs, CT 06269-3139
Nejat Olgac
Department of Mechanical Engineering,
University of Connecticut
, Storrs, CT 06269-3139J. Dyn. Sys., Meas., Control. Sep 2009, 131(5): 051013 (9 pages)
Published Online: August 19, 2009
Article history
Received:
August 25, 2008
Revised:
January 8, 2009
Published:
August 19, 2009
Citation
Sipahi, R., Fazelinia, H., and Olgac, N. (August 19, 2009). "Stability Analysis of LTI Systems With Three Independent Delays—A Computationally Efficient Procedure." ASME. J. Dyn. Sys., Meas., Control. September 2009; 131(5): 051013. https://doi.org/10.1115/1.3117220
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