Receptance-Based Dominant Eigenvalues Computation of Controlled Vibrating Systems with Multiple Time-Delays Using a Contour Integral Method
by
Jun-Shen Yang 1, Huajiang Ouyang 2
, Jia-Fan Zhang 1,3,*, Ke-Wei Zhang 1,3, Zhi-Gang Hu 1,3 and Hai-Min Liu 1
Jun-Shen Yang 1, Huajiang Ouyang 2, Jia-Fan Zhang 1,3,*, Ke-Wei Zhang 1,3, Zhi-Gang Hu 1,3 and Hai-Min Liu 1
1
School of Mechanical Engineering, Wuhan Polytechnic University, Wuhan 430023, China
2
School of Engineering, University of Liverpool, The Quadrangle, Liverpool L693GH, UK
3
Hubei Provincial Engineering Technology Research Center of Fish Processing Equipment, Wuhan 430023, China
*
Author to whom correspondence should be addressed.
Appl. Sci. 2019, 9(23), 5263; https://doi.org/10.3390/app9235263
Received: 26 October 2019 / Revised: 15 November 2019 / Accepted: 29 November 2019 / Published: 3 December 2019
(This article belongs to the Section Acoustics and Vibrations)
The computation of dominant eigenvalues of second-order linear control systems with multiple time-delays is tackled by using a contour integral method. The proposed approach depends on a reduced characteristic function and the associated characteristic matrix comprised of measured open-loop receptances. This reduced characteristic function is derived from the original characteristic function of the second-order time delayed systems based on the reasonable assumption that eigenvalues of the closed-loop system are distinct from those of the open-loop system, and has the same eigenvalues as those of the original. Then, the eigenvalues computation is equivalent to solve a nonlinear eigenvalue problem of the associated characteristic matrix by using a contour integral method. The proposed approach also utilizes the spectrum distribution features of the retarded time-delay systems. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach.
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Keywords:
second-order linear control system; retarded time-delay; dominant eigenvalue; receptance; contour integral method
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MDPI and ACS Style
Yang, J.-S.; Ouyang, H.; Zhang, J.-F.; Zhang, K.-W.; Hu, Z.-G.; Liu, H.-M. Receptance-Based Dominant Eigenvalues Computation of Controlled Vibrating Systems with Multiple Time-Delays Using a Contour Integral Method. Appl. Sci. 2019, 9, 5263.
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