A mass-dashpot-spring system with proportional damping is considered in this paper. On the basis of an appropriate nonlinear mapping and the root-locus technique, the interlacing property of transmission zeros and poles is investigated if the columns of the input matrix are in the column space generated by the transpose of the output matrix. It is verified that transmission zeros interlace with poles on a specific circle and the nonpositive real axis segments for a proportional damping system. Finally, three examples are given to illustrate the property.
Interlacing Properties for Mass-Dashpot-Spring Systems With Proportional Damping
Contributed by the Dynamic Systems, Measurement, and Control Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received by the ASME February 7, 2002; final revision August 29, 2003. Associate Editor: M. Goldfarb.
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Lin, J., Chan , K., Sheen , J., and Chen , S. (August 5, 2004). "Interlacing Properties for Mass-Dashpot-Spring Systems With Proportional Damping ." ASME. J. Dyn. Sys., Meas., Control. June 2004; 126(2): 426–430. https://doi.org/10.1115/1.1650384
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