Geodesic
PID controllers of a~two-mass system and complex pairs of multiplicity~2
Sibirskij žurnal industrialʹnoj matematiki, Tome 18 (2015) no. 1, pp. 56-68.

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We study the stability of a one-channel two-mass system controlled by a proportional integral differential (PID) controller. The controlling force is applied only to one of the masses and the output is the deviation of this mass. It is shown that, among PID controllers, the greatest stability is provided by the regulators for which the right vertical of the roots of the characterisitc polynomial contains a complex pair of multiplicity 2.
Keywords: modal synthesis, lowered-order regulator, greatest stability degree, maximum stability degree, limit stability degree. 
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A. N. Koryukin; A. A. Voevoda. PID controllers of a~two-mass system and complex pairs of multiplicity~2. Sibirskij žurnal industrialʹnoj matematiki, Tome 18 (2015) no. 1, pp. 56-68. http://geodesic.mathdoc.fr/item/SJIM_2015_18_1_a4/

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