Identifiability of feedback delays of linear controlled systems

The identifiability problem is addressed in this paper for two time delays in the displacement and velocity feedback paths respectively of a linear system of single degree of freedom. The condition is derived first for the case when two frequency response functions with different time delays are equal at some frequencies. Thus, it is pointed out that if the system is subject to a harmonic input of frequency ω the identified time delays may be deviated from the real values by 2pπ/ω, where p is a positive integer. Afterwards, the identifiability of short time delays is analyzed and some identifiability conditions are given. Finally, the sensitivity of modal parameters of the closed-loop system with respect to the time delays are derived and the delay identification from the experimental modal parameters is described.