Identification of time delay in nonlinear systems with delayed feedback control

In the present paper, an algorithm is proposed to identify time delay parameters appearing in feedback loop of controlled systems in which the structural factors are prior known. The algorithm, connecting to the principle of least squares (LS) and the frequency-response function derived from harmonic balance method (HBM), provides a technique to fit the observed input-output data in frequency domain. Since the delay included in the exponential function can be of multi-values in frequency domain, the uniqueness of the identified results is also discussed so that the provided algorithm has completeness. As applications of the algorithm, a single degree of freedom and a two-degree of freedom systems are considered as two typical examples to display the validity of the algorithm. It is seen that the identified delay may be determined uniquely and may reach any desired accuracy by the present algorithm. It is also shown that the algorithm is simple but robust.