Time delay identifiability and estimation for the delayed linear system with incomplete measurement

When the excitation and the response of a multiple degree-of-freedom (dof) active system is incompletely measurable, the identifiability of delay parameter turns into vague. It instantly brings confidence problems on health monitoring and fault diagnosing for the control loop. To fix this problem, this paper inspects the difference between the system’s frequency responses before and after control, and thereby gives practical criteria on parameter identifiability. It shows that when the active control only connects points within measurable ones, the delay parameters are all identifiable. In other words, if someone wants to identify all of the delay parameters in the control loop, only the frequency responses that are relative with the control connected points need to be measured. Based on this conclusion, a parameter identification algorithm based on Newton–Raphson method is proposed. Numerical simulation results show that this algorithm not only gives accurate parameters but also possesses a good quality of noise resistance.