Aim: In this paper, a novel estimator is presented, for online time delay estimation, in
single input-single output LTI systems, with time variant and uncertain delay in control input.
Background: The main studies made on systems with time-varying delay are divided into three
general categories: (1) Identification and estimation of the delay. (2) Criteria presented for stability
and robust stability. (3) Control methods presented with goals like tracking.
Objective: It is obvious that Laplace transfer function of a delayed system includes a time delay
factor (exponential and non-rational). In this study, it is assumed that the only uncertain and time
varying parameter in the system is the system’s time delay. The objective of this paper is to online
estimate of this time delay.
Methods: For designing the proposed estimator, first, a Pade approximation is used for exponential
factor of time delay to rationalize the system transfer function. Therefore, the new transfer
function, which is an approximation of the main transfer function of the system, will include a
time delay parameter (time-variant). After writing a state space realization of the mentioned transfer
function and considering time delay parameter as an extra state variable, a system of nonlinear
state equations will be generated. Eventually, using a kalman filter (linear and extended for linearized
and nonlinear state equations), the systems states, such as system time delay, are estimated.
Results: Simulations were made on a sample system with input time delay, for different types of
time delay signal.
Conclusion: Finally, simulations results show rather desirable performance of the proposed estimator
in dealing with time varying and uncertain delays.