Presentation of a New Online Method, for Time Variant and Unknown Input Time Delay Estimation, in Continuous SISO-LTI Systems

Abstract

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. 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. 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. finally, simulations results show rather desirable performance of the proposed estimator in dealing with time varying and uncertain delays.