Design of a New Observer for Unknown and Variable Input Time-Delay Estimation in Linear SISO Systems

In this paper, a novel observer is designed for online time delay estimation, in SISO linear systems, with variable and unknown time-delay in control input. It is clear that Laplace transfer function of a delayed system includes a time-delay operator (exponential and non-rational). In this article, it is assumed that the only unknown and variable parameter in the system is the system’s time-delay. For designing the proposed observer, first, a Pade approximation is used for exponential operator 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-variant delay parameter. After rewriting a state space realization of the mentioned transfer function and considering time delay parameter as an extra state variable, a system with nonlinear state equations will be formed. Eventually, using a Kalman filter, the systems states, such as system time-delay, are estimated. Finally, simulations results show rather desirable performance of the proposed estimator in dealing with unknown and variable time-delays.