S. Bab ji∗ and A.K. Tangirala∗∗
Mutual information, delay estimation, dither, closed-loop systems
Time-delay estimation in closed-loop systems is of critical value in the tasks of system identification, closed-loop performance assess- ment and process control, in general. In this work, we introduce the application of mutual information (MI) theory to estimate process delay under closed-loop conditions. The hallmark of the proposed method is that no exogenous (dither) signal is required to estimate the delay. Further, the method allows estimation of time-delays merely from the step response of the system. The method is based on the estimation of a quantity known as the average mu- tual information (AMI) computed between the input and output of the system. The estimation of AMI involves estimation of joint probability distribution of the input–output pair and therefore is a superset of the existing correlation-based methods, which only compute second-order moments of the joint distribution. Simulation studies are presented to demonstrate the practicality and utility of the proposed method.
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