Time-delay estimation in multivariate systems using Hilbert transform relation and partial coherence functions

The delay estimation problem for open-loop single-input single-output (SISO) systems has been widely studied to the effect that well-established methods are available now. On the other hand, the delay estimation for MIMO systems remains a challenge to-date due to the presence of interactions among input and output variables. In this work, a method based on partial coherence functions (PCF) and Hilbert transform (HT) relation is presented to estimate time-delay for MIMO systems. The key step in the proposed method involves decoupling interactions using the PCF. The HT relation provides a platform for obtaining robust estimates of the time-delay by exploiting the causal nature of the relationship. The highlight of this method in contrast to conventional correlation-based techniques is that the problem formulation explicitly incorporates the delay parameter. In addition, the proposed method uses frequency-domain analysis which allows one to take into effects of noise in a straightforward way. Under closed-loop conditions, time-delay is estimated by introducing a dither signal at the controller output. Results from simulation and experimental studies are presented to demonstrate the effectiveness and potential of this method.