Delay Estimation Of Time-delay Systems Based On Cross-correlation Function

When there is a delay in the system,the system input cannot affect the system output in time,that is,there is a significant lag effect in the system.In most industrial control processes,the delay in the system may reduce the stability of the system and increase the difficulty of control.In order to effectively control the delay system,the delay in the system must be estimated first.If the delay in the system cannot be accurately measured,the control quality of the system will deteriorate sharply.Therefore,more and more people pay attention to the problem of delay estimation,and the in-depth study of such problems has important theoretical and practical significance.This paper focuses on the time delay estimation of multiple-input multiple-output delay systems with unknown structures,and the following work is carried out:(1)By introducing the concept of delay matrix,the relative delay relationship between input and output signals of MIMO dynamic delay system is described,and a general mathematical description of MIMO dynamic delay system is given.Based on the signal cross-correlation function,a quantitative relationship constraint between the input,output signals,and time delay of the MIMO dynamic time-delay system is established by defining the delay correlation function.Based on this,a greedy search algorithm for time delay is proposed.The validity of the proposed algorithm is verified by simulation experiments.(2)Generalize the concept of cross-correlation functions to random variables.Delay correlation functions are all based on Pearson correlation coefficients.Pearson correlation coefficients are often used to characterize linear correlations between variables.When there is a non-linear relationship between variables,the effect becomes worse.The Copula function can describe arbitrary relationships between random variables.Therefore,Copula theory is introduced into delay estimation.The Cdependence is used to describe the cross-correlation relationship between random variables to describe the correlation between system inputs and outputs.Estimate the time delay in the system by maximizing C-dependence.C-dependence can be regarded as a "cross-correlation function" that measures the degree of correlation between random variables.In order to reduce the time complexity of delay estimation,a serial search algorithm for time delay is proposed.Simulation experiments and real data experiments verify the effectiveness of the algorithm.