Research On Time-delay Estimation Based On Copula

The delay system is a kind of control system which has the time-delay between the input signal(the control signal)and the output signal produced by the action system.In the process of industrial production,there is a widespread time-delay.Due to the existence of delay,the measured value cannot reflect the disturbance sustained by the system in time.Even if the measured signal arrives at the regulator,the regulating authority will act immediately after receiving the adjustment signal.After the pure delay time,the regulating signal will reach the regulated value,so that the regulated value will be controlled.Therefore,this process may inevitably produce more obvious overshoot and longer adjustment time,which makes the stability of the control system worse and increases the difficulty of system control.In order to solve the problem of controlling the object with time-delay in industrial production,the time-delay must be estimated first.To estimate the time-delay parameter effectively,the following work is carried out.(1)A delay estimation method based on Copula is proposed for SISO delay system.In this method,the input and input signal of the system are regarded as random variables,and the periodic sampling values of the input and output signal are considered as the observed values of the corresponding random variables.The Copula theory is introduced,and the delay relation between the input and output signals of the system is described by the Copula function.Based on the idea of maximum likelihood estimation,system delay is regarded as the parameter to be estimated.Then the system delay likelihood function is constructed,the system delay is estimated by maximizing the delay likelihood function of the system.The simulation results show that this method can effectively estimate the timedelay of the SISO delay system and has strong robustness to the noise.(2)The delay estimation method based on copula is extended to the delay estimation of MIMO system,and the delay estimation problem of MIMO system is considered to be equivalent to that of multiple multiple-entry single system.The Copula function is used to characterize the delay relationship between multiple input signals and output signals,then the system delay vector likelihood function is constructed.The delay of system is obtained by maximizing the system delay vector likelihood function.The simulation results show that the delay estimation method based on Copula is effective and feasible for time-delay estimation in MIMO delay system.