モーメント法によるプロセス動特性の測定

抄録

A method is presented by which the modified moments of the impulse response are determined from the exponentially weighted time moments of the input and output of the system or from those of the correlation functions. Modified moments are equal to the coefficients of the Taylor series expansion of the system transfer function about s=α(α>0). Relations between the coefficients of the Laguerre series expansion of the impulse response and the modified moments are also described.
In this paper, the statistical method of measuring the modified moments is one of the important subjects of investigation, and the precision of the evaluated first moment is estimated statistically for a single lag system. To reduce the statistical variances of the moments, it is recommended to shift the mesured correlation function along the time delay axis.
If an appropriate mathematical model for the system is made, the parameters of the model can be determined from the moments. The moment method is extended also to the system in a closed control system.
When the input signal of the system is a white noise, it is shown that the modified moments can be computed continuously on an analog computer without passing through the intermediate step of the correlation functions. That is, the moments of the correlation functions can be determined without the help of a correlator, and this identification method will be applicable to the adaptive control systems.