A Method of Identification by Time Moment

Abstract

In this paper, the parameters of transfer function are derived from time moments of its impulse response by use of the derivation in the s-plane and moments of impulse response is evaluated from input moments and output moments.
In this method, the transfer function is not expanded in the s-power series but determined in the actual form and the parameters of the transfer function are estimated by using the higher order moments of the input and the output as same as the order of the transfer function from the lower order terms. Futhermore, the method can be easily extended to the random process by means of the auto-and cross-correlation functions of the process input and the output signal.
It is not desirable to use the nonlinear equipments such as multipliers and t-power generators to measure the time moments, since the accuracy of this method depends upon how accurately they may be measured. The time moments, however, can be measured precisely by the simple operators such as the integrator, the adder and the comparator, since they are transformed to the multiintegration with fixed measuring time, by using the integration by part.
It is found from the experimental results that this method is available not only for off-line identification, but also the on-line identification in the adaptive control system, because the transfer function can be estimated by the relatively simple operation with sufficient accuracy.