On the Influence of the Observation Time in Consistent Nonparametric Identification Methods in Closed Loop Systems

Abstract

For systems in a closed loop disturbed by noise, several methods exist to obtain consistent transfer function estimates. A class of methods is based on the introduction of an external test signal. Because a transfer function estimator based on this principle is only asymptotically unbiased, it is important to know the consequences of a finite observation time. For the case of a test signal consisting of a sum of sinusoids and for a zero mean normally distributed system noise, frequency domain expressions are given for bias and variance of a transfer function estimate in a closed loop in relation to the observation time.The results can be extended to the case of stochastic test signals. It is shown, that with increasing observation time the bias term decreases very rapidly to zero.