On the Mean Square Error of Transfer Function Estimates with Applications to Control

Abstract: In this report we study the mean square error of transfer function estimates obtained by identification. The model quality is related to the use of models in regulator design, and the properties of affecting the bias part of the mean square error, both in fixed parameter control and adaptive control.We also study the variance part of the mean square error for transfer function estimates obtained by recursive identification. In the report we derive expressions for the variance as a function of the step length of the identification method, the input spectrum, the variations of the true system and the model order. These expressions are verified and utilized in simulations.