Bias of indirect non-parametric transfer function estimates for plants in closed loop

We consider non-parametric indirect transfer function estimates for plants in closed, loop. Such estimates are derived from the corresponding closed l oop system transfer function estimate and knowledge of the controller. In p articular, we give expressions for the bias of such estimates. We consider the application of the results to the spectral and empirical transfer funct ion estimates under the assumption of Gaussian noise. In these cases, the b ias can be expressed in terms of the experiment time, controller gain and t he levels of disturbance and noise. We also briefly consider corresponding expressions for the variance. (C) 2001 Elsevier Science Ltd. All rights res erved.