Robust Frequency Response Estimation Accounting for Noise and Undermodelling

This paper addresses the problem of providing bounds on estimated plant frequency response in a form suitable for robust control design. Our approach is to consider the undermodelling as a particular realisation of a random variable and to derive bounds based on averages over all possible noise realisations and over all possible undermodeling realisations. We critically examine the performance of these bounds relative to those that would be obtained by fitting a high order model to the data and then truncating to a low order model. We also show that the parameter in the distribution for the undermodelling can be estimated from the data analagously to the way measurement noise variance is estimated from prediction errors. We propose several new estimators and examine their finite data and asymptotic properties.