Model Validation in the Frequency

A summary of previous work on a generalization of the strnctured singular value, pg, and its application to constant matrix model validation is given. An algorithm using linear matrix inequalities for numerically computing an upper bound and a preliminary power algorithm for computing a lower bound for pg are presented. The application of the constant matrix bounds for solving the model validation problem in the frequency domain is developed. An end-to-end methodology making use of the frequency domain model validation techniques is proposed which provides a direct connection between experimental data and both nominal and uncertainty modeling. This methodology closes a circle, bringing together for the first time the disparate methods for identifying nominal models and the construction of uncertainty models suitable for robustness analysis and the synthesis of robust controllers. A simple spring-mass system provides an example of the use of the model validation bounds to “tune” noise and uncertainty weights, making use of simulated data. Model validation methodology is then applied to test the consistency between experimental data and two different uncertainty descriptions used in a helicopter hover model.