Data-Based Stochastic Evaluation of Closed-Loop Stability and Performance

Metrics for determining the stability- and performance-robustness of a given controller to variations in open-loop dynamics are examined. Of particular interest are the probability distributions that these metrics have given some amount of uncertainty in the plant. The analysis herein characterizes these distributions using frequency response data collected experimentally for the open-loop plant. In doing so, it avoids using a model for the plant, thereby reducing errors and uncertainty inherent to the modeling of a plant. For a proposed controller, a Monte-Carlo method is used to evaluate the closed-loop performance and stability metrics for a large ensemble of test data and thus create an estimate of their distributions. Since ensembles of test data are typically quite small, a Karhunen-Loeve expansion based method is used to synthetically expand the set of FRFs.