Application of Parametric Uncertainty Modeling to a Flexible Structure

We present the results of a study in uncertainty modeling applied to the flexible structure at the University of Minnesota. In addition to additive and multiplicative uncertainty models, we examine parametric uncertainty descriptions in which the weights are obtained directly from input-output data. Two methods are examined, one based on a minimum norm model validation (MNMV) test and another in which the estimated co-variance of the parameters is used to arrive at the uncertainty weights. The resulting uncertainty models are then used to design μ-synthesis controllers, and the resulting closed-loop performance is evaluated. Additional data is taken in a closed-loop setting, and this data is used to refine the model. For the flexible structure studied, we show that the use of parametric uncertainty leads to higher performance than that attainable with purely additive or multiplicative uncertainty. Refinement of the model based on closed-loop data is also shown to result in increased performance.