Controller tuning freedom under plant identification uncertainty: double Youla beats gap in robust stability

In iterative schemes of identification and control one of the particular and important choices to make is the choice for a model uncertainty structure, capturing the uncertainty concerning the estimated plant model. This is typically done in some norm-bounded form, in order to guarantee robust stability and/or robust performance when re-designing the controller. Structures that are used in the recent literature encompass include the gap metric uncertainty, coprime factor uncertainty, and Vinnicombe gap metric uncertainty. In this paper we study the effect of these choices when our aim is to maximize the (re)tuning freedom for a present controller under conditions of robust stability. Particular attention is given to the representation of plant uncertainty and controller tuning freedom in terms of Youla parameters. This so-called double Youla parametrization provides a norm-bounded set of robustly stabilizing controllers that is larger than corresponding sets that are achieved by using any of the other uncertainty structures