Robust tracking, error feedback, and two-degree-of-freedom controllers

The purpose of this paper is to establish first, that in the absence of error feedback, asymptotic tracking is a property that is fragile with respect to the controller parameters. This implies that arbitrary small perturbation of the parameters of such a controller will cause asymptotic tracking to fail. Second, we propose a general 2-DOF controller architecture. We prove that in this structure, asymptotic tracking is, in general, fragile with respect to the controller parameters F_r, F_y and C, while it is robust with respect to the plant parameters as well as the components H and L of the 2-DOF controller. Moreover, the only way to realize a 2-DOF controller in a nonfragile way is to generate the error signal exactly, which amounts to setting F_r=F_y=1. The results reconcile the requirements of the internal model principle, namely the necessity of error feedback, with the additional design freedom potentially offered by 2-DOF controllers. It specifies the controller architecture necessary for robustness and identifies the blocks whose parameters are available for tuning in the design process