Robust tracking and disturbance rejection with two DOF controllers and distributed internal models

We extend results on robust asymptotic tracking with 2 DOF controllers to the case where both asymptotic tracking and disturbance rejection must occur simultaneously and robustly with respect to plant parameter uncertainty. Necessary and sufficient conditions for the solvability of this problem are established and the structural constraints on the 2 DOF robust controllers are made explicit. These conditions show: 1) that error feedback is necessary, 2) that an internal model of the reference signals must be present in the error driven compensator and 3) that an internal model of the disturbances must be present in either the error driven compensator or in the output feedback compensator. The fact that an internal model of the disturbances need not necessarily be present in the error driven compensator is new and apparently contradicts the well known internal model principle which states that all exogenous signals must be modeled in the error driven controller. A discussion and illustrative examples are included.