Output regulation and internal models—A frequency domain approach

Abstract

The algebraic regulator problem is formulated and solved in a transfer matrix setting. It is shown that, provided the closed loop system disregarding disturbances is stable, a necessary and sufficient condition for output regulation to take place is that the open loop path consisting of the plant and compensator in cascade, contains a suitably defined internal model of the environment. The disturbance model is more general than the ones used before. The results also generalize earlier results on internal models since they are necessary and sufficient under weaker assumptions. The internal model property is used to construct a compensator which achieves output regulation and internal stability. It is shown that any such compensator can be obtained in two steps: (a) create an internal model of the environment in the forward path and (b) stabilize the system. Our concept of internal model generalize earlier definitions and, unlike most earlier results, is valid even if structural stability (robustness) is not imposed.