Steady-state response assignment for a given disturbance and reference: Sylvester equation rather than regulator equations
This work addresses control system design for engineers, offering a novel method to assign steady-state responses, though it is incremental as it builds on existing moment concepts.
The paper tackles the problem of actively controlling steady-state responses in linear systems by shifting from moment matching for approximation to moment assignment for control, resulting in a design framework that uses Sylvester equations instead of regulator equations.
Conventionally, the concept of moment has been primarily employed in model order reduction to approximate system by matching the moment, which is merely the specific set of steady-state responses. In this paper, we propose a novel design framework that extends this concept from ``moment matching'' for approximation to ``moment assignment'' for the active control of steady-state. The key observation is that the closed-loop moment of an interconnected linear system can be decomposed into the open-loop moment and a term linearly parameterized by the moment of the compensator. Based on this observation, we provide necessary and sufficient conditions for the assignability of desired moment and a canonical form of the dynamic compensator, followed by constructive synthesis procedure of compensator. This covers both output regulation and closed-loop interpolation, and further suggests using only the Sylvester equation, rather than regulator equations.