Multiple output response decoupling: With applications to vibration control of optical tables

Abstract

This paper introduces a novel control theorem called multiple output response decoupling (MORD) and applies it to the vibration control of optical tables. Control design for multivariable systems is challenging because improving a particular performance might compromise others. Hence, this paper proposes the MORD theorem, which allows independent, simultaneous modifications of all output responses. First, we develop the output response decoupling (ORD) lemma, which can modify specified output responses while keeping others unchanged. Second, we derive the MORD theorem, which can adjust all output responses as individual ORD controls without cross-influences. Third, we apply the MORD theorem to optical table models, enabling the design of particular ORD controllers to suppress ground disturbances and other ORD controllers to minimize strut deflections. Integrating these controllers using the MORD structure provides concurrent optimization of these output responses. Finally, we perform experiments that illustrate the feasibility and effectiveness of the proposed MORD theorem.