Multiple Output Responses Decoupling: With Application to Vibration Suppression of Optical Tables

This paper proposes a novel control theorem called multiple output response decoupling (MORD) and applies it to optical-table vibration control. Optical tables need to isolate environmental vibrations by limited suspension travels. Soft suspensions can significantly isolate ground disturbances but need large strut displacements, while stiff suspensions can reduce suspension displacements but allow significant table vibrations. Passive suspensions are usually trade-offs between these conflicting requirements. Though active suspensions could relieve the compromises, the coupling system dynamics might cause difficulties in control designs. Therefore, this paper proposes the MORD theorem, which allows simultaneous performance improvement by independent control design. First, we review the disturbance response decoupling (DRD) theorem and simplify it as the output response decoupling (ORD) lemma. We then develop the MORD theorem, which can integrate independent ORD control designs without affecting each other. Finally, we apply the MORD theorem to the optical table systems. We design optimal controllers to suppress ground disturbances and other optimal controllers to minimize strut travels. We then integrate these controllers to achieve optimal performance simultaneously as the individual designs with the MORD control design.