Decoupled multivariable control for vibration isolation of optical tables

Optical tables must effectively suppress vibrations originating from both ground- and table-induced disturbances while operating within constrained stroke limits. These requirements create intrinsic conflicts: the system must remain soft enough to isolate ground vibrations, yet stiff enough to suppress table-induced disturbances and limit strut displacements. Such trade-offs make multivariable control design particularly challenging, as improving one transmission path often compromises another due to strong dynamic coupling. This paper introduces a hybrid disturbance response decoupling (HDRD) control framework that resolves these conflicts by enabling independent optimization of all disturbance transmission paths. We first model the optical table system and design a baseline multivariable controller that balances the competing performance objectives. Building upon this baseline, we present the input-output disturbance response decoupling (IODRD) lemma and the HDRD theorem. The IODRD lemma allows adjustment of an individual transmission path without affecting the remaining paths, while the HDRD theorem integrates multiple IODRD designs to achieve simultaneous optimization of all transmission paths. Finally, the proposed HDRD controller is applied to an active optical table. Both simulation and experimental results confirm that HDRD achieves superior vibration suppression and strut-travel regulation compared with conventional multivariable approaches, demonstrating its effectiveness for high-performance optical table isolation systems.