Low-frequency vibration suppression in flexibly supported precision equipment using polytopic robust D-region H ₂ control

Flexible mounting interfaces in precision equipment can form lightly damped support–payload modes and amplify low-frequency vibration transmitted from the base. Suppression becomes difficult when support parameters vary and the available actuation is limited in bandwidth and force. This study presents a polytopic robust D-region H ₂ control design for the dominant response-amplification band. A control-oriented two-degree-of-freedom model represents the coupled motion of the payload and flexible support channel. The H ₂ performance output combines payload acceleration, support-channel relative displacement and control force. Independent ±15% variations in two equivalent masses and two stiffnesses define a 16-vertex polytope. Common-Lyapunov linear matrix inequalities minimize the worst-vertex H ₂ upper bound while enforcing minimum decay-rate and damping-ratio requirements. Candidate D-region parameters are screened using LMI feasibility, augmented closed-loop stability, acceleration transmissibility and force demand under a bandwidth-limited active-channel approximation and a 200 N force-capacity criterion. In simulation, the global acceleration-transmissibility peak is reduced from 36.34 to 2.40 dB, which is 6.37 dB below that obtained using a performance-tuned linear quadratic regulator. All 16 vertices and 1000 randomly sampled plants remain stable. Experiments on an equivalent flexible-support test rig under random base excitation showed reductions of 21.6 and 11.8 dB at the two uncontrolled response peaks, while the payload-acceleration RMS decreased from 7.157 to 2.505 m/s ² . Under half-sine excitation, the proposed controller further reduced the peak acceleration by 11.81% and shortened the 5% decay time by 64.4% relative to performance-tuned LQR. These results demonstrate target-band vibration attenuation and improved transient decay under the modeled uncertainty and tested implementation conditions.