Spatial Vibration Control of Thin Beams Using Multimode Modified Positive Position Feedback

Spatial multimode resonant vibration suppression using Modified Positive Position Feedback (MPPF) approach is presented in this paper. Spatial implementation of the MPPF controller considers vibration attenuation in the whole structure, rather than on a limited number of local control points. This approach utilizes spatial norm minimization of H₂ and H_∞, which considers vibration amplitude of all points on the structure in a model-based design. The designed controller is then evaluated using a clamped-clamped (c-c) and a cantilever beam as the test platforms. According to the numerical simulations and experimental results, spatial MPPF controller using both norm minimization techniques provides a high level of vibration suppression all over the structure, and for all active resonant modes. The MPPF-H_∞ controlled system has a smoother response in the frequency domain, which is more preferable when the closed-loop system experiences a frequency sweep disturbance. At exact resonant frequency however, experimental results confirm a better suppression performance using the spatial MPPF-H₂ method on different points of both beam structures.