Study on active control for multilinear and nonlinear vibration in piezoelectric structures through a secondary channel improved method

Focusing on multiline and narrowband spectral vibration control issues presented by engineering requirements, this study assessed the effectiveness of large-scale and high-rigidity structures equipped with piezoelectric stack actuators for the active control of vibration. By utilizing the modal decomposition approach, the derivation yielded a state-space equation for an Nth-order system of a piezoelectric cantilever beam was deduced. On this foundation, the traditional least mean square algorithm was improved, and a resettable uniformization filtered-x least mean square (RU-FxLMS) controller was designed, which effectively mitigated the adverse effects of filtering and prevented beating vibration phenomena during the control process. This improvement has, to a certain extent, compensated the deficiencies of the adaptive strategy over low frequency line spectral vibration. Afterwards, Simulations and experimental pertaining to active vibration control of piezoelectric cantilever beams were performed. Experimental data, gathered under the conditions of multiline spectra, narrowband spectra, and frequency-hopping vibration, exhibited a relatively obvious control effect. Under two typical vibration conditions, the simulations and experiments exhibited reasonable and consistent control trends at each characteristic line spectrum, which validated the feasibility and reliability of this strategy for vibration control in the low frequency domain with piezoelectric structures.