Multi-Modal Active Vibration Control of a Lightweight Stress-Ribbon Footbridge Based on Subspace Identification

Abstract

Experimental identification of the modal state-space model for Active Vibration Control (AVC) is proposed based on Subspace Identification Method (SIM). A stress-ribbon bridge built at the Technische Universität Berlin was taken as research object. A real-time control system with pneumatic muscle actuators and inertial sensors was set up for AVC of the bridge. For the purpose of AVC, the feedback control design requires a modal state-space model, which describes the multi-modal characteristics of resonance modes of the bridge and the input/output relationship of the controlled system. Analytically, a state-space model of the bridge can be derived from Euler-Lagrange mechanism. However this is computationally expensive and the determination of damping ratios is also inconvenient. Comparably, SIM offers an attractive alternative due to simple and general parametrisation for Multiple-Input Multiple-Output (MIMO) systems. The identified state-space model from SIM can easily be transformed into a reduced modal state-space model for the AVC controller design. The goodness of the identified state-space model and the truncated modal state-space model was investigated in the stabilization diagram of SIM and with model fit indexes. The identified modal parameters of the footbridge from SIM were compared with that of previous free-vibration tests and the analytical model. Implementation of a Delayed Modal Velocity Feedback Control (DMVFC) based on the obtained modal state-space model was carried out for the full-scale lightweight bridge. The effectiveness of the proposed experimental identification method was shown in case of vertical resonance modes in vibration control experiments.