DESTABILIZING EFFECTS OF RATE FEEDBACK ON STRAIN ACTUATED BEAMS

Abstract

The stabilizing and destabilizing effects of rate feedback control on all modes of a strain actuated beam are demonstrated here to support earlier theoretical findings by Balakrishnan [1] (1999Journal of Computational and Applied Mathematics18). The destabilizing effects being due to the actual implementation of the rate feedback controller which is unavoidably non-ideal. The main contribution here is the inclusion of the controller circuit model in the closed loop system equations to obtain correct stability estimates for all modes. Closed loop stability estimates computed from thiscircuitry enhanced modelwere corroborated by experiments. The strain actuated beam constructed for this work was made with a fiber glass lay-up and piezo ceramic wafers embedded throughout the length of the lay-up. A charge-to-voltage amplifier, a differentiator, a gain stage, and a power amplifier were also constructed. The most crucial of these components was the differentiator and its tank frequency. The first four modes and transmission zero frequencies, and the corresponding structural damping were obtained through open loop experiments. Mode estimates were within 5% of the computed values. Zero estimates were less accurate due to electric feedthrough, but modelling of this effect helped to improve zero frequency estimates. Closed loop experiments were run to demonstrate the destabilization of beam modes with frequencies higher than the differentiator's tank frequency.