Active buckling control of beams using piezoelectric actuators and strain gauge sensors

this paper, a finite element model incorporating active control techniques has been developed to stabilize the first two buckling modes of both a simply supported and a cantilevered beam. The goal is to increase the corresponding beam buckling loads by using piezoelectric actuators along with optimal feedback control. The uniform beams are bonded with two pairs of segmented piezoelectric actuators at the top and bottom. Resistive strain gauges are attached to the centres of the actuators as sensors. Measurements are taken using these, to estimate the system states. The beams are simply supported or cantilevered and subjected to a slowly increasing axial compressive load. Finite element formulations based on the classical Euler-Bernoulli beam theory and linear piezoelectric constitutive equations for the actuators are presented. The associated reduced-order modal equations and the state-space equations are derived for the design of a standard linear quadratic regulator (LQR). The finite element analysis and the active control simulation results are consistent with both theoretical analysis results and experimental data. The designed full state feedback LQR controller is shown to be successful in stabilizing the first two buckling modes of the beams. Also the control simulation shows that the present optimally located segmented actuator pairs along the beam are more effective for buckling control.