Hybrid Positive Feedback Control for Active Vibration Attenuation of Flexible Structures

A new controller is introduced in this paper as a novel method for active vibration suppression in flexible structures. The hybrid positive feedback (HPF) uses a second- and a first-order compensator that are fed by the displacement and velocity feedbacks, respectively. Parallel pairs of the HPF controller are implemented when suppression in multimode condition is issued. Since the controller uses two gains for each pair of the actuator/sensor patch for each mode, a suitable gain optimization method has to be used to ensure the optimum performance. To this end, H₂ and H_∞ optimization approaches are utilized. For validation purposes, the controller is verified numerically and experimentally for vibration control of a cantilever beam. System identification is performed, then closed-loop system responses to simultaneous multimode and swept frequency excitations are obtained. According to the results, the HPF controller has a superior performance compared to the conventional method of positive position feedback. Vibration displacement amplitudes were reduced by more than 85% relative to the uncontrolled state. The best performance was achieved by the H₂-optimized HPF, as the net value for vibration displacement amplitude reduction in the multimode condition was 90% of the uncontrolled amplitude.