Multimode Modified Positive Position Feedback to Control a Collocated Structure

Abstract

Multimode modified positive position feedback (MMPPF) is proposed to suppress vibrations at multiresonance frequencies in flexible collocated structures. Typically, flexible structures have large numbers of active modes in low frequency bandwidths, which make them susceptible to multifrequency resonant vibrations. Hence, it is essential for the controller to have effective suppression on all participating modes. The MMPPF controller consists of a firstand a secondorder compensator for each mode, as they are all set parallel for all active modes. Because of suppression performance sensitivity to controller gain parameters, proper gain selection is essential. Here, the linear quadratic regulator (LQR) approach and a proposed method called Mnorm are used for gain optimization of the MMPPF controller. The optimized controller is then evaluated experimentally using a cantilever beam, enhanced by a piezoelectric actuator. According to the obtained results, the MMPPF controller reduces vibration amplitudes to the expected lower level, under both LQR and Mnorm optimization methods. In some cases, vibration amplitude at the place of piezoactuator is reduced to even less than the vibration amplitude level of the disturbance input at clamped end.