Hybrid frequency domain control for large flexible structures

A hybrid finite frequency controller is proposed for the vibration suppression of a large flexible structure mounted with collocated sensors and actuators. The controller has passive characteristics at low frequencies and small gain characteristics at high frequencies. Compared with a strictly positive real controller based on the standard Kalman–Yakubovich–Popov lemma, the hybrid finite frequency controller has less energy consumption but can obtain approximately identical performance. Furthermore, when the plant passivity is violated at high frequencies by noncollocation of sensors and actuators, the strictly positive real controller based on the Kalman–Yakubovich–Popov lemma is no longer able to attenuate the vibration of the large flexible structures, while the hybrid finite frequency controller is effective in suppressing the vibration and avoiding spillover instability. Simulation results are presented to validate the effectiveness of the hybrid finite frequency controller.