Unit-rank output feedback control for antiresonance assignment in lightweight systems

Antiresonance assignment is an effective approach to vibration absorption in lightweight systems under harmonic excitation. The goal is shifting an antiresonance frequency of a receptance to match the one of the excitation force, for making a system coordinate experiencing no (or very small) forced vibrations. A novel method for antiresonance assignment through active control is proposed and validated in this paper. The method relies on the unit-rank output feedback control technique to shift one antiresonance. The assignment problem is solved for both point and cross-receptances exploiting either collocated or non-collocated control architectures. The gain computation is done analytically, either through the system mass, stiffness and damping matrices, or through the measured receptances. Two method extensions are also proposed. First, the output feedback technique is extended to account for an additional sensor, to perform the simultaneous pole-zero assignment based on the zero non-spillover condition. Second, to allow for larger frequency shifts without reducing too much the stability margins, a passive-active, hybrid strategy is proposed. In the first stage, modification of the inertial and elastic parameters is employed to shift the antiresonance frequency as more as possible; in the second stage, the prescribed antiresonance is exactly assigned by means of active control, with smaller gains compared to active control alone. Experimental validation of the method is proposed through a smart, flexible cantilever beam controlled by a non-collocated pair made by an on-the-shelf piezoelectric actuator and a laser vibrometer.