Pole-zero assignment by the receptance method: multi-input active vibration control

The famous receptance method for the active vibration control has been mainly applied for pole placement. In this paper, it is exploited to solve the multi-input antiresonance assignment and then it is extended to handle the simultaneous pole-zero assignment. The design of the controllers is achieved through the measured receptances. The chief advantage is that system model is not needed, and the controller gains are synthetized through the data collected through experimental measurements. Two different approaches are proposed to compute the gains: a single-step method and a multi-step method. Both the techniques are developed for either state or state-derivative control. Two techniques to handle the non-uniqueness of the solution are proposed as well: the first one allows including specification on the eigenvectors, and hence on the spatial response of the system when excited at the antiresonance frequency; the second one places approximately all the poles through an optimization-based formulation. The proposed methods are validated through some numerical examples taken from common benchmarks in this field of research.