On the link between pole-zero distance and maximum reachable damping in MIMO systems. (1st December 2022) - Piron, Dimitri; Pathak, Shashank; Deraemaeker, Arnaud; Collette, Christophe
Abstract: This paper studies the possibility of extending the already proved link between the pole-zero distance and the maximum reachable damping ratio in single input single output (SISO) systems to multiple inputs multiple outputs (MIMO) ones. This extension is shown to be possible when the considered system presents specific properties: (i) it is equipped with collocated transducers with small authority, (ii) the system has a small modal density in the frequency band of interest and (iii) a low authority control law is used. It is indeed demonstrated that when these three conditions are satisfied, the analytical development of the closed-loop poles convergence is equivalent to the one observed with SISO cases, except that the anti-resonances are replaced by the transmission zeros (TZs). Consequently, it is concluded that the maximum reachable damping ratio is directly proportional to the pole-transmission zero distance for such MIMO systems. This conclusion is demonstrated with two numerical examples (a cantilever beam and a simply supported plate) and experimentally validated on a cantilever beam where all the studied systems are equipped with two collocated pairs of piezoelectric patches. Highlights: The link between pole-zero distance and damping in SISO systems is extended to MIMO. This link is possible when the considered system presents specific properties. This new extension is numerically and experimentally validated.