Computation and Physical Interpretation of Multivariate Transmission Zeros for Lumped Parameters Colocated Systems

Abstract A novel result is presented for the computation of transmission zeros for a MIMO lumped parameters electro-mechanical system in terms of the minors of its dynamic matrix. A new structural interpretation is then given under the hypothesis that sensor-actuator pairs are colocated. It is shown how, for this arrangement, transmission zeros can be interpreted (and computed) as the natural frequencies ofthe substructure obtained by constraining the original system at the sensor-actuator colocated pairs locations. The computational efficiency and the physical insight allowed by the proposed method are then illustrated by two examples: a simple spring-mass-dashpot system and a realistic model of a spindle on active magnetic bearings.