Eigenvector analysis of an active vibration control system

In this paper active vibration control is studied via the system eigenvectors, me approach used, consideration of the open- and closed-loop eigenvectors, enables an analysis of how vibrations are distributed through a structure. The specific control system analyzed uses a single actuator-sensor pair in a one-dimensional system. The sensor and actuator are non-collocated and a proportional controller is applied. In addition to changing the eigenvalues, proportional control changes the mode shapes, resulting in a "one-way decoupling" across the sensor-actuator pair. The results illustrate the complexity that is overlooked by focusing exclusively on attenuation at a single point.