Spillover instability of a flexible structure equipped with a modal filter

Modal instability due to spillover is investigated of a flexible vibration control system that employs a modal filter as the state estimator. First the characteristic equation of the closed-loop system containing actuators, sensors and a modal filter is derived in a determinantal form. Then it is shown that the characteristic equation can be expanded in a mathematically tractable form. By applying the perturbation technique to the expanded characteristic equation, a criterion is obtained that determines whether or not a residual mode is destabilized. Finally it is proved through the use of the criterion that the control system equipped with one actuator and one sensor always has unstable modes if they are non-colocated.