Sensitivity of the transmission zeros of flexible space structures

The new pole/zero cancellation technique developed for the problem of sensitivity and robustness in vibration isolation systems for flexible spacecraft requires an analysis of the sensitivity of transmission zeros. This paper analyzes the sensitivity of the transmission zeros of flexible structures with compatible sensors and actuators, in terms of partial derivatives and condition numbers. It is shown that, in both measures, the sensitivities of the zeros of such a system are closely related to those of its poles. It is also shown that the closed-loop poles produced by applying the pole/zero cancellation to the structure have sensitivities approaching those of the zeros, so that these are given by the sensitivities of the open-loop poles. Examples are presented that illustrate these points.