Pole-zero modeling of flexible space structures

Abstract

Generic models of flexible space structures are investigated from the infinite discrete-spectrum viewpoint of distributed parameter systems. The models are simple enough to treat analytically, yet complicated enough to demonstrate the practical usefulness of the transcendental-transfer-function modeling for the purposes of preliminary control synthesis. Transfer functions of the various generic models are derived analytically, and their pole-zero patterns are investigated. The alternating pole-zero pattern of a transfer function from an actuator to the colocated sensor is well-known. It is, however, newly found that in certain colocated cases, each mode has an associated zero of higher frequency than the pole; in fact, the rigid-body mode has an associated zero very close to the origin. This direct transmission property must be taken into consideration when designing large space structures such as the dual-keel Space Station, which has a pole-zero pattern very similar to that of the generic models. The practical significance of such pole-zero patterns on colocated control is discussed.