Reduced-order models of a large flexible spacecraft

Abstract

Two reduced-order models of a large flexible spacecraft are proposed in this paper. The method is based on the component mode synthesis. The first one is expressed in terms of the modes of static deformation and the normal modes of vibration of the spacecraft. The reduced-order model can express the dynamic behavior of the spacecraft accurately in a low-frequency region with the proper choice of the modes of static deformation for the spacecraft. The second one is suited to the design of a control system of a spacecraft composed of the main body and subbodies. The reduced-order model is expressed in terms of two sets of the normal modes of vibration, the normal modes of the whole spacecraft and the normal modes of the subbodies. These reduced-order models are illustrated through application to a simple spacecraft model. DVANCED spacecraft are becoming increasingly flexible. Their low natural frequencies fall within the bandwidth of the control system. A dynamic model of this class of spacecraft becomes generally too large for a control designer to cope with. The size of the model must be reduced to perform the control system design. A reduced-order model for this purpose need not express displacements at all the points of the spacecraft in a wide frequency region accurately; it is sufficient that it express displacements at important points to the control system in a certain frequency region. This paper will propose two new reduced-order models of a large flexible spacecraft based on the component mode synthesis.1'2 Usually, equations of motion for this class of spacecraft are expressed in terms of the normal modes of vibration of the spacecraft, and a reduced-order is derived by deletion of certain elements of the normal modes of vibration. This reduced-order model has some disadvantages. One is as follows: Since a displacement of the spacecraft is expressed in all the normal modes of vibration of the spacecraft, deletion of certain elements of the normal modes of vibration may cause an error in the displacements at important points to the control system, which results in a serious degradation of performance of the control system. In order to overcome this disadvantage, the following reduced-order model will be established: A dynamic model of the spacecraft is expressed in terms of the normal modes of vibration and the modes of static displacement of the spacecraft. A reduced-order model is derived by the deletion of certain components of the normal modes of vibration. By the proper choice of static displacements, this reduced-order model accurately expresses the displacements at certain points of the spacecraft in a low-frequency region. On the other hand, a large flexible spacecraft is generally composed of a main body and subbodies with mission equipment. The control system for this class of spacecraft usually consists of the global and local controllers; the former controls the attitude of the whole spacecraft and the latter the attitude of the subbodies. A reduced-order model for a design of this type of controller must express displacements of the whole spacecraft and the subbodies accurately. A reduced-order model based on the normal modes of vibration of the whole spacecraft is not suited to this purpose. For example, at the design phase, the