Control-Oriented Order Reduction of Finite Element Model

In the dynamics modeling of a structure, finite element analysis employs reduction techniques, such as Guyan\´s reduction, that remove some of the "insignificant" physical coordinates, that is, degrees of freedom at a node point. Despite such reduction, the resultant model is still too large for control design. This warrants further reduction as is frequently done in control design by aipproximating a large dynamical system with a fewer number of state variables. A problem, however, arises because a model usually Lundergoes, before being reduced, some form of coordinate transformations that destroy the physical meanings of the states. To correct such a problem, we developed a method that expresses a reduced model in terms of a subset of the original states. The proposed method starts with a dynamic model that is originated and reduced in finite element analysis. The model is then converted to a state-space form, and reduced further by the internal balancing method. At this stage, being in the balanced coordinate system, the states in the reduced model have no apparent resemblance to those of the original model. Through another coordinate transfornation that is developed in this paper, however, this reduced model is expressed by a subset of the original states, so that the states in the reduced model can be related to the degrees of freedom of the nodes in the original finite element model.