On the Selection of Finite Element Models for Control Design

The purpose of this paper is to show that the modal cost method of weighting the importance of the open loop modes will provide a useful criteria in the selection of finite element models to be used in control system design for flexible structures. The conventional cubic beam element, which is known to have good convergence characteristics for system natural frequencies, may not be the best approach to modeling structures for control design purposes. For beam-like structures, a quintic beam element is shown to be more efficient than a cubic beam element for the convergence of the open loop modal costs; where efficiency is measured by the accuracy of the computed natural frequencies and system costs for a given number of degrees of freedom. A more important result involves the closed loop performance of the optimal regulator designed using the finite element models. In particular, it is shown that when the output is the rotation rate of a point on the beam and the input is a torque at one end, the quintic beam element is significantly more efficient than the cubic beam element. This suggests that control objectives will affect modeling decisions and that modal cost analysis may help provide a unified criteria for the selection of finite element models for control design.