MODELING STRUCTURES FOR CONTROL DESIGN

Abstract A simply supported beam is used as an example to illustrate the need for more theoretical research on the unification of the modeling and control problems of flexible structures. This paper shows that finite element methods that focus on the convergence of modal data may not be the best approach to modeling structures for control design. This is due primarily to the fact that (1) the importance of a mode in the control problem is measured by its modal costs, and modal cost errors may exceed (by large margins) the errors in modal frequency; (2) the modal costs are not ordered by frequency; and (3) convergence of the modal costs is not monotonic with the number of uniform finite elements. Hence, non-uniform finite element grids may be more efficient. Theorems for convergence of the modal costs are also presented.