Controllability and observability measures for Craig-Bampton substructure representations

Measures of controllability and observability are derived for a Craig-Bampton substructure representation for which fixed interface modes and constraint modes are computed relative to control actuator locations. The measures facilitate modal ordering and act as an index of dynamic completeness for modal truncation. Example problems are given to demonstrate that the controllable and observable reduced substructure models have a greater accuracy in predicting closed loop pole locations, transfer functions and actuation commands than conventional normal mode models.