were then used to analyze the controllability and observability aspects of finite element models of an illustrative system from a modal perspective -this aided in the identification of computational artifacts in the models and helped predict points at which to halt the truncation of balanced states.Balanced reduced-order reference models of the illustrative system were implemented as part of a direct adaptive control algorithm to observe the effectiveness of the models. It was learned that the truncation point selected by observing the mean percent error plot produced the most satisfactory results overall -the model closely approximated the dominant modes of the system and eliminated the computational artifacts.The problem of improving the performance of the system was also considered. The truncated balanced model was recast in modal form so that its damping could be increased, and the settling time decreased by about eighty percent. iv AcknowledgmentsTo my professors, friends, and family -I extend my most sincere gratitude.v
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