| Structural damage is a potential hazard to every aerospace vehicle. Damage to an adaptive structure carries with it the additional hazard of a servo-elastic instability. To prevent an impact damage from causing a servo-elastic instability, the control system must either: be robust enough to tolerate the change in the plant; identify the change and switch to a more appropriate control law; or adaptively control the structure.; This research focuses on the latter approach. The adaptive theory Direct Model Reference Adaptive Control (DMRAC), developed by Wen and Balas, is the foundation for this research. The applicability of this approach with a piecewise constant plant is evaluated. Model matching conditions are derived for a general plant, and these conditions are evaluated for a second order plant to gain insight into the physical significance of these matching conditions. Additionally, criteria to ensure the strict positive real condition are developed for the second order example.; The theoretical foundations for using the DMRAC approach with a reduced order reference model are also presented. Of particular significance, is the use of the asymmetric Lyapunov matrix equation to provide sufficient conditions for the existence of ideal gains. These conditions determine whether or not a plant can be matched by a reduced order reference model.; Simulation results are presented for both a first order and a second order system. Based on the simulation results, DMRAC shows significant potential for maintaining control in the presence of damage, and for forcing the damaged plant to track a desired trajectory. Additionally, the frequency of the damaged plant was found to have a more significant effect on the response than does the damping ratio. Using the simulations as a guide, a designer should base the selection of the reference model on desirable transient behavior, and not be concerned with how the damaged structure will behave. |
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