A CRUDE METHOD OF LOOP-SHAPING ADAPTIVE STRUCTURES THROUGH OPTIMUM SPATIAL COMPENSATOR DESIGN

This work continues the development of methods for optimum spatial compensator design of adaptive structures and is based upon the use of a computationally efficient estimate of the Hankel singular values of the open-loop controllability and observability Gramians to form the design metric. Results demonstrate that when a range of transducer sizes is considered in the candidate set, the proper spatial compensator design metric is the product of a coupling cost and a de-coupling cost. This leads to designs that provide a balance between coupling to modes that are important for control and de-coupling from modes not important for control. As demonstrated on a simply supported plate structure, the optimum design resulting from the application of the approach detailed herein significantly limits coupling to all modes except those present in the performance metric. The method provides the ability to crudely loop-shape the adaptive structure, as demonstrated through modification of both the actuator-to-sensor frequency response function and the system loop gain. It is concluded that emphasis should be placed on designing spatial compensators in order to facilitate the design of controllers for adaptive structures.