Design methodologies for optimum spatial compensation of adaptive structures.

摘要

A design metric is established that appropriately quantifies spatial compensator coupling to selected structural modes and de-coupling to all other structural modes. This metric is formed by Hankel singular values of the open-loop controllability and observability Gramians, and is computationally efficient. Three design methods are presented to maximize the design metric value: candidate set method, genetic algorithms method, and nearest neighbor method. The optimum results from each method are discussed in terms of the transfer functions of the system and classical compensator design goals (i.e., loop shaping, high-frequency roll-off, bandwidth constraints).; As demonstrated on a simply-supported plate test structure, the application of each design method increases closed-loop performance by determining optimum transducer designs that couple well to the selected structural modes. Each optimum design also does not couple well to de-selected modes. These methods provide the ability to “spatially loop-shape” adaptive structures, as demonstrated through modification of both actuator-to-sensor frequency response functions and the system loop gain.; The rewards and benefits of each design method are discussed and compared. The candidate set method is shown to be limited by the richness of the candidate set considered. The genetic algorithms method is efficient and effective at determining transducer placements and sizes for maximum design metric value. Within the genetic algorithms method, forced decoders are developed to constrain transducer sizes to a given range. Finally, the nearest neighbor method provides further increases in the design metric value by shaping transducers. The maximum design metric value is achieved when the genetic algorithms method determines optimum transducer placements and sizes, and the nearest neighbor method shapes the final transducer design.; Transducers are an integral part of the adaptive structure design process. It is concluded that emphasis should be placed on designing adaptive structures to be controlled versus designing controllers for adaptive structures. A recommendation of future work is the development of techniques to adapt spatial compensator designs for varying operating conditions.