Partial Differential Equation Approach to Robust Control Design of Smart Materials and Structures; Theoretical and Computational Aspects

摘要

Our research efforts under the ARO Grant have developed a robust control design methodology for distributed interactive systems, such as they arise within the technology of smart materials and structures. The proposed approach is based on the Partial Differential Equations (PDE) that model the structures from first physical principles. As such, this methodology Covers the entire range of frequencies, and, moreover, accounts for new pathological phenomena, of which there is no counterpart in the case of lumped (finite dimensional) systems. A benchmark problem of paramount importance in itself, which also serves as a vehicle to test the proposed PDE-based approach, is the noise reduction (or structural acoustic) problem. Here the goal is to reduce, or attenuate, or dampen out the unwanted noise field, which is caused within an acoustic chamber by an external source. To this end, one makes use of the destructive interference of the acoustic pressure generated by one of its moving elastic walls, under the bending action produced by wired smart materials bonded to it. A balanced combination of passive (stabilization) and active (optimization) controls was used, which turned out to be effective over a wide band of frequencies, high and low frequencies. When tested in a simplified canonical model, the PI's design produced a 70% noise reduction rate. Numerical tests are available. This research has resulted in a large number of publications in top-ranked professional journals by the PI's and their Ph.D. students, which are listed in the full size Final Technical Report. Many results of this research were presented by the PI's at numerous international conferences in U.S., Europe and China.