Causality Constraints on the Analysis and Active Control of Structures

摘要

This research has integrated the causality condition into frequency- domain analysis and control of structural vibration, acoustic scattering, and acoustic radiation. As a result of these efforts, a variety of active and passive control approaches are now physically realizable. In the time domain, causality simply requires that a system's response cannot precede its cause. In active control problems, the causality condition further requires that one cannot use future disturbance information to determine control actuation. These conditions are more subtle in the frequency domain, where one typically interprets experimental data and constructs active and passive control approaches. In the frequency domain, the causality condition assumes the form of Hilbert transform relations between elements of the complex Fourier transform of a causal response. This research produced analytical formulations of the causality condition to enhance experimental data and to devise physically realizable control approaches in the frequency domain. Two contemporary active control approaches were used to illustrate the inclusion of causality. The research developed such formulations, and their algorithmic implementations, with a close association to experimental data and control approaches that are of contemporary importance to the Office of Naval Research.