A hierarchy of performance analysis techniques for adaptive active control of sound and vibration

Abstract

Active control for silencing sound and vibration has recently become the subject of much investigation and is now being enhanced by the advent of adaptive filtering techniques. In this paper, an approach to adaptive active control performance analysis is developed that involves a hierarchy of techniques, starting with an ideal simplified problem and progressively adding practical constraints and other complexities. Four levels of performance analysis are defined: Level I derives fundamental performance limits given continuous measurements over the entire performance surface; level II brings in the practical constraint of a fixed number of sensors at discrete locations; level III incorporates knowledge of the transfer function structure; and, level IV adds in all of the other practical effects and design constraints required for detailed performance calculations. At each step, a degree of confidence is gained and a benchmark is established for comparison and cross-checking with the next level of complexity. Following this methodical process leads to a baseline architecture, which can then be subjected to detailed performance analysis in order to arrive at a final design. The four levels of performance analysis are discussed in detail and are illustrated by numerical example for a vibrating cantilever beam using a graphics display that was developed for real-time interactive design.