Complete Response of Distributed Systems Controlled by a Finite Number of Linear Feedback Loops

The analysis of the effect of active control forces on distributed systems, such as elastic mechanical structures, is complicated by the complex coupling between the infinite number of degrees of freedom which may occur. Conventional truncation of the representation of the passive system to a finite-order representation may lead to erroneous conclusions about the controlled system response. In this paper, it is shown that the complete closed-loop system response may be computed without a priori truncation. An example involving an elastic body under the action of an identically located sensor and force source is given which shows that the techniques also are useful for certain passive coupled mode systems.