On the problem of observation spillover in self-adjoint distributed-parameter systems

Abstract

The problem of observation spillover in self-adjoint distributed-parameter systems is investigated. Observation spillover occurs when the output of a limited number of sensors, located at various points on the distributed domain, cannot synthesize the modal coordinates exactly. To this end, two techniques of state estimation (namely, observers and modal filters) are described. Both techniques can be used to extract modal coordinates from the system output and to implement feedback controls. It is shown that, if the residual modes are included in the observer dynamics, observation spillover cannot lead to instability in the residual modes. The problem of the unmodeled modes does remain, however. It is also shown that the modal filters have some very attractive features. In particular, modal filters can be designed to estimate the modal coordinates with such accuracy that observation spillover can be virtually eliminated. In addition, when modal filters are used, in conjunction with a sufficiently large number of sensors, the entire infinity of the system modes can be regarded as modeled, which implies that actual distributed control of the system is possible. It is also demonstrated that modal filters are quite easy to design and are not plagued by instability problems.