Sensitivity of distributed structures to model order in feedback control

Abstract

In designing feedback control for distributed structures, practical considerations dictate the use of a finite-dimensional controller. Because there as no ways of determing control gains for infinite-dimensional plants, this requires that the structure be discretized in space. The possibility exists, however, that the feedback control forces designed on the basis of a discretized model can induce instability in the actual distributed structure. This gives rise to the problem of sensitivity of a distributed structure to model order in feedback control. To study this sensitivity problem, in this paper the feedback controls generated on the basis of the discretized model are applied to the actual distributed system and the corresponding closed-loop poles are computed. Then, the sensitivity is investigated by examining the incremental change in the closed-loop poles corresponding to a reduction in the order of the discretized model. A second form of sensitivity study consists of plots of the closed-loop poles versus the order of the discretized model. A numerical example demonstrates the sensitivity of the closed-loop poles to model order in feedback control of a distributed structure.