Control of Flexible Structures: An Instantaneous Optimal Control Approach

An application of instantaneous optimal control algorithm using the Newmark integration scheme to flexible structures is presented. The proposed control design procedure involves only a few simple algebraic manipulations, and this differs from the Riccati equation approach in which one needs to solve a large dimension of eigenvalue/eigenvector problem. However, in the proposed approach the closed-loop stability is not always guaranteed, as opposed to the classical optimal control problem in which the "performance" guarantees the closed-loop stability. In this paper, we propose a systematic way of choosing and characterizing the weighting matrices so that the closed-loop stability is ensured. We use an example of a flexible plane truss structure subjected to an impact to illustrate our results