A survey of the large structures control problem

The problem of controlling a large structure is difficult because the dynamic model of such systems is a partial differential equation. The controller must be finite dimensional, so the problem arises immediately of how to develop a finite dimension controller for an infinite dimensional plant. When this question is posed the ancillary question of guaranteeing that the resulting design is insensitive to parameter uncertainties arises. The design must not only be of low order, but must also be "robust" in the sense of gain and phase margins etc. The design must also be stable despite uncertainties in the placement of actuators and sensors (the spatial distribution) and the design procedure must also be able to specify where and how many sensors and actuators are to be used. Lastly, all of these problems must be solved in such a way that practical control designs may be developed - in particular the design of digital control systems of large state dimension with high precision is required. This paper is the first of a sequence of invited papers on the large structures control problem, and is meant to be an overview of the problem. It, of necessity, must be a short introduction to the problem with some mention of the open questions. Any survey paper is a reflection of the authors' bias, likes and dislikes. We have attempted to eliminate those as much as possible, but if we have failed in some way to mention a particularly important issue it is but an oversight that we appologize for at the outset.