Control of Distributed Structures

Abstract

The motion of distributed structures is governed by partial differential equations to be satisfied inside a given domain defining the structure and by boundary conditions to be satisfied at points bounding this domain. In essence, distributed structures are infinite-dimensional systems, so that control of distributed structures presents problems not encountered in lumped-parameter systems. Indeed, for the most part, the control theory was developed for lumped-parameter systems, and many of the concepts are not applicable to distributed systems. The situation is considerable better in using modal control, which amounts to controlling a structure by controlling its modes. In this case, many of the concepts developed for lumped-parameter structures do carry over to distributed-parameter structures, as both types of structures can be described in terms of modal coordinates. The main difficulty arises in computing the control gains, as this implies infinite-dimensional gain matrices. This question can be obviated by using the independent modal-space control method, but this requires a distributed control force, which can be difficult to implement. Implementation by point actuators is possible, but this implies control of a reduced number of modes, i.e., modal truncation. Another approach to the control of distributed structures is direct feedback control, whereby the sensors are collocated with the actuators, and the actuator force at a given point depends only on the sensor signal at the same point. Here the difficulty is in deciding on suitable control gains. Damping tends to complicate matters, except for the case of proportional damping. Indeed, in this case modal controls can be designed with the same ease as for undamped structures.