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The design of large, high performance structures has led to problems with structural control. A specific example of such a problem occurs in the simultaneous position and vibration control of active surface structures, such as large radio telescopes. This type of structure features a precision surface which has significant mass, but which does not contribute stiffness to its supporting backstructure. The surface is connected to the backstructure via a large number of positioning actuators, and these actuators serve to maintain the precise surface figure in the presence of disturbances to the structure. Previous work has addressed the problem of simultaneous positioning of the active surface elements and suppressing structural vibrations using independent modal space control. However, the previous work has been limited to surfaces which employ force actuators. While it is possible to implement control for such a structure, it has the disadvantage that the decoupling of the system requires knowledge of the support structure in absence of the active surface, which is difficult to obtain experimentally. This work investigates the problem of simultaneously controlling backstructure vibration and active surface positioning using displacement actuators. In this type of system it is shown that it is still possible to decouple the problem modally, allowing for a straightforward controller. Additionally, it is shown that this problem decouple using the model of the complete system, and is thus suitable for practical applications in which experimental measurement data is used to verify the theoretical model of the system. Because the controller design is based upon the eigenvalues and eigenvectors of the model, this allows for a more accurate controller design. A method for decoupling the system is presented, and the effects of the control on other modes is investigated.
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