POSITIONING AND ACTIVE DAMPING OF FLEXIBLE BEAMS

In this paper, we investigate the design of controllers for the positioning and damping of flexible beams. The approach taken has previously been shown to be effective in the design of controllers for the positioning and active damping of spring-mass systems.1 The control design is based on open-loop positioning followed by closed-loop control for damping. By so doing, it is possible to avoid a conflicting requirements problem associated with traditional state variable feedback design. The open-loop portion of the control is based on optimal control theory, which allows for control saturation. In particular, during this phase of the control, the time to position is minimized. This results in a bang-bang type of control, which is distributed among some "redundant" controllers to allow for flexible mode suppression. Once the beam has been "positioned," the controller switches to a closed-loop phase. The particular closed-loop control used here is based on energy methods and is not a full state variable feedback design. The method is illustrated using a free-free beam example, and the results are compared with a linear system/quadratic cost control design. © 1990 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.