On the controllability and observability of flexible beams under rigid-body motion

The authors consider the transverse vibrational control of a single flexible beam undergoing large planar rotational motion. The beam is modeled using a cubic spline technique, which approximates the linearly elastic, continuous beam with a finite number of nodal points. This spatial discretization method provides a useful linear relationship between displacement and curvature, which allows the use of strain gages to measure curvature along the beam. It is shown that kinetic boundary conditions such as those associated with tip loads can be included in the cubic spline model. An optimal control strategy is used to suppress the transverse vibrations while forcing the end tip to follow a prescribed trajectory, and a Kalman filter is used to optimally estimate state variables which are not obtained through direct measurement. Using the optimal controller with the Kalman filter, extensive simulations have been carried out to assess the feasibility of real-time control using the proposed modeling approach. The possibility of using a reduced number of curvature measurements is investigated