A spline-based state reconstructor for active vibration control of a flexible beam

In this paper a technique for "instantaneous" reconstruction of state variables of a flexible beam is proposed. The reconstructor uses spline shape functions to interpolate the available measurements and to take into account the boundary conditions. Unlike usual dynamic observers, this technique does not require a copy of the system neither any information about the inputs hence it is able to work even in the presence of persistent disturbances and uncertain parameters. The spline functions introduce a sort of "spatial filtering" on the high-frequency modes, this phenomenon increases the robustness of the control scheme against spillover. Computer simulations show that this reconstructor, joined to a suitable controller, is able to reduce the vibration of beams subject to persistent multifrequency disturbances acting at unknown beam abscissae. © 1998 Academic Press Limited.