Spline approach to state reconstruction for optimal active vibration control of flexible systems

In this paper a new technique for 'instantaneous' reconstruction of the state variables of a flexible system is proposed. The reconstructor is based on the use of spline shape functions to interpolate available measurements by taking into account both constraints and boundary conditions. Unlike the usual dynamic observers, this technique does not require the use of a copy of the system neither any information about the inputs hence it is able to work still well even in presence of persistent disturbances and uncertain parameters. The spline shape property of smoothest interpolation introduces a 'spatial filtering' phenomenon on the high-frequency modes which increases the robustness of the control scheme against spillover.