A fast on-line frequency estimator of lightly damped vibrations in flexible structures

A significant research effort has been conducted in the past to achieve a reliable on-line vibration mode estimator. Frequently, pure sinusoidal models of the underlying mechanical system have been used to accomplish the estimation task. In this paper, an algebraic approach is proposed for the fast and reliable, on-line identification of the natural frequency of a flexible-link manipulator. The proposed method uses the pure sinusoidal model in combination with the algebraic derivative method for parameter identification. The method leads, in the time domain, to an exact computation formulae for the unknown frequency parameter. This formula is synthesized in terms of time-varying linear unstable filters in combination with classical low-pass filters of the Butterworth type. The computations are performed in a quite small-time interval which is only a small fraction of the first full cycle of the measured sinusoidal signal. The proposed method is verified to be robust with respect to un-modeled small attenuations, present in the flexible structure, and to measurement noise. An experimental setup has been developed as a benchmark to test and compare the proposed method with other recently developed parameter estimation techniques.