A quick-response and high-precision dynamic measurement method with application on small-angle measurement

Small-angle measurement tools with pendulum mechanical structure face two major challenges. One is that it takes a long time to wait for the pendulum structure to completely stop swinging, and the other is that the instrument has poor anti-interference ability. Inspired by the two challenges, in this paper we propose a dynamical measurement method to achieve a fast and accurate measurement synchronously. Specifically, a damped oscillation modeling of the pendulum with nonlinear least-squares fitting is presented to estimate the model parameters, which includes the angle of the oblique plane. In addition, it is proved that the minimum sample size required for data fitting is decided by one oscillation period, which guarantees the shortest measuring time within high precision. Moreover, in this paper we also present the precision criterion of fitting parameters to judge whether the fitting results meet the requirements. This proposed method is applied to a developed small-angle measurement tool. The error of the proposed measurement system is better than 3.25 '' and the uncertainty is 4.8 '' within a measurement angle of 2000 '', and the settling time is 0.45 s. The experimental results confirm that this method can not only greatly shorten the measuring time, but enhance the anti-interference ability and realize high-precision measurement.