Acceleration harmonic identification algorithm based on the unscented Kalman filter for shaking signals of an electro-hydraulic servo shaking table

Since there are nonlinearities in an electro-hydraulic servo shaking table, when the shaking table corresponds to sinusoidal shaking tests, its response contains higher harmonics, resulting in harmonic distortion and deteriorating the control performance. It needs to provide harmonic information for harmonic cancellation. The purpose of the paper is to develop an online acceleration harmonic identification algorithm for the shaking table. The unscented Kalman filter is applied to achieve this task. A nonlinear state space of the sinusoidal acceleration response is built for the unscented Kalman filter, which estimates the state of the nonlinear model, and the amplitude and phase of each harmonic, including the fundamental, can be directly decomposed from the identified state vector. The state transition equation is linear and the measurement equation is nonlinear. The efficiency and real-time performance of the developed acceleration harmonic identification are validated by simulation and experiment, in which the estimation error is further used to testify the estimation accuracy.