Sinusoidal acceleration harmonic estimation using the extended Kalman filter for an electro-hydraulic servo shaking table

Shaking tables play a vital role in mechanical environmental simulation. Sinusoidal shaking tests are usually applied to specimens for simulating periodic motions. Due to the nonlinearities in the electro-hydraulic servo shaking table, its sinusoidal acceleration response contains higher harmonics, which lower the system control performance. To cancel those harmonics, the harmonic information should be firstly known. The paper proposes an acceleration harmonic identification scheme by using the extended Kalman filter. A nonlinear state space model of the acceleration response is then built for the extended Kalman filter. The harmonic information, including the amplitude and phase of each harmonic, is directly derived from the estimated states. The features of the algorithm are that the state transition equation is linear and the measurement equation is nonlinear. It also inherits the advantages of the traditional linear Kalman filter. Both simulation and experimentation are carried out to validate its efficiency and accuracy. The online estimated harmonic information can provide a basis for the further harmonic cancellation.