Inversion feedforward control based on FIR filters for a 2-degree-of-freedom electro-hydraulic shaking table

Electro-hydraulic shaking tables (EHSTs) with multiple degrees-of-freedom (DOFs) are vital to large-scale structural-reliability experiments. The EHST control accuracy directly influences the qualitative and quantitative assessments of the reliability tests. Conventional three-variable control (TVC) fails to account for the coupling between the DOFs in multi-DOF EHSTs. Furthermore, TVC cannot adequately compensate for fluctuations in the acceleration frequency characteristics; thus, the waveform tracking accuracy is poor and suboptimal performance is achieved during high-precision vibration tests. An inversion feedforward control (IFC) based on the design of finite impulse response (FIR) filters is designed during this study to enhance the acceleration-waveform tracking accuracy in multi-DOF vibration tests. The iterative reweighted least squares (IRLS) algorithm is used to design the FIR filters, which are used to fit the impedance characteristics of a multi-DOF EHST. By using the designed FIR filters to filter the acceleration reference waveform, the coupling between the DOFs is compensated for, and this compensation reduces the fluctuations in the acceleration frequency characteristic and the influence of high-frequency noise. The IRLS algorithm is used to transform the passband and stopband filter design specifications into constrained least squares optimization problems. The frequency characteristics of the developed FIR filters enable high-precision fitting of both the impedance magnitude frequency and phase frequency characteristics within the bandwidth of the multi-DOF EHST system. Outside the bandwidth of the multi-DOF EHST system, the filters achieve high-decibel attenuation of the magnitude-frequency characteristic. Experimental acceleration frequency response and random waveform tracking results demonstrate that the filter-based IFC significantly enhances the random acceleration signal tracking accuracy for a multi-DOF EHST.