Minimizing phase delay of feedback control signals for electromagnetic vibrators to reduce measurement uncertainty in ultra-low frequency vibration calibration

Suppressing the distortion of ultra-low frequency (ULF) vibration waveforms produced by an electromagnetic vibrator (EMV) presents significant challenges, leading to considerable measurement uncertainty during vibration calibration. A phase delay minimization method for feedback control signals is proposed to reduce the harmonic distortion of ULF vibration waveforms. The method quantitatively describes the influence law of the active viscoelastic approach on system frequency response characteristics. By selecting appropriate active stiffness and damping coefficients, the method minimizes the phase delay of the feedback control signal, thereby enhancing the disturbance suppression capability of the displacement and velocity composite negative feedback control. Experimental results indicate that harmonic distortion of the vibration waveform is reduced to less than 1.70 % within the ULF frequency range of 0.001 Hz ≤ f ≤ 1 Hz. Furthermore, the amplitude sensitivity calibration uncertainty, which arises from vibration waveform distortion, has been reduced to 0.038 % (k = 1.8), thereby improving the accuracy of vibration calibration.