An Active Geophone Sensor with Optimized State Variable Filter for Measuring Low-Band Frequencies

An active vibration-isolation system (AVIS) utilizes a geophone sensor, a type of velocity sensor, to control microvibration. The structure of the sensor is modeled by mass, damper, and spring. The mathematical model of the geophone sensor is a second-order model with a resonant frequency. However, at low-band frequencies, the response characteristic is nonlinear and phase delay occurs. Compared with the ideal velocity signals of the system, the velocity signals measured from the geophone sensor were distorted in low-band frequencies. Consequently, this measurement issue in feedback control loops can affect the stability and performance of the AVIS. This paper proposes design rules for a state-variable filter (SVF) that can compensate for the nonlinearity of the geophone sensors in low-band frequencies and evaluates vibration attenuation performance of the AVIS by applying the proposed SVF. To evaluate the effectiveness of the filter in compensating for the nonlinear response of the geophone sensor, we compared Bode plots generated through simulation and experimental results obtained using a dynamic signal analyzer. The experimental results demonstrated that the proposed SVF effectively reduces the resonance peak of the geophone sensor and expands the frequency bands that maintain a constant magnitude in range of 0.8–10 Hz. By applying the geophone sensor with SVF to AVIS, the microvibration attenuation improved to − 18.4 dB near 4.5 Hz.