A differentially amplified Hall effect displacement sensor for positioning control of a long-range flexure stage

This paper presents a novel positioning feedback sensor using a pair of Hall effect elements on a long-range flexure stage. The proposed Hall effect positioning feedback sensor eliminates error and uncertainty by measuring the center of the flexure stage, where a machine tool or measurement probes would take place in the industrial application. A pair of Hall effect elements were amplified in a differential configuration as the cylindrical permanent magnet enclosed in the center of the shuttle in the flexure stage that moves back and forth, generating a uniform gradient magnetic flux intensity. Nonlinear magnetic flux characteristics of a single Hall effect element were eliminated, and high-quality sensor sensitivity was achieved by differential amplification of the two Hall effect elements. The magnetic field analysis to characterize the linearity of the proposed displacement sensor was simulated using the finite element method to prove that the non-linearity of a single hall effect element may be mitigated by employing the differential amplification technique. The flexure stage was additively manufactured into a monolithic structure, and the permanent magnet was fitted into the shuttle of the flexure stage. Each Hall effect element was placed on either side of the magnet at a certain distance on the axis of shuttle movement. The proposed sensor was characterized by performing dynamic system identification of the flexure stage: open-loop response and closed-loop response. The Laser Displacement Sensor (LDS) with the 10 nm resolution was used for baseline comparison and datum line with respect to the proposed sensor. The proposed sensor responses agreed well with LDS in various dynamic inputs. The sensor response was analyzed with two differential amplification signal processing techniques. The maximum sensitivity of the two signal processing techniques was determined to be 16.55 mV/μm, and the resolution was observed as 2.5 μm. In sum, the differentially amplified Hall effect displacement sensor achieved positioning feedback with high sensitivity and linearity and minimized the sensor placement error while maintaining low cost and simple configuration.