Self-Calibrating Position Measurements: Applied to Imperfect Hall Sensors

TL;DR

The paper tackles the problem of accurate rotor-position estimation using low-cost linear Hall sensors that suffer from position-dependent inaccuracies due to manufacturing tolerances. It proposes a data-driven, encoderless calibration workflow: collect closed-loop data, identify an accurate flux-density model $oldsymbol{g}(y_0)$ via simulation-error minimization, and construct a reconstruction function $f_oldsymbol{ extPhi}^ agstar$ that compensates higher-order harmonics through a lightweight LUT-based correction. With a known flux-density model, the method achieves simulation-level precision and, on an industrial setup, reduces RMS position error by a factor of $2.6$ without external encoders. Overall, the approach enables practical, cost-effective Hall-sensor-based position sensing suitable for mass-produced actuators by removing the need for expensive test benches or external encoders.

Abstract

Linear Hall sensors are a cost-effective alternative to optical encoders for measuring the rotor positions of actuators, with the main challenge being that they exhibit position-dependent inaccuracies resulting from manufacturing tolerances. This paper develops a data-driven calibration procedure for linear analog Hall sensors that enables accurate online estimates of the rotor angle without requiring expensive external encoders. The approach combines closed-loop data collection with nonlinear identification to obtain an accurate model of the sensor inaccuracies, which is subsequently used for online compensation. Simulation results show that when the flux density model structure is known, measurement errors are reduced to the sensor noise floor, and experiments on an industrial setup demonstrate a factor of 2.6 reduction in the root-mean-square measurement error. These results confirm that Hall sensor inaccuracies can be calibrated even when no external encoder is available, improving their practical applicability.

Figures (8)

• Figure 1: Experimental setup: Linear Hall sensors $h$ on the stator measure flux density $d_h$ from rotor-mounted magnets. Blue and red blocks indicate south and north poles. The flux density depends on the rotor position $y_0$, but reconstructing $y \approx y_0$ is complicated by unmodeled manufacturing defects. Stator windings are omitted from the scheme for simplicity.
• Figure 2: Illustrative example of a position-dependent measurement inaccuracy, plotted along two out of $n_m$ pole-pairs. When the position is reconstructed () from flux density signals while neglecting higher order harmonics, the estimate of true rotor angle () is not accurate and potentially varies along each pole pair.
• Figure 3: Closed-loop data collection scheme. Rotor position estimates $y\approx y_0$ are reconstructed from flux density signals $\mathbf{d}$ and are used for position feedback control, suppressing external disturbances $T_d$. Solid and dashed lines represent continuous-time and discrete-time signals, respectively.
• Figure 4: Simulation example. The first Hall signal $d_1(t_k)$ () is approximately periodic with the magnet pitch, with slight variations across magnets. The estimates $\hat{d}_1=\hat{{g}}_{1,\boldsymbol{\theta}^\star}(\mathbf{d}(t_k))$ () from the model in Step \ref{['step:model']} of Algorithm \ref{['algo:hall']} closely match the true function.
• Figure 5: Measurement error in the simulation. Using the initial $f_\phi^{\text{init}}(\mathbf{d})$ results in a large measurement error (). Using $f_\phi^{\star}(\mathbf{d})$ from Algorithm \ref{['algo:hall']} reduces the measurement error down to the noise floor ().