Position error compensation in quadrature analog magnetic encoders through an iterative optimization algorithm

This paper analyses the position error compensation in quadrature analog magnetic encoders through the iterative linear search optimization algorithm of "steepest descent". In current literature, the sine/cosine signals from the encoder are compensated considering only the gain mismatch, the DC offset components and the non-orthogonality. Nevertheless, the magnetic field distortion due to the non-homogeneity of the magnet and the distortion of the signals due to the mechanical misalignment between the rotation axis of the motor shaft, the magnet center and the chip sensor are generally neglected. In this work, all of these factors are taken into account. The results show that a higher order approximation for modeling the harmonic distortion contained in the encoder signals leads to a slight biasing in the convergence of the compensating parameters. However, the unconstrained and multivariate optimization algorithm of steepest descent fairly minimizes the error from the objective function F(x_n) allowing achieve a compensation efficiency of up to 66%, thus increasing the overall accuracy of this kind of magnetic encoders and improving the performance of any application where they provide rotary position feedback.