Fourier Series Analysis for Mitigating Encoder Nonlinearities and BLdc Motor Asymmetries

High-precision applications using brushless direct current (BLdc) motors demand accurate angular measurements. However, minor mechanical flaws in commercial sensors introduce nonlinear distortions in position readings, causing torque ripple. Further ripple is generated by slight asymmetries in stator windings and rotor magnets. Typically, sensor nonlinearities are addressed using external equipment, while motor asymmetries are often overlooked and left to the current control loop, which, due to limited bandwidth, cannot fully suppress their effects. This article analyzes both sensor and motor nonlinearities and proposes a compensation technique that requires no additional hardware. It leverages the intrinsic properties of BLdc motors to derive an algebraic correction function for angular measurements. Exploiting the periodicity of the distortions, this function is expressed as a Fourier series. Lower order terms address sensor errors, while higher order terms compensate for motor asymmetries. The experimental validation confirms that the method enhances control performance by reducing current ripple, mechanical vibrations, and energy consumption.