A Stable Adaptive Gradient Descent Harmonic-Disturbance Rejection for Improving Phase-Tracking Accuracy

This paper proposes a stable adaptive gradient descent for harmonic-disturbance rejection as a tool for grid-power signal processing, magnetic rotary encoders, and permanent-magnet synchronous motors. The method can be widely applied to increase the accuracy of phase or position estimation in various systems in which harmonic disturbances exist. The proposed technique is based on learning the harmonic amplitudes by means of gradient descent on the feedback phase error. To compensate for the disadvantages of existing gradient-descent methods, the derivative expansion is fully developed with system transfer function integration for stable weighting update. In addition, an adaptive learning rate is also proposed based on discrete Lyapunov standard to achieve stability, and theoretical analysis is discussed. The performance of the method is evaluated by numerical simulation in MATLAB with various scenarios, and by the experiment with the rotary magnetic encoders. The results show that the proposed method achieves stability and high performance in harmonic rejection.