A novel orthogonalized fractional order filtered-x normalized least mean squares algorithm for feedforward vibration rejection. (15th March 2019) - Yin, Weidi; Wei, Yiheng; Liu, Tianyu; Wang, Yong
Highlights: The Fx-NLMS algorithm for feedforward vibration rejection is improved. Fx-NLMS algorithm using fractional order descent method is proposed. Orth-FONLMS algorithm using orthogonal transform method is formed. Abstract: This paper mainly discusses a pattern of vibration rejection by using a feedforward controller. Conventional filtered-x normalized least mean squares (Fx-NLMS) algorithm converges slow especially when signals are not independent on each other. Therefore, a novel orthogonalized fractional order filtered-x normalized least mean squares (Orth-FONLMS) algorithm is proposed to obtain the precise parameters of the feedforward controller. The proposed algorithm is an improved Fx-NLMS algorithm by using fractional calculus and orthogonal transform. To implement the algorithm, fractional order gradient method and adaptive lattice filter are introduced, respectively. Numerical simulation proves that the proposed algorithm outperforms over the Fx-NLMS and fractional order filtered-x normalized least mean squares (Fx-FONLMS) algorithm in terms of convergence rate and accuracy.