Variable Learning Rate LMS Based Linear Adaptive Inverse Control

Abstract

Adaptive \u00a0inverse \u00a0control \u00a0of \u00a0linear \u00a0system \u00a0with \u00a0fixed \u00a0learning \u00a0rate \u00a0least \u00a0mean \u00a0square \u00a0(LMS) algorithm is improved by varying the learning rate. This variable learning rate LMS algorithm is proved to be convergent by using Lyapunov method. It has better performance especially when there is noise in command input \u00a0signal. \u00a0And \u00a0it \u00a0is \u00a0simpler \u00a0than \u00a0the \u00a0Variable \u00a0Step-size \u00a0Normalized \u00a0LMS \u00a0algorithm. \u00a0A \u00a0water \u00a0box temperature \u00a0control \u00a0example \u00a0is \u00a0quoted \u00a0in \u00a0this \u00a0paper. \u00a0Simulation \u00a0results \u00a0are \u00a0carried \u00a0out \u00a0and \u00a0show \u00a0that \u00a0the adaptive inverse control with variable learning rate LMS is better than that with the fixed learning rate LMS algorithm and the Variable Step-size Normalized LMS algorithm.