Performance of Variable Step-Size LMS Algorithms for Linear Adaptive Inverse Control Systems

Variable Step-size LMS algorithms (VS LMS) have been widely applied to the inverse modeling of an unknown plant in linear adaptive inverse control system due to their advantages over standard LMS in reducing the trade-off between the convergence speed and steady-state error. Plant dynamics, however, can cause eigenvalue spread in the autocorrelation matrix of the controller’s input signal, resulting in slow convergence of the plant inverse model and hence long training sequence. This paper analyzes and compares a class of VS LMS algorithms for linear adaptive inverse control and shows that the Variable Step-size NLMS (VS NLMS) algorithm highly increases the convergence rate while remaining low misadjustment error.