Parametric Tuning of Direct Adaptive Inverse Control via NLMS Algorithm with Fuzzy Adaptive Step Size

Abstract

The relation between the convergence speed and the steady-state Mean Square Error (MSE) during the update of the estimation of a weights vector by an optimization algorithm is a fundamental issue for a good performance of adaptive filters. Thus, in the context of optimization algorithms based on stochastic gradient descent, in this paper a new version of the Normalized Least Mean Square (NLMS) algorithm is proposed, aiming to obtain a good trade-off between the convergence speed and the steady-state MSE. For this, the step size is adapted by a Mamdani Fuzzy Inference System (MFIS), as a function of the squared error and of the normalized time instant by the Min-Max method. For validation of the proposed algorithm, the Direct Adaptive Inverse Control (DAIC) design was performed for application on a non-minimum phase plant in the presence of a disturbance signal added to the control signal.