Adaptive Estimation of Asymmetric Dead-Zone Parameters for Sandwich Systems

Abstract

This brief presents a novel one-step adaptive parameter estimation framework for identification of unknown asymmetric dead-zone characteristic parameters (e.g., width and slopes) in the sandwich systems, which avoids using the intermediate variables or carrying out a two-step recursive identification procedure. By applying a continuous piecewise linear neural network (CPLNN), the asymmetric dead-zone nonlinearities can be represented into a parameterized form, where the dead-zone characteristic parameters can be derived based on the online updated CPLNN weights. Moreover, after representing the sandwich system into an augmented system, an adaptive observer is designed to reconstruct the immeasurable internal variables, and an adaptive law with guaranteed convergence is used to online update the CPLNN weights so as to estimate the dead-zone parameters. In this adaptive law, the parameter estimation error information is extracted using simple filters and introducing several auxiliary variables. It is proven that the observation error and estimation error both converge to a small set around zero. The efficiency of the estimation method is exemplified via practical experiments on an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$X$ </tex-math></inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Y$ </tex-math></inline-formula> positioning platform.