Robust Black-Box Modeling of Piezoelectric Actuators for Vibration Drilling Control

Abstract

In this paper, we study a new modeling approach which is experimentally validated on piezoelectric actuators, in order to derive black-box pseudolinear models for the vibration drilling control. A common way is to use physical based approaches. However, sometimes, complex phenomena occur in the system due to atypical changes of the process behavior, output noise or some hard non-linearities. Therefore, identification methods to achieve the modeling task are adopted. The micro-displacements of the piezoelectric systems generate atypical data named observation outliers in the output signal, involving large errors named innovation outliers in the predicted output signal. Since the normal distribution of these estimation errors is disturbed, and present heavy tails, we choose here as model of contaminated distribution the gross error model (GEM) approach. In order to deal with the innovation outliers, we extend the noise interval range of the scaling factor, tuning the robust Huber's ?-function chosen. We propose from this function, a parameterized robust estimation criterion (PREC) and we give the asymptotic covariance matrix of the M-estimator for the Output Error (OE) model structure. A new decisional tool for the models quality, named L 1-contribution function is proposed. Experimental results are presented and discussed.