Journal of Applied Mathematics
Volume 2012 (2012), Article ID 457603, 16 pages
Research Article

Nonsmooth Recursive Identification of Sandwich Systems with Backlash-Like Hysteresis

1College of Mechanical and Electronic Engineering, Shanghai Normal University, Shanghai 200234, China
2Department of Automation, Southeast University, Nanjing 210096, China
3School of Electronic Engineering, Xi’dian University, Xi’an 710071, China

Received 29 March 2012; Revised 10 June 2012; Accepted 10 June 2012

Academic Editor: Zhiwei Gao

Copyright © 2012 Ruili Dong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A recursive gradient identification algorithm based on the bundle method for sandwich systems with backlash-like hysteresis is presented in this paper. In this method, a dynamic parameter estimation scheme based on a subgradient is developed to handle the nonsmooth problem caused by the backlash embedded in the system. The search direction of the algorithm is estimated based on the so-called bundle method. Then, the convergence of the algorithm is discussed. After that, simulation results on a nonsmooth sandwich system are presented to validate the proposed estimation algorithm. Finally, the application of the proposed method to an X-Y moving positioning stage is illustrated.