Nonsmooth Recursive Identification of Sandwich Systems with Back...
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Hindawi Publishing Corporation
Journal of Applied Mathematics
Volume 2012, Article ID 457603, 16 pages
doi:10.1155/2012/457603
Research Article
Nonsmooth Recursive Identification of Sandwich
Systems with Backlash-Like Hysteresis
Ruili Dong,
1
Yonghong Tan,
1
Hui Chen,
2
and Yangqiu Xie
3
1
College of Mechanical and Electronic Engineering, Shanghai Normal University, Shanghai 200234, China
2
Department of Automation, Southeast University, Nanjing 210096, China
3
School 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 q 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.
1. Introduction
Usually, a sandwich system with backlash-like hysteresis is defined as the system that
a backlash-like hysteresis is sandwiched between two linear dynamic subsystems. In
engineering applications, many mechanical systems such as mechanical transmission
systems, servo control systems, and hydraulic valve systems can be described by the so-
called sandwich systems with backlash-like hysteresis. The reason to cause the backlash-
like hysteresis phenomenon is mainly due to the gaps existing in transmission mechanism
systems such as gearbox and ball screw.
Recently, identification of sandwich systems has become one of the interesting issues
in the domain of modeling and control for complex systems. References 1–3 proposed the
recursive identification methods for the sandwich system with smooth nonlinearities. The
main ideas of those approaches are to extend the linear system identification methods to
smooth nonlinear cases. Moreover, there have been some methods for the identification of
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