Adaptive Parameter Identification for Nonlinear Sandwich Systems with Hysteresis Nonlinearity Based Guaranteed Performan

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ISSN:1598-6446 eISSN:2005-4092 http://www.springer.com/12555

Adaptive Parameter Identification for Nonlinear Sandwich Systems with Hysteresis Nonlinearity Based Guaranteed Performance Linwei Li, Huanlong Zhang*, Fengxian Wang, and Xuemei Ren Abstract: The paper presents an adaptive identification algorithm via data filtering and improved prescribed performance function for Sandwich systems with hysteresis nonlinearity. By developing a filter in which the filter is simple and easy to realize online and several variables, the estimation error vector can be derived. To improve the transient performance of estimator, a modified prescribed performance function is proposed to constrain the estimation error data through the usage of the predefined domain. For the constrained estimation error condition, the error transformation technique is utilized to simplify the design of the estimator thanks to that the restricted condition is transformed into unconstrained condition. To achieve the convergence of the parameter estimation and assure the predetermined property, a fresh adaptive law is developed. Moreover, the theoretical analysis indicates that the error can converge to a small region based on martingale difference theorem. According to the numerical verification and experimental results, the advantage and practicability of the invented estimator are inspected by comparing the estimators with unconstrained condition. Keywords: Constrained parameter estimation, data filtering, error transformation idea, hysteresis, prescribed performance function, Sandwich systems.

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INTRODUCTION

In the last few decades, the nonlinear system identification plays a vital role in understanding the real-world process systems [1]. Here are all sorts of nonlinear characteristics (e.g., dead-zone nonlinearity, backlash, hysteresis nonlinearity, etc.) in actual engineering applications. To describe nonlinear systems, a lot of specific nonlinear models are proposed such as Neural network [?], NARMAX [3], nonlinear state-space model [4], TS fuzzy model [5], LPV model [6] and Block-oriented model (i.e., Hammerstein, Wiener, Hammerstein-Wiener and Sandwich model) [7], etc. Thanks to the combining way of flexible connecting different linear and static nonlinear blocks, Block-oriented models have become a promising modeling method of nonlinear systems. Among the Block-oriented models, Sandwich model (i.e.,WienerHammerstein model), which consists of two linear subsystems with a nonlinear element in the middle, can describe more complex nonlinear life systems than Hammerstein and Wiener models as shown in Fig. 1, such as, servo system [8], microwave crystal detector [9], circuit system [10] and bionic systems [11], to name a few. Thus, the study for Sandwich system identification has been a hot

Fig. 1. Sandwich system. topic over recent decades. Since the identification problem of Sandwich system was put forward at the 2009 15th IFAC Symposium on System Identification conference by J. Schoukens, J. Suykens and L. Ljung, the identification of Sand