Adaptive control of Hammerstein–Wiener nonlinear systems

Abstract

The Hammerstein-Wiener model is a block-oriented model, having a linear dynamic block sandwiched by two static nonlinear blocks. This note develops an adaptive controller for a special form of Hammerstein-Wiener nonlinear systems which are parameterized by the key-term separation principle. The adaptive control law and recursive parameter estimation are updated by the use of internal variable estimations. By modeling the errors due to the estimation of internal variables, we establish convergence and stability properties. Theoretical results show that parameter estimation convergence and closed-loop system stability can be guaranteed under sufficient condition. From a qualitative analysis of the sufficient condition, we introduce an adaptive weighted factor to improve the performance of the adaptive controller. Numerical examples are given to confirm the results in this paper.

Intelligent control for Hammerstein nonlinear systems with arbitrary deadzone input

“…This work is an extension of the results of Womack (1984a, 1984b) and Zhang and Mao (2014), since it deals with asymmetric deadzone input. Based on a deadzone compensating control law, the manner in which the closed-loop stability of the switching system is proven forms another contribution.…”

“…In order to derive the deadzone compensating control law, we introduce a new function as follows (Zhang and Mao, 2014):…”

“…Such systems have been found to be a simple and effective representation for capturing the properties of nonlinear processes encountered in engineering practice (Giri and Bai, 2010). Some existing controller design methods can only be employed when the input nonlinearity is represented either through algebraic polynomial expressions (Ding et al, 2007; Fruzzetti et al, 1997; Zhang et al, 2014; Zhao and Chen, 2009) or as neural network models (Hong et al, 2014; Wang and Hsu, 2010; Wu and Jhao, 2012).…”

“…To overcome the need for precise model parameters, an adaptive controller can operate successfully in environments with large uncertainties. However, as was reported by Zhang and Mao (2014), in the literature of discrete adaptive control of H nonlinear systems with nonsmooth input, very few approaches are available: Womack (1984a, 1984b) studied symmetric preload nonlinearity and two-segment piecewise-linear nonlinearity; recently, Zhang and Mao (2014) considered symmetric deadzone nonlinearity. As far as we know, no discrete adaptive control approach has yet been reported for H models with arbitrary deadzone input.…”

Identification of nonlinear block-oriented systems with backlash and saturation

“…In control systems, the use of this model is motivated by considering the input nonlinear block as the actuator nonlinearity and the output nonlinear block as the process nonlinearity or sensor nonlinearity. More identification approaches are using this model; see eg [27][28][29][30][31][32][33]. Note that the nonlinear blocks of Hammerstein model, Wiener model and their combinations are assumed to be static, ie without memory.…”