Adaptive fuzzy output feedback control of nonlinear uncertain systems with unknown backlash-like hysteresis based on mod
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ORIGINAL ARTICLE
Adaptive fuzzy output feedback control of nonlinear uncertain systems with unknown backlash-like hysteresis based on modular design Yongming Li • Shaocheng Tong • Tieshan Li
Received: 6 November 2012 / Accepted: 29 January 2013 Ó Springer-Verlag London 2013
Abstract In this paper, an adaptive fuzzy output feedback control approach is presented for a class of single-input single-output uncertain nonlinear systems with unknown backlash-like hysteresis and unmeasured states. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a state filter observer is designed to estimate unmeasured states. Combining the backstepping recursive design with modular design techniques, a new adaptive fuzzy output control scheme is developed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are semiglobally uniformly ultimately bounded, and the tracking error converges to a small neighborhood of the origin. A simulation is included to illustrate the effectiveness of the proposed approach. The important feature of the proposed control approach is that it can solve the states immeasurable problem of nonlinear systems with unknown backlash-like hysteresis and the problem of unknown virtual control coefficients. Keywords Output feedback control Adaptive fuzzy control Backlash-like hysteresis Backstepping design Modular design Stability analysis
Y. Li (&) S. Tong Department of Basic Mathematics, Liaoning University of Technology, Jinzhou 121001, Liaoning, People’s Republic of China e-mail: [email protected] Y. Li T. Li Navigation College, Dalian Maritime University, Dalian 116026, Liaoning, People’s Republic of China
1 Introduction The control of nonlinear systems preceded by hysteresis has been a challenging and yet rewarding problem. This is because hysteresis can be seen in a wide range of physical systems and devices [1]. On the other hand, since the hysteresis nonlinearity is nondifferentiable, the system performance is severely limited and usually exhibits undesirable inaccuracies or oscillations and even instability [2]. To address such a challenge, it is important to find a model to describe the hysteresis nonlinearity and utilize this model for controller design. Various models have been proposed for hysteresis nonlinearity, among them, Ishlinskii hysteresis operator [3], Preisach model [4], Krasnosel’skii–Pokrovkii hysteron [3], Duhem hysteresis operator [5], and backlash and backlash-like hysteresis [6]. However, from modeling point of view, an effective model should be simple enough to facilitate the design, yet complex enough to give the engineer confidence that the model-based designs will work in reality. Inspired by the recent papers and studies [1–6], it can be seen that the backlash-like hysteresis model is simple enough to facilitate the controller design, at the same time is complex enough to mitigate the effects of real hysteresis. In [7], an adaptive state feedback control scheme of a
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