This article proposes an adaptive implicit inverse control scheme for a class of discrete-time hysteretic nonlinear systems. The Prandtl–Ishlinskii model is employed to characterize the hysteresis loop in piezoelectric actuator. The main contributions are as follows: 1) by using the dynamic surface control technique, which introduces the digital first-order low-pass filter, the original control system are not required to be transformed into an unknown special form; 2) the hysteresis implicit inverse compensator is constructed to overcome the hysteresis, which implies that the hysteresis item coupled with control signal is treated as the temporary control signal from which the method of searching the approximately control signal is designed; and 3) by employing the experimental platform of the piezoelectric positioning stage, the experimental verifications of the designed discrete-time adaptive controller are implemented. It is proved that all the signals in the closed-loop system are semiglobally uniformly ultimately bounded and the experimental results show the effectiveness of the proposed adaptive dynamic surface discrete-time motion control (ADSDMC) scheme.

中文翻译：

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一类离散滞后非线性系统的自适应隐式逆控制及其应用

本文针对一类离散时间滞后非线性系统提出了一种自适应隐式逆控制方案。使用Prandtl–Ishlinskii模型来表征压电执行器中的磁滞回线。主要贡献如下：1）通过采用动态表面控制技术，引入了数字一阶低通滤波器，不需要将原始控制系统转换为未知的特殊形式。2）构造磁滞隐式逆补偿器以克服磁滞，这意味着将与控制信号耦合的磁滞项视为临时控制信号，从中设计了搜索近似控制信号的方法；3）通过压电定位平台的实验平台，对所设计的离散时间自适应控制器进行了实验验证。实验证明，闭环系统中的所有信号都是半全局一致的最终有界，实验结果表明了所提出的自适应动态表面离散时间运动控制（ADSDMC）方案的有效性。