Tracking control of piezoelectric actuators is considered in the article. A Hammerstein model is used to depict the rate-dependent hysteresis characteristics of piezoelectric actuators, in which a Bouc–Wen model is to describe the static hysteresis characteristic, and a linear time-invariant system is to describe its rate-dependent characteristics. An inverse Bouc–Wen model connected in series with the piezoelectric actuator is used to compensate the static hysteresis nonlinearity of piezoelectric actuators. Furthermore, an extended state observer–based fractional order sliding-mode control is designed to deal with higher order unmodelled dynamics and inverse compensation errors. Moreover, the bounds of the estimation error of the extended state observer are estimated, and the convergence of the proposed control strategy is proved. Experimental results show that the proposed scheme can track both single and composite input signals within a certain frequency range. Compared with extended state observer–based conventional sliding-mode controller, the proposed scheme has faster response time and smaller tracking error.

中文翻译：

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基于扩展状态观测器的压电致动器分数阶滑模控制

文章中考虑了压电致动器的跟踪控制。Hammerstein模型用于描述压电执行器的速率相关滞后特性，其中Bouc-Wen模型用于描述静态滞后特性，线性时不变系统用于描述其速率相关特性。与压电执行器串联的反向 Bouc-Wen 模型用于补偿压电执行器的静态滞后非线性。此外，基于扩展状态观测器的分数阶滑模控制旨在处理更高阶的未建模动力学和逆补偿误差。此外，估计了扩展状态观测器的估计误差范围，并证明了所提出的控制策略的收敛性。实验结果表明，所提出的方案可以在一定频率范围内跟踪单个和复合输入信号。与基于扩展状态观测器的传统滑模控制器相比，所提出的方案具有更快的响应时间和更小的跟踪误差。