In this investigation, a fuzzy-based micrometer level control design with a guaranteed trajectory tracking performance for piezoelectric actuators which naturally have hysteresis effects is proposed. Nominal dynamics of the controlled piezoelectric actuators are described by adopting Takagi and Sugeno fuzzy models initially. Via interpolating Takagi and Sugeno local fuzzy model, a robust fuzzy-based controller is developed to eliminate hysteresis, modeling uncertainties and external disturbances. Meanwhile, the tracking error is expected to be reduced as small as possible with respect to all bounded desired trajectories. This proposed fuzzy-based controller has an easy to implement control structure. The trajectory tracking design problem of piezoelectric actuators of this study is transferred to a linear matrix inequality problem, and based on the convex optimization technique, the solution of the trajectory tracking design problem of piezoelectric actuators can be solved efficiently. From the simulation results, it is obvious that this proposed fuzzy-based control design possesses robustness property and can converge tracking errors to zero in micrometer level.

在这项研究中，提出了一种基于模糊的微米级控制设计，该设计可保证自然具有滞后效应的压电致动器的轨迹跟踪性能。受控压电执行器的标称动力学最初采用 Takagi 和 Sugeno 模糊模型进行描述。通过内插 Takagi 和 Sugeno 局部模糊模型，开发了一种基于模糊的鲁棒控制器，以消除滞后、建模不确定性和外部干扰。同时，对于所有有界的期望轨迹，期望跟踪误差尽可能小。这种提出的基于模糊的控制器具有易于实现的控制结构。本研究压电执行器的轨迹跟踪设计问题转化为线性矩阵不等式问题，基于凸优化技术，可以高效求解压电执行器的轨迹跟踪设计问题。从仿真结果可以看出，这种基于模糊的控制设计具有鲁棒性，可以将跟踪误差收敛到微米级的零。