Opt Express. 2023 May 22;31(11):17250-17267. doi: 10.1364/OE.488188.
Piezoelectric deformable mirrors (DM) are benefited from the high accuracy and swift dynamics. The hysteresis phenomenon, which inherently exists in piezoelectric materials, degrades the capability and precision of the adaptive optics (AO) systems. Also, the dynamics of piezoelectric DMs make the controller design more complicated. This research aims to design a fixed-time observer-based tracking controller (FTOTC), which estimates the dynamics, compensates the hysteresis, and ensures tracking to the actuator displacement reference, in the fixed time. Unlike the existing inverse hysteresis operator-based methods, the proposed observer-based controller overcomes the computational burdens and estimates the hysteresis in real-time. The proposed controller tracks the reference displacements, while the tracking error converges in the fixed time. The stability proof is presented by two consecutive theorems. Numerical simulations demonstrate superior tracking and hysteresis compensation by the presented method, from a comparison viewpoint.
压电变形镜（DM）受益于高精度和快速动力学。迟滞现象存在于压电材料中，降低了自适应光学（AO）系统的性能和精度。此外，压电 DM 的动力学使得控制器设计更加复杂。本研究旨在设计一种基于固定时间观测器的跟踪控制器（FTOTC），该控制器能够在固定时间内估计动态、补偿迟滞并确保跟踪执行器位移参考。与现有的基于逆迟滞算子的方法不同，所提出的基于观测器的控制器克服了计算负担并实时估计迟滞。所提出的控制器跟踪参考位移，同时跟踪误差在固定时间内收敛。通过两个连续的定理给出了稳定性证明。数值模拟结果表明，所提出的方法在跟踪和迟滞补偿方面具有优越性。
