In this paper, three parallel piezoelectric actuators (PEAs) are utilized in a Fabry-Perot (F-P) system for tuning the gap spacing between two optical lenses. Due to the nonlinear hysteresis effect in the PEAs and uneven preload conditions in the F-P system, the motion of the three PEAs is not synchronized and their input and output responses show coupled hysteresis behaviors. To compensate for the coupled hysteresis effects, a coupled hysteresis model combining with available hysteresis operators and neural network is proposed and its inverse compensator is constructed. Since the inverse compensation method is an open-loop method, the synchronization of three PEAs cannot be guaranteed. To overcome this problem, an linear-quadratic-gaussian (LQG) controller with a synchronization strategy is deployed with the developed inverse compensation method. The experimental results demonstrate that the proposed method can effectively mitigate the coupled hysteresis effects and guarantee the synchronized motion of the three PEAs.
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Li et al. (2017) studied this question.