Intelligent Hysteresis Compensation and Tracking Control of Piezoelectric Fast Steering Mirror

The inherent nonlinear characteristics of piezoelectric materials, encompassing phenomena such as creep, hysteresis, and uncertainties under different operating conditions, significantly compromise the positioning accuracy of piezoelectric fast steering mirrors (PFSMs). To overcome this challenge, this paper presents a novel feedforward-feedback controller. First, an intelligent hybrid hysteresis model is proposed, which cascades the long short term memory (LSTM) network with the kinematics model. This devised LSTM-based hybrid model synergistically merges the LSTM’s proficiency in approximating static hysteresis with the kinematic model’s capability to represent the high dynamics of the PFSM accurately. Second, by employing the inverse multiplicative structure (IMS), the inverse LSTM-based hybrid model can be directly constructed, serving as a feedforward hysteresis compensator. Third, a proportional-integral-derivative (PID) controller is integrated to address both creep and uncertainties. Finally, comparative experiments are implemented to ascertain the accuracy of hysteresis modeling. The outcomes reveal that the presented LSTM-based hybrid model outperforms the rate-dependent Bouc-Wen (BW) model and the standalone LSTM neural network-based model regarding hysteresis modeling accuracy. Moreover, the tracking experiments of the PFSM are conducted to demonstrate the effectiveness of the developed feedforward-feedback controller.