Closed-LSTM neural network based reference modification for trajectory tracking of piezoelectric actuator

In this article, we propose a trajectory tracking control method for piezoelectric actuators (PEAs) based on long short-term memory neural network (LSTM-NN). Different from traditional control framework where neural network is used to approximate the open-loop PEA dynamics, LSTM-NN is used to establish the mapping between the actual trajectory and the reference trajectory of the closed-loop PEA, leading to a Closed-LSTM neural network control framework. With this framework, the trained LSTM-NN is used to modify the reference trajectory to compensate for the tracking error without changing the controller. First, we analyze and simplify the modeling of the linear and nonlinear characteristics of the PEA, and select the training input features of the LSTM-NN. Then, we use the actual trajectory and reference trajectory of the closed-loop PEA to train the LSTM-NN. The Closed-LSTM neural network control framework enables independent designs of the baseline feedback controller and feedforward compensator. In particular, the feedback controller is used to guarantee the system stability, and the LSTM-NN reference modification module is used as the feedforward compensator to achieve high-precision trajectory tracking, which does not affect the system stability and can be easily applied to off-the-shelf motion control systems. Its validity is experimentally verified on a PEA platform.