Study on dual-layer MPC-SMC control strategy for piezoelectric platforms based on extended kalman filter

In visual servoing micromanipulation, the hysteresis nonlinearity of piezoelectric stages and image transmission delay significantly degrade positioning accuracy. To address these issues, this paper proposes a dual-layer control strategy based on an improved Extended Kalman Filter (B-W-EKF). First, image block matching combined with a Gaussian kernel interpolation algorithm is employed to obtain high-precision displacement measurements from microscopic image sequences, from which the voltage-displacement hysteresis loop is constructed. Then, the EKF is integrated with the Bouc-Wen (B-W) model, incorporating hysteresis nonlinearity into the state observation equations. Based on this model, a dual-layer control architecture that combines upper-layer Model Predictive Control (MPC) with lower-layer Sliding Mode Control (SMC) is designed: the upper-layer MPC performs global optimization, while the lower-layer SMC regulates position and velocity, thereby improving tracking accuracy. Experimental results show that the RMSE values for SMC, MPC, SMPC, iMPC, and the proposed dual-layer MPC-SMC are 0.1292 µm, 0.1366 µm, 0.0635 µm, 0.0827 µm, and 0.0372 µm, respectively, under triangular wave reference input, demonstrating the effectiveness of the control strategy in enhancing tracking precision.