Iterative Learning-based Model Predictive Control for Precise Trajectory Tracking of Piezo Nanopositioning Stage

Model predictive control (MPC) has recently been proposed to achieve real-time trajectory tracking of piezo nanopositioning stages. Due to the requirement of high-accuracy system modeling in MPC, precise tracking of high-bandwidth/large displacement-range trajectories for nanopositioning stages is still challenging. Although this issue might be solved by using iterative learning control (ILC) approaches, new issues, such as large initial tracking error and low convergence rate will be induced. To address these issues in MPC and ILC, an iterative learning-based MPC (IL-MPC) algorithm is proposed in this paper to achieve accurate and high-efficacy trajectory tracking of nanopositioning devices through the integration of ILC and MPC. Specifically, the ILC is applied to a system consists of the MPC controller and the piezo nanopositioning stages where the output of ILC is regarded as the reference signal of the MPC controller. The convergence analysis of the proposed IL-MPC with the existence of measurement noise and model uncertainty is presented. Based on the convergence analysis, the upper bound of the tracking error in frequency domain was estimated. To demonstrate the efficacy of the proposed method, experiments were conducted on a nano-piezo stage to track periodic and broadband trajectories and the tracking performances of IL-MPC and ILC were compared in detail.