Data-Based Dynamic Decoupling Control for MIMO Precision Motion Stages With Position-Dependent Disturbances

Decoupling control is a widely employed technique used to mitigate coupling effects and bridge the gap between multiple-input multiple-output (MIMO) and single-input single-output (SISO) control. In the field of precision motion control, the cross-talk resulting from coarse decoupling poses a significant challenge to achieving high performance. Static decoupling control fails to completely decouple the MIMO system due to dynamic disparities between drives, actuators, and the flexible modes of the plant. Consequently, dynamic decoupling control methods have gained attention for their potential to enhance performance. However, existing dynamic decoupling control methods suffer from limitations such as reliance on system models, and susceptibility to disturbances and noise. In this paper, these deficiencies are addressed by 1) a data-based optimization with no involvement of model knowledge, and 2) using the augmented vector and instrumental variable to eliminate the estimation bias caused by position-dependent disturbances and measurement noise. The effectiveness and superiority of the proposed method are substantiated through numerical simulations and experiments conducted on an ultra-precision wafer stage.
Note to Practitioners
—This paper presents a non-iterative dynamic decoupling method, which is suitable for LTI multivariable systems with stringent precision requirements, such as the wafer stage and the atomic force microscope. In the field of precision motion control, the feedback controller plays a crucial role in the stability and robustness of the system. However, to achieve the desired performance, additional methods may be necessary, such as feedforward control method, nonlinear control method, etc. Especially for multiple-input multiple-output systems, it is essential to maintain high decoupling accuracy to avoid the cross-talk, which emerges due to a coarse decoupling. Given the practical differences in dynamic characteristics between drives and actuators, as well as non-rigid modes in the system, dynamic decoupling is recommended over static decoupling. Furthermore, it is promising to develop a data-based method that enables inevitable uncertainties between the model and the actual plant. In the dynamic decoupling method proposed in this paper, the impact of position-dependent disturbances and the measurement noise are jointly taken into consideration, which has not been previously addressed in literature. The augmented vector and instrumental variable are introduced to eliminate the adverse effects of these irrelevant data. Consequently, an unbiased estimate of the dynamic decoupling controller can be obtained. The practicality and effectiveness of the proposed method have been demonstrated. In future work, we will focus on the optimal selection of the dynamic decoupling controller under bounded disturbances and its application to redundant systems.