Data-driven calibration of decoupling matrix for MIMO precision motion stages

Decoupling control is a commonly employed technique for achieving high precision in multiple-input multiple-output (MIMO) motion control systems. A static decoupling matrix, which can be determined using geometric construction, is widely used due to its practicality and simplicity. However, inaccurate geometric parameters will lead to a coarse decoupling matrix, and result in interactions among the system axes and performance deterioration. To tackle this challenge, various attempts have been undertaken to calibrate the decoupling matrix. Data-driven on-line approaches have gained considerable attention for their ability to calibrate the decoupling matrix without interrupting the normal operation of the system. This paper presents a data-driven approach to calibrate the decoupling matrix for MIMO and linear time invariant (LTI) systems. Through some reasonable assumptions, a calibrated static decoupling matrix can be derived to improve the performance of the system. Moreover, considering the inevitable presence of measurement noise, the consistency of the proposed method has been analyzed. As a result, the instrument variable is introduced in the improved method to eliminate the impact of the measurement noise. Finally, the effectiveness and practicality of the proposed method are demonstrated through both numerical simulations and experiments carried out on an ultraprecision wafer stage.