A Data-Driven Iterative Decoupling Feedforward Control Strategy With Application to an Ultraprecision Motion Stage

Abstract

This paper develops a data-driven decoupling feedforward control scheme with iterative tuning to meet the challenge of the crosstalk problem in multiple-input multiple-output (MIMO) motion control systems. In contrast to model-based approaches, iterative tuning fully utilizes the available data to address the practical difficulty in obtaining an accurate dynamic model. The MIMO feedforward signal is iteratively updated by minimizing the developed crosstalk criterion. Specifically, to make the optimal problem convex, the MIMO feedforward controller is structuralized with a finite impulse response (FIR) filter and is parameterized by corresponding coefficients. A data-driven unbiased gradient approximation based on the Toeplitz matrix is then developed for updating the parameter vector. Furthermore, to deal with the Hessian inverse problem encountered in the numerical calculation of the update law, a stable inversion method combined with singular value decomposition is employed. The basic characteristics of the proposed scheme, including convergence accuracy and convergence rate, are illustrated through simulation. Finally, the proposed data-driven decoupling control scheme is applied to a developed ultraprecision motion stage, and the results show that the approach can significantly attenuate the servo error caused by the crosstalk problem. This simplicity and accuracy oriented control method without need of dynamic modeling is definitely suitable for industrial applications.