High-Precision Dynamic Tracking Control Method Based on Parallel GRU–Transformer Prediction and Nonlinear PD Feedforward Compensation Fusion

Yimin Wang, Junjie Wang, Kaina Gao, Jianping Xing () and Bin Liu ()
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Yimin Wang: School of Integrated Circuits, Shandong University, Jinan 250101, China
Junjie Wang: 45th Research Institute of China Electronics Technology Group Corporation, Beijing 100176, China
Kaina Gao: 45th Research Institute of China Electronics Technology Group Corporation, Beijing 100176, China
Jianping Xing: School of Integrated Circuits, Shandong University, Jinan 250101, China
Bin Liu: 45th Research Institute of China Electronics Technology Group Corporation, Beijing 100176, China

Mathematics, 2025, vol. 13, issue 17, 1-23

Abstract: In high-precision fields such as advanced manufacturing, semiconductor processing, aerospace assembly, and precision machining, motion control systems often face challenges such as large tracking errors and low control efficiency due to complex dynamic environments. To address this, this paper innovatively proposes a data-driven feedforward compensation control strategy based on a Parallel Gated Recurrent Unit (GRU)–Transformer. This method does not require an accurate model of the controlled object but instead uses motion error data and controller output data collected from actual operating conditions to complete network training and real-time prediction, thereby reducing data requirements. The proposed feedforward control strategy consists of three main parts: first, a Parallel GRU–Transformer prediction model is constructed using real-world data collected from high-precision sensors, enabling precise prediction of system motion errors after a single training session; second, a nonlinear PD controller is introduced, using the prediction errors output by the Parallel GRU–Transformer network as input to generate the primary correction force, thereby significantly reducing reliance on the main controller; and finally, the output of the nonlinear PD controller is combined with the output of the main controller to jointly drive the precision motion platform. Verification on a permanent magnet synchronous linear motor motion platform demonstrates that the control strategy integrating Parallel GRU–Transformer feedforward compensation significantly reduces the tracking error and fluctuations under different trajectories while minimizing moving average (MA) and moving standard deviation (MSD), enhancing the system’s robustness against environmental disturbances and effectively alleviating the load on the main controller. The proposed method provides innovative insights and reliable guarantees for the widespread application of precision motion control in industrial and research fields.

Keywords: Parallel GRU–Transformer; nonlinear PD controller; feedforward compensation; precision motion platform (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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