Parameter optimization of nonlinear friction models and trajectory control of linear motor stage

Abstract

Achieving high positioning accuracy with low-resolution encoders is vital for reducing sensor costs in industrial systems. However, nonlinear friction between linear motors and sliding rails, especially at low velocities, causes hysteresis and creep, severely affecting motion accuracy. To address this, we propose a high-precision control method that does not rely on high-resolution encoders. By separating static and dynamic friction modeling, and using particle swarm optimization (PSO) to tune parameters, the proposed models achieve RMSEs of 0.43 μm and 1.14 mm, respectively. Our novel friction feedforward compensation strategy automatically switches between these models based on experimentally determined thresholds, helping the feedback controller reduce nonlinear disturbances. Furthermore, we develop a friction feedforward PD-type iterative learning control (FFPDILC), integrating PID and PDILC with friction compensation. This enhances the learning effect and improves convergence speed. Experiments show a significant RMSE reduction from 18 μm to 0.83 μm (95.4 % improvement), and tracking errors are reduced by 51.1 % compared to PDILC under standard conditions and 48.9 % under additional load conditions. These results validate the method's effectiveness in improving precision under limited sensor resolution.