A tracking differentiator optimized by deep reinforcement learning with application to slitter machine

The precise management of transient processes is a fundamental challenge in velocity control for slitter machine. In velocity planning process, the conventional linear velocity profile may induce tension fluctuation due to acceleration mutation, which can adversely affect the film transportation. To enable effective transient process arrangement, the dynamic velocity and acceleration characteristics of the First-order Saturation (SAT) Tracking Differentiator (FSTD) and Fast Tracking Differentiator (FTD) are analyzed. Subsequently, we propose Fast-First-SAT Tracking Differentiator (FFSTD), which integrates the functionalities of both FSTD and FTD to enhance velocity tracking for the film slitter. The parameters of FFSTD are optimized by Minimax Q-learning-based multi-agent reinforcement learning algorithm in conjunction with Nash Equilibrium strategy. The efficacy of the FFSTD and the reinforcement learning algorithm optimization is evaluated through two sets of numerical simulations conducted via a multi-axis web winding dynamic simulation model. Additionally, experiment is carried out to validate that the proposed FFSTD is applicable for tracking various velocities. The results demonstrate that following the optimization through reinforcement learning, the proposed FFSTD achieves a steady-state error of 1.2403% and shorter length in comparison to the non-optimized FFSTD under various parameter configurations. In terms of two key performance metrics—initial lead length and steady-state error—FFSTD attains superior holistic performance.