2025/08/10 by Kimura, Masato, Kuma, Hirotaka, Liu, Yikan +3
#34H05 #34K35 #34K99 #93C43 #Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.2508.07268
This paper addresses a press control problem in straightening machines with small time delays due to system communication. To handle this, we propose a generalized β-control method, which replaces conventional linear velocity control with a polynomial of degree β≥ 1. The resulting model is a delay differential equation (DDE), for which we derive basic properties through nondimensionalization and analysis. Numerical experiments suggest the existence of a threshold initial velocity separating overshoot and non-overshoot dynamics, which we formulate as a conjecture. Based on this, we design a control algorithm under velocity constraints and confirm its effectiveness. We also highlight a connection between threshold behavior and finite-time blow-up in DDEs. This study provides a practical control strategy and contributes new insights into threshold dynamics and blow-up phenomena in delay systems.