Keywords: pantograph-catenary system, contact force, Luenberger observer design, fast analytical simulation, estimation, particle swarm optimization.

In the realm of railway transportation, maintaining stable operation of pantograph systems for high-speed trains is crucial for ensuring passenger safety and system reliability. This study addresses the challenge of estimating contact force in pantograph systems, a key factor in maintaining stable operation. We proposed a simple but efficient method utilizing the Luenberger observer within a closed-loop system to estimate contact force based on measured accelerations. By conducting careful numerical analysis and computer simulations, we offered insights into the dynamic behavior of pantograph systems under varying operational conditions. Our results demonstrated the efficacy of the proposed algorithm in accurately estimating contact force, even under different train speeds and system uncertainties. Specifically, our analysis revealed that the algorithm could significantly estimate contact force across a range of train speeds, with only minor degradation observed at higher speeds. Furthermore, our investigation into system uncertainties highlighted the robustness of the algorithm, showing no significant degradation in performance up to 20% uncertainty in system parameters. By bridging theoretical modeling with practical application, this research contributed to advancing railway technology, ultimately enhancing operational efficiency and system reliability in high-speed railway networks.

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