Dynamic Model for Umbrella Antenna Pointing Performance and Sensitivity Considering Interrib Tension Rope Stiffness Uncertainty

The performance of umbrella antennas is severely affected by external disturbances and structural parameters. However, existing research has yet to quantify the impact of interrib tension rope stiffness uncertainty on antenna performance. This paper proposes a stiffness-parametrized state-space modeling method: first, tension rope stiffness is incorporated as a variable into the antenna dynamic equations; second, a complete uncertainty quantification chain - from stiffness variation to structural deformation and ultimately pointing performance - is established by integrating dynamic equations with pointing error models; finally, sensitivity analysis is employed to reveal the relationships between the dynamic and pointing performance of the antenna and stiffness uncertainty across tension rope layers. The proposed method is validated using models with three different tension rope stiffness configurations under two types of disturbances. Validation demonstrates good agreement between the proposed algorithm and commercial software [root mean square error (RMSE) less than 1.45×10-3 (m)] along with a significant improvement in computational efficiency. Case studies reveal a pointing stability zone at a stiffness of [75-100] (N/m), corresponding to fundamental frequencies of [2.6-2.85] (Hz); Within this zone, adjusting rope stiffness tunes system frequency while maintaining pointing stability. Sensitivity analysis shows that stiffness uncertainty in outer-layer tension ropes has a substantially greater impact on the antenna pointing performance than that in inner-layer tension ropes. This study provides direct design guidelines: Optimizing performance by maintaining stiffness within the stability zone, avoiding sensitive frequency bands through stiffness adjustment, and implementing fine-grained control via layer-specific stiffness regulation.