Modeling and stability analysis for high altitude tethered balloon
Zhu Ming1, Zuo Zongyu2*
1. School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;
2. School of Automation Science and Electrical Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
Stratosphere high altitude tethered balloon (HATB) is a typical under-damping autonomous system, so it is required for the platform itself to be stable. However, it is hardly to investigate the platform stability theoretically through the classical Lyapunov first method, because there exist zero eigenvalues in the linearized model. The rigid translation and rotation equations with respect to any arbitrary point were presented, and then the general coordinate-based, second order, nonlinear dynamic model was proposed for HATB. In view of the limitation of the Lyapunov method, Lagrange theorem was applied to prove the platform stability problem from the perspective of energy. Numerical simulations demonstrate the coincidence with the theoretical analysis.