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Closed-Loop Control Law for Low Thrust Orbit Transfer with Guaranteed Stability

Suraj Kumar, Aditya Rallapalli, Nivriti Priyadarshini, Bharat Kumar GVP, Ravi Kumar L

TL;DR

The paper tackles onboard closed-loop control for long-duration low-thrust orbit transfers by proposing a Lyapunov-based modification of the Q-law to guarantee stability and enable real-time implementation. It develops a theoretical framework with state-dependent Lyapunov terms to address semi-major axis overshoot and sacrificial eccentricity/inclination corrections, and validates the approach through high-fidelity simulations across coplanar, equatorial-to-polar, and GTO-to-GEO transfers. Results show the modified Q-law achieves performance comparable to the classical approach while providing formal stability guarantees, including effective coasting strategies. The work paves the way for fully autonomous, onboard low-thrust maneuvers and outlines future extensions to RAAN, argument of perigee, and adaptive gain tuning."

Abstract

Electric propulsion is used to maximize payload capacity in communication satellites. These orbit raising maneuvers span several months and hundreds of revolutions, making trajectory design a complex challenge. The literature typically addresses this problem using feedback laws, with Q-law being one of the most prominent approaches. However, Q-law suffers from closed-loop stability issues, limiting its suitability for real-time on-board implementation. In this work, we focus on closed-loop orbit raising rather than offline trajectory planning and address the stability limitations of the Q-law through a Lyapunov based control design. A Lyapunov-guided modification of the classical Q-law is proposed to ensure closed-loop stability and enable real-time implementation. The effectiveness of the proposed method is demonstrated through closed-loop orbit transfers across various scenarios, including co-planar transfers, equatorial to polar orbit transfers, and geostationary transfer orbit (GTO) to geostationary earth orbit (GEO) transfers.

Closed-Loop Control Law for Low Thrust Orbit Transfer with Guaranteed Stability

TL;DR

The paper tackles onboard closed-loop control for long-duration low-thrust orbit transfers by proposing a Lyapunov-based modification of the Q-law to guarantee stability and enable real-time implementation. It develops a theoretical framework with state-dependent Lyapunov terms to address semi-major axis overshoot and sacrificial eccentricity/inclination corrections, and validates the approach through high-fidelity simulations across coplanar, equatorial-to-polar, and GTO-to-GEO transfers. Results show the modified Q-law achieves performance comparable to the classical approach while providing formal stability guarantees, including effective coasting strategies. The work paves the way for fully autonomous, onboard low-thrust maneuvers and outlines future extensions to RAAN, argument of perigee, and adaptive gain tuning."

Abstract

Electric propulsion is used to maximize payload capacity in communication satellites. These orbit raising maneuvers span several months and hundreds of revolutions, making trajectory design a complex challenge. The literature typically addresses this problem using feedback laws, with Q-law being one of the most prominent approaches. However, Q-law suffers from closed-loop stability issues, limiting its suitability for real-time on-board implementation. In this work, we focus on closed-loop orbit raising rather than offline trajectory planning and address the stability limitations of the Q-law through a Lyapunov based control design. A Lyapunov-guided modification of the classical Q-law is proposed to ensure closed-loop stability and enable real-time implementation. The effectiveness of the proposed method is demonstrated through closed-loop orbit transfers across various scenarios, including co-planar transfers, equatorial to polar orbit transfers, and geostationary transfer orbit (GTO) to geostationary earth orbit (GEO) transfers.

Paper Structure

This paper contains 15 sections, 34 equations, 14 figures, 3 tables.

Table of Contents

  1. INTRODUCTION
  2. BACKGROUND
  3. Dynamics
  4. Q-law Controller
  5. Limitations of Classical Q-law
  6. Modified Q-law Controller
  7. Semi-major Axis Transfer:
  8. Eccentricity Transfer:
  9. Inclination Transfer:
  10. Relative Effectivity and Coasting Arcs
  11. Results
  12. Coplanar LEO to GEO Transfer
  13. Equatorial Orbit to Polar Orbit Transfer
  14. GTO to GEO Transfer
  15. Conclusion and future work

Figures (14)

  • Figure 1: Semi-major axis
  • Figure 2: Eccentricity
  • Figure 3: $\dot{V}$
  • Figure 4: Pareto Front
  • Figure 6: Semi-major axis
  • ...and 9 more figures