Adaptive Backstepping Control for Satellite Formation Flying with Thruster Magnitude Error
- Paper number
IAC-06-C1.7.02
- Author
Mr. Hyung-Chul Lim, Korea Astronomy and Space Science Institute, Korea
- Coauthor
Mr. Hyochoong Bang, Korea Advanced Institute of Science and Technology, Korea
- Coauthor
Dr. Byoungsoo Kim, Korea Institute of S&T Evaluation and Planning, Korea
- Year
2006
- Abstract
Recently, satellite formation flying has been a topic of significant research interest in aerospace society because it provides potential benefits compared to a single large spacecraft. Most satellite formation flying control laws have been designed by using the simplified relative dynamic equations such as Hill’s equations. Control designs based on Hill’s equations require high fuel consumption and can degrade the performance of the formation flying missions for the case of a long duration and large separation between satellites since the Hill’s equations disregard the perturbation and nonlinear terms on the relative motion dynamics. Thus, many nonlinear control theories have been studied for satellite formation flying, which include full-nonlinear dynamics, disturbances and mass uncertainties of the leader and follower satellites. In particular, some adaptive control laws have been developed to track the given reference trajectories in the presence of unknown satellite mass properties. It has been found, in calibration simulations for an ion propulsion system, that the thrust magnitude of satellite can be tuned to an accuracy of 1.2% with a maximum error of 0.5mN and thrust orientation to within 0.5 to 5 degrees. In this paper, an adaptive backstepping control scheme is used based on the Lyapunov stability theory to solve the relative position tracking problem of the satellite formation flying under the presence of thruster magnitude error. We assume that the thruster magnitude error is proportional to the thruster magnitude. Thus, the proportion of the thruster magnitude error is considered constant, and can be regarded as an unknown parameter in this study. In addition, it is assumed that the reference satellite moves in the circular orbit, and the external disturbances are unknown and bounded. We introduce new variables such as a tracking error, a stabilizing function, and an unknown parameter error for the design of an adaptive backstepping controller. A switching σ-modification is also introduced to reduce the vibrations induced by external disturbances and to prevent the parameter drift, which is included in the parameter update law. The control law and parameter update law are chosen such that the derivative of a Lyapunov function becomes negative. The Lyapunov function is shown to be globally uniformly ultimately bounded, which implies that the tracking error, the derivative of tracking error, and the unknown parameter error are bounded. As a consequence, the bounded control input is derived, and it is shown that the transient and asymptotic tracking performances depends on the design parameters.
Simulation results are provided to demonstrate the controller performance under the unknown periodic disturbance. Those results illustrate that the satellite tracks the given reference trajectory, and the control inputs are kept within a range of small values.
- Abstract document
- Manuscript document
IAC-06-C1.7.02.pdf (🔒 authorized access only).
To get the manuscript, please contact IAF Secretariat.