Efficient feedbacks for low thrust orbital transfers
- Paper number
IAC-06-C1.P.7.01
- Author
Mr. Bombrun Alex, INRIA, France
- Year
2006
- Abstract
The development of low thrust engines introduced new questions in satellite guidance, that raise new problems in control theory. For instance, the time optimal transfer between two elliptic Keplerian orbits is of primary interest for spatial industry because low thrust transfers are indeed time consuming.
Optimal control is the theoritical answer. But it raises many practical difficulties. In particular, the duration and the number of revolutions around the central body become very large as the magnitude of the thrust diminishes, inducing a higher and higher numerical sensitivity. A lot of research has been done on the development of optimization algorithms to overcome the inherent difficulties of the time optimal orbital transfer problem.
Many practitioners duly object that, apart from being difficult to compute, optimal control provides an open-loop control that is difficult to adress in practice because of its sensitivity to pertubations. Instead of trying to follow a numerical optimal control, one may design controls that perform the desired task (here reach the target orbit) robustly and chose among them one that performs reasonably well with respect to the criterion.
Liapunov control (or "Jurdjevic-Quinn control", or "dampling control") has been proposed by some authors, leading to very simple and naturally robust transfers; these authors however did not insist on achieving better performances.
Taking advantage of the wide choice of possible Liapunov functions provided by the first integrals of the two body problem, we select an efficient Liapunov interpolation of an optimal control. Applying this method to a wide range of referenced trajectories computed with the optimization program Mipelec (developed by CNES, France) provides extremely conclusive results.
The talk will detail the method for constructing these "interpolating Lyapunov feedback" and present some numerical studies. For instance, for a satellite with an intial mass of 1000kg, a specific impulse 1500s and a maximal thrust u=0.1N, the relative error between the optimal time of GTO-GEO transfer and its best Liapunov interpolation is less than 1% time loss. An illustration of the robustness properties: multiplying u by a positive number λ, for example 0.1, changes the time of the feedback transfer by a rate of 1/λ. Optimization algorithms do not provide this flexibility.
- Abstract document