Analysis of a Nonlinear Continuous Control Algorithm, in the Case of Discontinuous Actuation
- Paper number
IAC-07-E2.1.05
- Author
Mr. Esten Ingar Grotli, Norwegian University of Science and Technology, Norway
- Year
2007
- Abstract
In many of the schemes for spacecraft control, the stability and convergence analysis is performed assuming continuous actuation, especially for nonlinear control schemes. What happens when the actuation signal is pulse width or pulse frequency modulated are quite often not considered. In this paper we look at a specific algorithm for relative position control of a spacecraft formation, and we give a proof of sufficient conditions for when the system is uniformly asymptotically stable to a neighborhood - mathematically speaking - around the desired trajectory, when the actuation is binary. We consider a neighborhood because with binary actuation, which is the case for most spacecraft, it is not possible to fully diminish all disturbances, and there is neither a desire to, since this would be very fuel inefficient. For the sake of fuel efficiency, the desired trajectories are chosen to be as far as possible to be consistent with naturally existing trajectories, and the fuel expenditure of the suggested algorithms are easily calculated. The control scheme we use in this paper makes the formation globally uniformly exponentially stable to a ball which can be arbitrarily diminished around the desired trajectory, even under non vanishing disturbances. This means that disturbances, due to gravitational variations, non-spherical shapes of planets, atmospheric drag and solar radiation can be handled, by choosing the control gains sufficiently large. This brings up another important contribution of this paper, since we given the maximum impulse of the spacecraft actuator, can give an upper bound on the disturbances and still achieve asymptotic convergence to the above mentioned neighborhood. We claim that our approach is of great practical importance, since it gives a recipe for how to analyze the performance of continuous nonlinear algorithms for real applications.- Abstract document
- Manuscript document
IAC-07-E2.1.05.pdf (🔒 authorized access only).
To get the manuscript, please contact IAF Secretariat.