Multiobjective LMI based attitude control design for a telecommunication satellite
Résumé
The applicability of modern control techniques based on the Linear Matrix Inequality (hereafter denoted LMI) framework is investigated in this paper. Once the problem has been formulated in terms of LMI, it can be solved efficiently using interior point, polynomial-time algorithms. The main interest of these methods lies in the fact they allow to turn the multi-objective control problem into a convex optimisation one, in which the criterion is composed of various different specifications. The objectives addressed in this paper include stability, time constraints expressed in terms of peak output amplitude and command input peak bound, as well as frequency constraints such as H-2 and/or H-infinity performance and gain and phase margins. The main application of the control methods considered in this study is the attitude control of a telecommunication satellite from the Spacebus family, during a station keeping manoeuvre (SKM). In this work, various LMI optimisation criteria are compared in terms of performance and robustness of the derived control laws: it is especially shown that H-2 and/or H-infinity frequency constraints are necessary to obtain satisfactory results.