Abstract

When designing a controller, the conflict between various specifications can become very hard so that the feasibility of the control problem becomes an important question. One of the main dilemmas in satellite control is the conflict between the need to increase the bandwidth (in order to improve the time domain performances) and the instability brought by flexible modes (which are located more and more in low frequencies). To solve this problem the bending modes should be controlled in phase, by guaranteeing a sufficient phase margin for the controlled plant. Although there are different works giving a solution of the phase margin specification, the use of other classical criterion leads to poles-zeros compensations, resulting in a high sensibility to uncertainties. In this context, this paper presents a procedure based on convex constraints to control the phase of flexible modes together with handling other robust and performance objectives. The approach proposed in this work associates LMI formulations, the Youla parameterization and a cutting plane algorithm; it enables to decide on the feasibility of the problem and gives a corresponding controller.

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