Robust limit cycle control in an attitude control system with switching-constrained actuators

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In this paper the robust behavior in some piecewise affine systems with minimally spaced transition times is studied. Such systems are found e.g. in satellites and satellite launchers. On-off thrusters are frequently used as actuators for attitude control and are typically subject to switching constraints. In these systems, persistent motions of different nature may occur, such as limit cycles, quasi-periodic-like and chaotic motions. Thus, in the presence of model uncertainties, the emergence of bifurcations can seriously affect performance. In this contribution, we use Tsypkin¿s method in order to investigate the robustness of the condition for the existence of limit cycles. Robustness frontiers in the space of control parameters are identified. These frontiers are verified via simulation and compared to those given by the describing function method, revealing the difficulties of this latter method to address the robustness analysis in this system. Moreover, we present a design method for robust controllers based on the Hamel locus. An evaluation of performance requirements such as fuel consumption, limit cycle amplitude and transient response is carried out in the identified regions of robust behavior.