The objective of this work is to study the domain of attraction (DOA) around an autonomous oscillation, generated in an underactuated system. First, some previous results are recalled on the generation of stable oscillations using backstepping. Then, the impact of saturation of the control law is analyzed, giving conditions for realizability of the autonomous oscillation. It is shown how to use a weighted Lyapunov function, based on backstepping, and how to determine from it an estimation of the DOA. The given solution is simple and transparent, so that the designer easily sees how to tune the main related parameters. The proposed technique is illustrated on two underactuated systems: a saturated triple integrator, and a third-order ball and beam.
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