L.T. Aguilar, R. Rascón, and C. Trejo (USA)
Nonlinear H∞ control, output feedback, orbital stabiliza tion, underactuated systems.
Nonlinear H∞ synthesis is developed to solve the track ing control problem restricted to a two degrees-of-freedom (DOF) underactuated mechanical manipulator where posi tion measurements are the only available information for feedback. A local H∞-controller is derived by means of a certain perturbation of the differential Riccati equations, appearing in solving the H∞-control problem for the lin earized system. Stabilizability and detectability properties of the control system are thus ensured by the existence of the proper solutions of the unperturbed differential Riccati equations, and hence the proposed synthesis procedure ob viates and extra verification work of these properties. Due to the nature of the approach, the resulting controller ad ditionally yields the desired robustness properties against unknown but bounded external disturbances. The desired trajectory is centered at the upright position where the ma nipulator becomes a non-minimum-phase system. Simula tion results made for a double pendulum show the effec tiveness of the proposed controller.
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