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Asymptotic stabilization of the desired uniform motion in underactuated Hamiltonian systems by linear feedback

In some cases the desired uniform motion may be described
by a pair of first integrals of the system with zero control input.
These two integrals and the integration of nonlinear function
of saturation are used to construct Lyapunov function
The control is designed from the condition of decreasing Lyapunov
function on the trajectories of the closed loop system. This
control may be chosen a priori bounded and linear in a small viciniti
of the desired motion. This method is applied to
stabilize rotating body beam, for damping the oscillations of
blades of an elastic propeller and for stabilization
of the uniform transition of the pendulum on a cart.
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