Control of Plane Motions of a Helicopter with Cargo on the Basis of the Double Pendulum Model

摘要

— The problem of constructing asymptotically stable program motions of the double pendulum with variable length and movable pivot is solved. This program motions are given arbitrarily. The solution is obtained by synthesis of the active program control applied to the system of bodies. Also, it’s obtained by the synthesis of the stabilizing control based on the feedback principle. The control is constructed in the form of an exact analytic solution in the class of continuous functions. The problem is solved based on the direct Lyapunov method of stability theory. The Lyapunov’s function with sign-constant derivative is used.