Control of the oscillation of the variable-length pendulum

The problem of parametric control of plane motions of the variable-length pendulum is considered. The pendulum is a weightless rod with a point unit which is slides along it within bounded limits. The control is the distance from the suspension point to the moving point. The proposed control law of pendulum damping consists in continuously varying the pendulum suspension length depending on the phase state. The asymptotic stability of the pendulum lower position in the respective cases of increase and decrease in length are numerically shown for the proposed control law. The theoretical results are confirmed by graphical representation of the numerical results.