The damping of pendulum oscillations using a parametric controller

In the paper, the efficiency of a parametric damping system for the oscillations of a linear, initially, lightly damped pendulum has been studied. A closed-loop stabilization system included the feedback based on the deviation of the simple pendulum's position from the prearranged one. Our system was equipped with a controller whose structure followed from the Mathieu equation, and the variable coefficients were selected taking into account the proposed methodology. The parametric controller (PC) was shown to be able to shorten the settling time via increasing the damping. Because of this, it makes sense to add the PC to a system with a traditional offset-based P-controller to improve dynamic performance and to increase accuracy in the steady state. Moreover, the PC successfully suppressed harmonic external disturbances. The PC based on the offset of one link was constructed for a planar two-link pendulum. The controller damped lower frequency oscillations, but this turned out to be enough to significantly improve the stabilization response.