Effect of vertical acceleration on the frequency of a pendulum: impact on input shaping

The vibration of a pendulum is often linearized to obtain a natural frequency that can be used by vibration control techniques to reduce or eliminate pendulum sway. Vertical acceleration will alter this effective natural frequency. Therefore, this paper studies the impact that vertical acceleration has on a pendulum's linearized natural frequency and studies how input shaping can be used to counteract this effect. Simulation results show that robust input shapers perform well in reducing vibration in the midst of frequency variation, and that new input shapers can be specifically designed based on studying how vertical acceleration influences pendulum oscillations.