Swing-up and Down Control of Translational Pendulums Using Finite-time Settling Functions with Elliptic Integrals in the Period

(Angle and Operation Time Dependence of the Optimum Trolley Manipulation)

Abstract

In this research, we attempted to control the swing-up and swing-down of the pendulum through experiments and simulations. The vibration manipulation function (VFM), which is a finite-time-settling function, was used as the acceleration of the trolley. Considering the nonlinearity of the pendulum, the operation time of VFM was changed according to the natural period of the pendulum. In addition, the amplitude of VMF was modified by multiplying with a parameter α, which is a function of the lifting angle. This time, the operation time was limited to the natural period (τ) or half of it. Precise swing up and down control of the pendulum was succeeded at an angle of nearly 170 degrees, including the transitional states. Since these features are similar to the phenomenon in parametric resonance, their relationship is interesting.