Rapid Swing-up and Inverted Stability Control of a Pendulum under Sampled-data Control with Vibration Manipulation Function

Abstract

By using piecewise sampled-data control with deadbeat function, we try to swing up pendulum with trolley in simulation. We use vibration manipulation function as deadbeat control to determined acceleration of the trolley. We use two or three operations for swing up. In case of raid control, whose first operational period, Δt₁, is as fast as 5% of the natural period of the pendulum, τ, swing-up control was succeeded. Or in case Δt₁≦τ/4 or Δt₁= τ, it can be done by choosing small angular velocity. In case τ/2≦Δt₁>τ, swing-up control is associated with cyclic rotations. Or in case proper angular velocity was chosen, swing-up control can be made. Although rapid swing up requires high acceleration of the trolley, it can be done easily with different angular velocities.