Effect of Second-Stage Operation to Rapid Swing-up Control of a Pendulum under Piecewise Sampled-data Control with Vibration Manipulation Function

Using piecewise sampled-data control with finite-time settling function called vibration manipulation function (VMF), we tried to swing up a pendulum, whose natural period is τ, by driving a trolley under numerical simulations. We used VMF under the finite-time settling control to determine an acceleration of the trolley. In this study, we used three staged operations with equivalent angular displacement for swinging the pendulum up. After fixing the operational period as τ/4 and aimed angular velocity as 0.7 for the first-stage operation, we fixed the operational period as τ/10 and aimed angular velocity as 0 for the third-stage operation. Then we tried to change the operational period and aimed angular velocity for the second-stage operation in a simulation. In case the operational period as τ/20 and the aimed angular velocity as 0 or small negative value in the second-stage operation, we could swing up the pendulum much easier.