Feedforward Control of Inverted Pendulum by Using Vibration Manipulation Function

(Discrete Sampled-data Stable Control by Sequential Piecewise Feedforward Functions)

Abstract

We applied a rotational vibration manipulation function (rVMF), which is a piecewise feedforward function of a 1DOF oscillator, for stability control of an inverted-pendulum-type vehicle. In intermittent feedforward control or discrete sampled-data control by rVMF, stable area of initial angle and angular velocity becomes narrower in case operational period (Δt) becomes larger. The stability control succeeds in case Δt is less than 1/10 of the natural period of the pendulum. By limiting the initial condition to the rest-inverted point, we design trajectories of the vehicle for stable rest-to-rest constant motion by using 2-staged sequential acceleration or deceleration method. Although an inverted pendulum has a negative spring constant, rVMF can manage its stability control, as far as Δt and initial condition are suitable.