Swing-up control of double-inverted pendulum systems

This article deals with presenting a new swing-up control approach of a double-inverted pendulum on a trolley. The dynamic model of the double-inverted pendulum is derived and linearized. Two different linearization approaches are used: first, the traditional Taylor's series approach and, second, using partial linearization. A state feedback control algorithm has been implemented based on the linearized model from Taylor's series. Furthermore, a method for swinging up the pendulum to the inversion position from rest (swing-up) has been presented. The design and implementation of the swing-up function of the pendulum are implemented using the partial linearized model. The swing-up control procedure depends on using the feedforward-feedback controllers' combination to transfer the pendulums from the downward to the upward position. The time-variant controller gain is used for the sake of the swing-up control procedure. The performances of these algorithms are shown in this paper through simulations.