The swing-up and stabilization of the triple inverted pendulum
三级倒立摆的自动摆起与稳定控制

The swing-up of the triple inverted pendulum is achieved by inversion-based trajectory control. The variablegain linear quadratic regulator is designed to stabilize the triple inverted pendulum in the upward position. The transient process of swing-up of the triple inverted pendulum is treated as a nonlinear two-point boundary value problem. The normal trajectories of swing-up are obtained by solving a two-point boundary value problem, and a feedforward control is designed by using the inverse system method. A gain-scheduled feedback is used to stabilize the system during the swing-up. In addition, the triple inverted pendulum in the upward position is stabilized by utilizing the variable-gain linear quadratic regulator. Simulation results demonstrate the effectiveness of the proposed control scheme.