Energy-based swing up control of rotary parallel inverted pendulum

Rotary parallel inverted pendulum (RPIP), which belongs to underactuated community, consists of a pivot arm driven by the DC motor and two rotary pendulums located on it. Considering the underactuated systems are typically passive, we propose the energy-based controller for the RPIP which simultaneously achieves the swing up of the rotary pendulums and the minimum of the mechanical energy when the rotary pendulums are in their respective vertical positions. The stability analysis of the resulting closed-loop system is given rigorously by making use of Lyapunov energy function and LaSalle's invariance theorem. In addition, the designed controller takes a simpler structure and therefore is convenient for implementing and calibrating control parameters. Simulation results are provided to demonstrate the satisfactory control performance of the proposed control method.