Abstract:Considering an unstable and under-actuated two-degree-freedom rotary inverted pendulum system, this article proposes a double closed-loop disturbance rejection PID control method based on differential flatness theory. Firstly, a nonlinear dynamic model is formulated for the rotating inverted pendulum. The unstable zero-dynamics and non-minimum phase properties have been analyzed by the approximate linearization method. Then, the differential flatness theory is used to design flat output and derive state reconstruction. The relationship between the flat state and the angle out is established. In this way, the non-minimum phase can be removed by flatness transformation. The disturbance rejection PID control is developed for the designed flatness system with a dual closed-loop and the bandwidth tuning method is also derived. The two angles of the rotary inverted pendulum are controlled precisely based on active disturbance rejection mechanism. Finally, simulation and experiment are implemented to illustrate the effectiveness of the proposed method, which provides a simple and robust control scheme for underactuated systems.