Improved Active Disturbance Rejection Control of Inverted Pendulum Based on Differential Flatness

Aiming at the control problem of an underdriven inverted pendulum with instability and uncertain external disturbances, a novel improved active disturbance rejection control (ADRC) method based on differential flatness is proposed. Firstly, the non-minimum phase characteristics of the inverted pendulum model are established and analyzed. A flat output is found to overcome the input-output imbalance inherent in underdriven system. Secondly, to address the limitations of the fal function, an improved extended state observer based on a new nonlinear functions is proposed. The theoretical analysis demonstrates the improved performance in terms of tracking speed and accuracy. Furthermore, based on the improved extended state observer, an ADRC method is designed for the flat inverted pendulum system, enabling precise control of the cart displacement and pendulum angle with external disturbances. Finally, simulation results show the effectiveness of the proposed observer and control strategies.