This paper proposes a novel robust control scheme for tip trajectory tracking of a lightweight flexible single-link arm. The developed control scheme deals with the influence of tip payload changes and disturbances during the working process of the flexible arm, thus realizing the accurate tracking for the tip reference trajectory. The robust control scheme is composed of an inner loop and an outer loop. The inner loop adopts the traditional PD control, and an active disturbance rejection control (ADRC) with a sliding mode (SM) compensation is designed in the outer loop. Moreover, the sliding mode compensation is mainly used to cope with the disturbance estimation error from the extended state observer (ESO), by which the insensitivity to tip payload variations and strong disturbance resistance is achieved. Finally, some numerical simulations are performed to support the theoretical analysis. The results show that the system is more robust to the tip mass variations of the arm and more resistant to the external torque after adding the sliding mode robustness term to the ADRC.

Usually, the order of active disturbance rejection control (ADRC) is equal to the relative order of the plant. To improve the control performance, a robust reduced-order method for ADRC is investigated in this paper. Firstly, frequency domain analysis shows that the lower-order extended state observer (ESO) has a smaller disturbance estimation error, so disturbance attenuation capability can be improved by reducing the order of ADRC. However, using only reduced-order ADRC will worsen the robustness of closed-loop systems. Therefore, a robust ADRC method based on a modified noise reduction disturbance observer (MNRDOB) is proposed. The main role of the MNRDOB is to improve the control performance of the closed-loop system by modifying the structure of the controlled object. In addition, the robust stability of the closed-loop control system based on the MNRDOB is discussed. Moreover, some simulations are used to demonstrate the robustness and noise suppression effects of the compound control method reduced-order ADRC with MNRDOB, and the parameter tuning method for the MNRDOB to improve the robustness of the system is given. Finally, some experiments on speed control of a one-dimensional gimbal are performed, and the results show that the proposed method is excellent in overshoot, tracking accuracy, and disturbance attenuation.