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In this research, a new method based on the equivalence of modal characteristics, differential flatness (DF), and active disturbance rejection control (ADRC) is proposed for the stabilization control of the long flexible arm (LFA). There are two major problems in the system of the LFA. The first problem is that the LFA is very prone to the multiple-mode coupling, while the control systems need as few sensors as possible. Another problem is that the structure of the LFA in practice is often complex and subject to various disturbances. Therefore, in this paper, the equivalent multirigid body dynamic model of a LFA is derived from the modal information of the equivalent rigid body model of the prototype. Then, the output values of the three tilt sensors are synthesized into an output based on the DF method. Finally, the effectiveness of the proposed method is verified through physical experiments. Compared with PID, the proposed method has shorter settling time. The LFA can be restored within 7 seconds under the ADRC, while it needs 90 seconds or more to calm down without the control.

Research on Vibration Suppression of the Long Flexible Arm Based on Three Tilt Sensors