Abstract
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.
Highlights
long flexible arm (LFA) is subject to many disturbances such as working load, bumping, or wind
In the arm structure, the driving action point is located at the lower part of the arm, which leads to the multimode coexistence under the action of variable amplitude force
This method is difficult to be concise and effective due to the complex structure, uncertain contact condition, complex interference, and other factors in the real LFA. He et al [6, 7] modeled the flexible arm and end-effector as a homogeneous cantilever beam and a concentrated mass and used the neural network control method in conjunction with the lumped spring-mass model to realize the stability of the flexible beam on the Quanser platform
Summary
According to the principle of the mode superposition method, the lower modes are the main components of the dynamic response. e internal structure of the LFA is often so complex that it is difficult to build an accurate kinetic model according to the mechanism. In order to construct an algorithm with wide applicability, the LFA on the left side in Figure 1 is equivalent to the plane multirigid body and spring system on the right side according to the modal information. In order to obtain more valuable dynamic information, we use the method of arranging tilt sensors at the root, middle, and top of the LFA to establish the feedback control system. We need to determine the mass and length of each rod in the equivalent model and the stiffness coefficient of the torsion spring
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