Vibration Control of Flexible Arm Based on Adaptive Robust Sliding Mode Control and LQR Control
Authors: Chencheng Qian , Li Zhang , Wenjie Wang , Letian Zhang 
Published: May 2024

Abstract:
This paper studied the problems of trajectory tracking and vibration suppression of the
end for single-linked flexible arm. The dynamic model of the flexible manipulator is established by
the Lagrange method and assumed mode method, and then, we decomposed the model into a double
time scale model, which is fast and slow based on singular perturbation theory. We design the
controller for the two models separately. As to the slow time scale model, we created a controller
with adaptive robust sliding mode, and for the fast one, we designed a controller based on Linear-
Quadratic Form (which is LQR). By improving particle swarm optimization, the weight matrix Q in
the LQR was optimized independently. Combining the control rate of the fast and the slow, tracked
the flexible arm’s trajectory and suppressed its terminal vibration at the same time. The simulating
results show that the proposed method greatly improves the trajectory tracking accuracy of flexible
manipulator, and reduces the end vibration effectively.

Background:
Since flexible robotic arms generate free vibration during operation due to the special
characteristics of the material, vibration suppression and control are the primary problems in this
field.

objective:
The research objective of this paper is to design an improved controller for a single link flexible robotic arm system that utilises a new control method to achieve more accurate tracking accuracy and less end vibration during the movement of the robotic arm.

Objective:
The research objective of this paper is to design an improved controller for a single-link
flexible robotic arm system that utilizes a new control method to achieve more accurate tracking
accuracy and less end vibration during the movement of the robotic arm.

Methods:
An adaptive robust sliding mode controller is designed for the slow time scale model, a
linear quadratic (LQR) controller is designed for the fast time scale model, and the weight matrix Q
in the LQR is autonomously optimised by an improved particle swarm algorithm, which combines
the control rates of the two to control the trajectory tracking of the flexible robotic arm while suppressing
the end vibration.

Results:
Experimental and comparative studies show that the method proposed in this paper substantially
improves the trajectory tracking accuracy of the flexible robotic arm and reduces the end
vibration to a large extent with obvious advantages, which verifies the reasonableness of the improved
controller.

Conclusion:
The method proposed in this paper has more prominent advantages in trajectory tracking
of flexible robotic arms, which is reflected in its smaller trajectory tracking error and relatively
shorter time to track the target curve. At the same time, the search speed and convergence accuracy
of the optimal value are improved to make the end vibration smaller, which largely reduces the end
vibration of the flexible robotic arm and reduces the mechanical fatigue damage of the flexible robotic
arm, which is of great significance for the research and development in this field.