Vibration Control of Flexible Arm Based on Adaptive Robust Sliding Mode Control and LQR Control

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 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.