Robust tracking control of a flexible manipulator with limited control input based on backstepping and the Nussbaum function

Jia Tan; ShiLong Chen; ZhengQiang Li; Jia Tan; ShiLong Chen; ZhengQiang Li

doi:10.3934/mbe.2023906

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 12: 20486-20509. doi: 10.3934/mbe.2023906

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Robust tracking control of a flexible manipulator with limited control input based on backstepping and the Nussbaum function

1.
Kunming University of Science and Technology, Kunming 650500, China
2.
Foshan Power Supply Bureau of Guangdong Power Grid Co., Ltd., Foshan 528000, China

Received: 03 August 2023 Revised: 13 October 2023 Accepted: 17 October 2023 Published: 13 November 2023

A flexible manipulator is a versatile automated device with a wide range of applications, capable of performing various tasks. However, these manipulators are often vulnerable to external disturbances and face limitations in their ability to control actuators. These factors significantly impact the precision of tracking control in such systems. This study delves into the problem of attitude tracking control for a flexible manipulator under the constraints of control input limitations and the influence of external disturbances. To address these challenges effectively, we first introduce the backstepping method, aiming to achieve precise state tracking and tackle the issue of external disturbances. Additionally, recognizing the constraints posed by control input limitations in the flexible manipulator's actuator control system, we employ a design approach based on the Nussbaum function. This method is designed to overcome these limitations, allowing for more robust control. To validate the effectiveness and disturbance rejection capabilities of the proposed control strategy, we conduct comparative numerical simulations using MATLAB/Simulink. These simulations provide further evidence of the robustness and reliability of the control strategy, even in the presence of external disturbances and control input limitations.
- flexible manipulator,
- input limitation,
- backstepping method,
- Nussbaum function
Citation: Jia Tan, ShiLong Chen, ZhengQiang Li. Robust tracking control of a flexible manipulator with limited control input based on backstepping and the Nussbaum function[J]. Mathematical Biosciences and Engineering, 2023, 20(12): 20486-20509. doi: 10.3934/mbe.2023906

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Abstract

A flexible manipulator is a versatile automated device with a wide range of applications, capable of performing various tasks. However, these manipulators are often vulnerable to external disturbances and face limitations in their ability to control actuators. These factors significantly impact the precision of tracking control in such systems. This study delves into the problem of attitude tracking control for a flexible manipulator under the constraints of control input limitations and the influence of external disturbances. To address these challenges effectively, we first introduce the backstepping method, aiming to achieve precise state tracking and tackle the issue of external disturbances. Additionally, recognizing the constraints posed by control input limitations in the flexible manipulator's actuator control system, we employ a design approach based on the Nussbaum function. This method is designed to overcome these limitations, allowing for more robust control. To validate the effectiveness and disturbance rejection capabilities of the proposed control strategy, we conduct comparative numerical simulations using MATLAB/Simulink. These simulations provide further evidence of the robustness and reliability of the control strategy, even in the presence of external disturbances and control input limitations.

References

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