Regular Papers

International Journal of Control, Automation, and Systems 2024; 22(6): 1791-1806

https://doi.org/10.1007/s12555-023-0368-9

© The International Journal of Control, Automation, and Systems

Adaptive Recursive Terminal Sliding Mode Control for Uncertain Systems With Input Saturation Based on Positive Semi-definite Barrier Function

Chao Jia*, Lijie Li, and Xuanyue Shangguan

Tianjin University of Technology

Abstract

In this article, a novel positive semi-definite barrier function based adaptive recursive terminal sliding mode control for a class of uncertain nonlinear systems with actuator saturation is proposed. The method explicitly considers the actuator saturation and uncertainty, and achieves high-speed and high-precision control of the system with a lower amplitude adaptive gain, while without require the knowledge of the upper bound of the disturbance. First, in order to avoid the singularity problem and effectively improve the tracking accuracy, an error-based adaptive recursive terminal sliding surface is constructed; Then, a positive semi-definite barrier function, which realizes the adaptive adjustment of the controller gain in a lower amplitude mode is considered. It ensures that the sliding variable converges to a predefined region even when it is in the presence of actuator saturation and external disturbance. In addition, in order to prevent the problem of excessive positive semi-definite barrier function gain caused by sudden large disturbances, a modified barrier function gain form which can vary with the disturbance amplitude is also proposed, therefore the overestimation of the gain which may be difficult to achieve in reality is effectively avoided; Finally, the stability analysis of the above two control strategies is carried out in detail, and it is proved that both the systematic error and its derivative can converge to a predefined region in finite time. Numerical simulations show that in the presence of actuator saturation and external disturbances, the proposed control method not only improve the convergence performance and the control accuracy of the system, but also better prevent actuator saturation. The proposed method is also applied to a multi-cylinder hydraulic press servo system, and the results show its effectiveness.

Keywords Adaptive recursive terminal sliding mode, barrier function, input saturation, robust control.

Article

Regular Papers

International Journal of Control, Automation, and Systems 2024; 22(6): 1791-1806

Published online June 1, 2024 https://doi.org/10.1007/s12555-023-0368-9

Copyright © The International Journal of Control, Automation, and Systems.

Adaptive Recursive Terminal Sliding Mode Control for Uncertain Systems With Input Saturation Based on Positive Semi-definite Barrier Function

Chao Jia*, Lijie Li, and Xuanyue Shangguan

Tianjin University of Technology

Abstract

In this article, a novel positive semi-definite barrier function based adaptive recursive terminal sliding mode control for a class of uncertain nonlinear systems with actuator saturation is proposed. The method explicitly considers the actuator saturation and uncertainty, and achieves high-speed and high-precision control of the system with a lower amplitude adaptive gain, while without require the knowledge of the upper bound of the disturbance. First, in order to avoid the singularity problem and effectively improve the tracking accuracy, an error-based adaptive recursive terminal sliding surface is constructed; Then, a positive semi-definite barrier function, which realizes the adaptive adjustment of the controller gain in a lower amplitude mode is considered. It ensures that the sliding variable converges to a predefined region even when it is in the presence of actuator saturation and external disturbance. In addition, in order to prevent the problem of excessive positive semi-definite barrier function gain caused by sudden large disturbances, a modified barrier function gain form which can vary with the disturbance amplitude is also proposed, therefore the overestimation of the gain which may be difficult to achieve in reality is effectively avoided; Finally, the stability analysis of the above two control strategies is carried out in detail, and it is proved that both the systematic error and its derivative can converge to a predefined region in finite time. Numerical simulations show that in the presence of actuator saturation and external disturbances, the proposed control method not only improve the convergence performance and the control accuracy of the system, but also better prevent actuator saturation. The proposed method is also applied to a multi-cylinder hydraulic press servo system, and the results show its effectiveness.

Keywords: Adaptive recursive terminal sliding mode, barrier function, input saturation, robust control.

IJCAS
June 2024

Vol. 22, No. 6, pp. 1761~2054

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