Second-Order Hierarchical Fast Terminal Sliding Model Control for a Class of Underactuated Systems Using Disturbance Observer

Wei Liu; Siyi Chen; Huixian Huang

doi:doi:10.11648/j.acis.20190702.12

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Second-Order Hierarchical Fast Terminal Sliding Model Control for a Class of Underactuated Systems Using Disturbance Observer

Wei Liu, Siyi Chen, Huixian Huang

Received: 15 April 2019 Accepted: 23 May 2019 Published: 15 June 2019

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Abstract

A second-order hierarchical fast terminal sliding mode control method based on disturbance observer (DOSHFTSM) is proposed for a class of fourth-order underactuated systems. In the first step, the fourth-order underactuated system is divided into two subsystems, and the integral sliding surface is designed for each subsystem. Then, the first-order fast terminal sliding surface is defined by using the integral sliding surface and its derivatives of each subsystem, and the switching control items of the system are designed according to the first-order fast terminal sliding surface of the subsystem. Secondly, the second-order sliding surface is designed by using the first-order fast terminal sliding surface of each subsystem. On the premise of ensuring the stability of Lyapunov, the switching control term is designed by using the variable coefficient double power reaching law to eliminate the system jitter. Finally, based on the principle of hyperbolic tangent nonlinear tracking differentiator, a hyperbolic tangent nonlinear disturbance observer (TANH-DOC) is designed to estimate the uncertainties and external disturbances of the system and compensate them to the sliding mode controller to improve the robustness of the system. The stability of the system is proved by using Lyapunov principle. The validity of this method is verified by numerical simulation and physical simulation of inverted pendulum system.

DOI	10.11648/j.acis.20190702.12
Published in	Automation, Control and Intelligent Systems (Volume 7, Issue 2, April 2019)
Page(s)	65-78
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Underactuated System, Disturbance Observer, Hierarchical Sliding Mode, Double Power Reaching Law, Stability Analysis

References

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APA Style

Wei Liu, Siyi Chen, Huixian Huang. (2019). Second-Order Hierarchical Fast Terminal Sliding Model Control for a Class of Underactuated Systems Using Disturbance Observer. Automation, Control and Intelligent Systems, 7(2), 65-78. https://doi.org/10.11648/j.acis.20190702.12

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ACS Style

Wei Liu; Siyi Chen; Huixian Huang. Second-Order Hierarchical Fast Terminal Sliding Model Control for a Class of Underactuated Systems Using Disturbance Observer. Autom. Control Intell. Syst. 2019, 7(2), 65-78. doi: 10.11648/j.acis.20190702.12

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AMA Style

Wei Liu, Siyi Chen, Huixian Huang. Second-Order Hierarchical Fast Terminal Sliding Model Control for a Class of Underactuated Systems Using Disturbance Observer. Autom Control Intell Syst. 2019;7(2):65-78. doi: 10.11648/j.acis.20190702.12

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@article{10.11648/j.acis.20190702.12,
  author = {Wei Liu and Siyi Chen and Huixian Huang},
  title = {Second-Order Hierarchical Fast Terminal Sliding Model Control for a Class of Underactuated Systems Using Disturbance Observer},
  journal = {Automation, Control and Intelligent Systems},
  volume = {7},
  number = {2},
  pages = {65-78},
  doi = {10.11648/j.acis.20190702.12},
  url = {https://doi.org/10.11648/j.acis.20190702.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acis.20190702.12},
  abstract = {A second-order hierarchical fast terminal sliding mode control method based on disturbance observer (DOSHFTSM) is proposed for a class of fourth-order underactuated systems. In the first step, the fourth-order underactuated system is divided into two subsystems, and the integral sliding surface is designed for each subsystem. Then, the first-order fast terminal sliding surface is defined by using the integral sliding surface and its derivatives of each subsystem, and the switching control items of the system are designed according to the first-order fast terminal sliding surface of the subsystem. Secondly, the second-order sliding surface is designed by using the first-order fast terminal sliding surface of each subsystem. On the premise of ensuring the stability of Lyapunov, the switching control term is designed by using the variable coefficient double power reaching law to eliminate the system jitter. Finally, based on the principle of hyperbolic tangent nonlinear tracking differentiator, a hyperbolic tangent nonlinear disturbance observer (TANH-DOC) is designed to estimate the uncertainties and external disturbances of the system and compensate them to the sliding mode controller to improve the robustness of the system. The stability of the system is proved by using Lyapunov principle. The validity of this method is verified by numerical simulation and physical simulation of inverted pendulum system.},
 year = {2019}
}

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TY  - JOUR
T1  - Second-Order Hierarchical Fast Terminal Sliding Model Control for a Class of Underactuated Systems Using Disturbance Observer
AU  - Wei Liu
AU  - Siyi Chen
AU  - Huixian Huang
Y1  - 2019/06/15
PY  - 2019
N1  - https://doi.org/10.11648/j.acis.20190702.12
DO  - 10.11648/j.acis.20190702.12
T2  - Automation, Control and Intelligent Systems
JF  - Automation, Control and Intelligent Systems
JO  - Automation, Control and Intelligent Systems
SP  - 65
EP  - 78
PB  - Science Publishing Group
SN  - 2328-5591
UR  - https://doi.org/10.11648/j.acis.20190702.12
AB  - A second-order hierarchical fast terminal sliding mode control method based on disturbance observer (DOSHFTSM) is proposed for a class of fourth-order underactuated systems. In the first step, the fourth-order underactuated system is divided into two subsystems, and the integral sliding surface is designed for each subsystem. Then, the first-order fast terminal sliding surface is defined by using the integral sliding surface and its derivatives of each subsystem, and the switching control items of the system are designed according to the first-order fast terminal sliding surface of the subsystem. Secondly, the second-order sliding surface is designed by using the first-order fast terminal sliding surface of each subsystem. On the premise of ensuring the stability of Lyapunov, the switching control term is designed by using the variable coefficient double power reaching law to eliminate the system jitter. Finally, based on the principle of hyperbolic tangent nonlinear tracking differentiator, a hyperbolic tangent nonlinear disturbance observer (TANH-DOC) is designed to estimate the uncertainties and external disturbances of the system and compensate them to the sliding mode controller to improve the robustness of the system. The stability of the system is proved by using Lyapunov principle. The validity of this method is verified by numerical simulation and physical simulation of inverted pendulum system.
VL  - 7
IS  - 2
ER  -

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Author Information

Wei Liu

School of Information Engineering, Xiangtan University, Xiangtan, China
Siyi Chen

School of Information Engineering, Xiangtan University, Xiangtan, China
Huixian Huang

School of Information Engineering, Xiangtan University, Xiangtan, China

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APA Style

Wei Liu, Siyi Chen, Huixian Huang. (2019). Second-Order Hierarchical Fast Terminal Sliding Model Control for a Class of Underactuated Systems Using Disturbance Observer. Automation, Control and Intelligent Systems, 7(2), 65-78. https://doi.org/10.11648/j.acis.20190702.12

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ACS Style

Wei Liu; Siyi Chen; Huixian Huang. Second-Order Hierarchical Fast Terminal Sliding Model Control for a Class of Underactuated Systems Using Disturbance Observer. Autom. Control Intell. Syst. 2019, 7(2), 65-78. doi: 10.11648/j.acis.20190702.12

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AMA Style

Wei Liu, Siyi Chen, Huixian Huang. Second-Order Hierarchical Fast Terminal Sliding Model Control for a Class of Underactuated Systems Using Disturbance Observer. Autom Control Intell Syst. 2019;7(2):65-78. doi: 10.11648/j.acis.20190702.12

Copy | Download

@article{10.11648/j.acis.20190702.12,
  author = {Wei Liu and Siyi Chen and Huixian Huang},
  title = {Second-Order Hierarchical Fast Terminal Sliding Model Control for a Class of Underactuated Systems Using Disturbance Observer},
  journal = {Automation, Control and Intelligent Systems},
  volume = {7},
  number = {2},
  pages = {65-78},
  doi = {10.11648/j.acis.20190702.12},
  url = {https://doi.org/10.11648/j.acis.20190702.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acis.20190702.12},
  abstract = {A second-order hierarchical fast terminal sliding mode control method based on disturbance observer (DOSHFTSM) is proposed for a class of fourth-order underactuated systems. In the first step, the fourth-order underactuated system is divided into two subsystems, and the integral sliding surface is designed for each subsystem. Then, the first-order fast terminal sliding surface is defined by using the integral sliding surface and its derivatives of each subsystem, and the switching control items of the system are designed according to the first-order fast terminal sliding surface of the subsystem. Secondly, the second-order sliding surface is designed by using the first-order fast terminal sliding surface of each subsystem. On the premise of ensuring the stability of Lyapunov, the switching control term is designed by using the variable coefficient double power reaching law to eliminate the system jitter. Finally, based on the principle of hyperbolic tangent nonlinear tracking differentiator, a hyperbolic tangent nonlinear disturbance observer (TANH-DOC) is designed to estimate the uncertainties and external disturbances of the system and compensate them to the sliding mode controller to improve the robustness of the system. The stability of the system is proved by using Lyapunov principle. The validity of this method is verified by numerical simulation and physical simulation of inverted pendulum system.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Second-Order Hierarchical Fast Terminal Sliding Model Control for a Class of Underactuated Systems Using Disturbance Observer
AU  - Wei Liu
AU  - Siyi Chen
AU  - Huixian Huang
Y1  - 2019/06/15
PY  - 2019
N1  - https://doi.org/10.11648/j.acis.20190702.12
DO  - 10.11648/j.acis.20190702.12
T2  - Automation, Control and Intelligent Systems
JF  - Automation, Control and Intelligent Systems
JO  - Automation, Control and Intelligent Systems
SP  - 65
EP  - 78
PB  - Science Publishing Group
SN  - 2328-5591
UR  - https://doi.org/10.11648/j.acis.20190702.12
AB  - A second-order hierarchical fast terminal sliding mode control method based on disturbance observer (DOSHFTSM) is proposed for a class of fourth-order underactuated systems. In the first step, the fourth-order underactuated system is divided into two subsystems, and the integral sliding surface is designed for each subsystem. Then, the first-order fast terminal sliding surface is defined by using the integral sliding surface and its derivatives of each subsystem, and the switching control items of the system are designed according to the first-order fast terminal sliding surface of the subsystem. Secondly, the second-order sliding surface is designed by using the first-order fast terminal sliding surface of each subsystem. On the premise of ensuring the stability of Lyapunov, the switching control term is designed by using the variable coefficient double power reaching law to eliminate the system jitter. Finally, based on the principle of hyperbolic tangent nonlinear tracking differentiator, a hyperbolic tangent nonlinear disturbance observer (TANH-DOC) is designed to estimate the uncertainties and external disturbances of the system and compensate them to the sliding mode controller to improve the robustness of the system. The stability of the system is proved by using Lyapunov principle. The validity of this method is verified by numerical simulation and physical simulation of inverted pendulum system.
VL  - 7
IS  - 2
ER  -

Copy | Download