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

| Peer-Reviewed

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

Wei Liu, Siyi Chen, Huixian Huang

Published in Automation, Control and Intelligent Systems (Volume 7, Issue 2)

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

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

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.

Published in	Automation, Control and Intelligent Systems (Volume 7, Issue 2)
DOI	10.11648/j.acis.20190702.12
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), 2019. Published by Science Publishing Group

Keywords

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

References

[1]	Reyhanoglu, M., Schaft, A. V. D., Mcclamroch, N. H., and Kolmanovsky, I. V. "Dynamics and control of a class of underactuated mechanical systems. "IEEE Transactions on Automatic Control 44.9 (2017): 1663-1671.
[2]	She, J., Zhang, A., Lai, X., and Wu, M. "Global stabilization of 2-DOF underactuated mechanical systems—an equivalent-i nput-disturbance approach." Nonlinear Dynamics 69.1-2 (2012): 495-509.
[3]	Sarras, I., Acosta, J. á., Ortega, R., and Mahindrakar, A. D. "Constructive immersion and invariance stabilization for a class of underactuated mechanical systems." Automatica 49.5 (2013): 1442-1448.
[4]	Lu, Biao, Y. Fang, and N. Sun. "Continuous Sliding Mode Control Strategy for a Class of Nonlinear Underactuated Systems." IEEE Transactions on Automatic Control PP.99 (2018): 1-1.
[5]	Liu. “Control of a class of multibody underactuated mechanical systems with discontinuous friction using sliding-mode.” Transactions of the Institute of Measurement and Control 40.2 (2016): 514–527.
[6]	Yue, B. Y. Liu, C. An, and X. J. Sun. “Extended state observer-based adaptive hierarchical sliding mode control for longitudinal movement of a spherical robot.” Nonlinear Dynamics 78.2 (2014.): 1233-1244.
[7]	He, C. Zhang, N. Yang, and H. Li. “Exquisite disturbance attenuation control for a rotary inverted pendulum.” Transactions of the Institute of Measurement and Control 40.3 (2018.): 812–818.
[8]	Wang, S. Li, and Q. W. Chen. “Robust adaptive finite-time tracking control of uncertain mechanical systems with input saturation and dead zone.” Transactions of the Institute of Measurement and Control, 41.2 (2019): 560–572.
[9]	Wang, J. Q. Yi, D. B. Zhao, and D. T. Liu. “Design of a stable sliding-mode controller for a class of second-order underactuated systems.” IEE Proceedings-Control Theory and Applications 151.6 (2004): 683-690.
[10]	Ning S, Wu Y, Fang Y, et al. Nonlinear Continuous Global Stabilization Control for Underactuated RTAC Systems: Design, Analysis, and Experimentation [J]. IEEE/ASME Transactions on Mechatronics, 2017, 22 (2): 1104-1115.
[11]	Dian S, Chen L, Hoang S, et al. Gain scheduled dynamic surface control for a class of underactuated mechanical systems using neural network disturbance observer [J]. Neurocomputing, 2018, 275: S0925231217316934.
[12]	Binh N T, Tung N A, Nam D P, et al. An Adaptive Backstepping Trajectory Tracking Control of a Tractor Trailer Wheeled Mobile Robot [J]. International Journal of Control Automation and Systems, 2019 (7): 1-9.
[13]	Wang, J. Q. Yi, D. B. Zhao, and D. T. Liu. “Adaptive sliding mode controller for an underactuated manipulator.” Proceedings of 2004 International Conference on Machine Learning and Cybernetics (IEEE Cat. No.04EX826), Shanghai, China, 2004, pp. 882-887 vol. 2.
[14]	Almutairi, Naif B., and M. Zribi. "On the sliding mode control of a Ball on a Beam system." Nonlinear Dynamics 59.1-2 (2009): 221-238.
[15]	Xu, Rong, and Özgüner, Ümit. "Sliding mode control of a class of underactuated systems." Automatica 44.1 (2008): 233-241.
[16]	Xu, Jian Xin, Z. Q. Guo, and T. H. Lee. "Sliding mode controller design for underactuated systems." (2012).
[17]	Musmade, and B. Patre. “Sliding mode control design for robust regulation of time-delay processes.” Transactions of the Institute of Measurement and Control 37.6 (2014): 699–707.
[18]	Lan, S. Li, J. Yang, and L. Guo. “Finite-time soft landing on asteroids using nonsingular terminal sliding mode control.” Transactions of the Institute of Measurement and Control 36.2 (2013): 216–223.
[19]	Tian, Zhixiang, and H. Wu. "Hierarchical Terminal Sliding Mode Control for Underactuated Space Robots." International Conference on Machine Vision & Human-machine Interface IEEE, 2010.
[20]	Lee, J. B. Park, and Y. H. Choi. “Finite time control of nonlinear underactuated systems using terminal sliding surface.” IEEE International Symposium on Industrial Electronics (2009) pp. 626-631.
[21]	Wang, Y. Wu, E. Zhang, J. Guo, and Q. Chen. “Adaptive terminal sliding-mode controller based on characteristic model for gear transmission servo systems. Transactions of the Institute of Measurement and Control 41.1 (2018): 219–234.
[22]	Zhu, Qidan Zhu Qidan, R. Y. R. Yu, and Z. L. Z. Liu. "A discontinuous control law of an underactuated surface vessel based on fast terminal sliding mode." World Congress on Intelligent Control & Automation IEEE, 2010.
[23]	Yu, and X. Huo. "Fast terminal sliding-mode control design for nonlinear dynamical systems." IEEE Transactions on Circuits & Systems I Fundamental Theory & Applications 49.2 (2009): 261-264.
[24]	Zheng, Naijia, et al. "Hierarchical fast terminal sliding mode control for a self-balancing two-wheeled robot on uneven terrains." Control Conference IEEE, 2017.
[25]	Boukattaya M, Mezghani N, Damak T. Adaptive nonsingular fast terminal sliding-mode control for the tracking problem of uncertain dynamical systems. [J]. Isa Transactions, 2018, 77: S0019057818301538.
[26]	Pai M C. Synchronization of unified chaotic systems via adaptive nonsingular fast terminal sliding mode control [J]. International Journal of Dynamics and Control, 2018.
[27]	Haibo L, Heping W, Junlei S. Attitude control for QTR using exponential nonsingular terminal sliding mode control [J]. Journal of Systems Engineering and Electronics, 2019, 30 (1): 191-200.
[28]	Ding, Feng, et al. "Sliding mode control with an extended disturbance observer for a class of underactuated system in cascaded form." Nonlinear Dynamics (2017).
[29]	Yue, X. Wei, and Z. Li. “Zero-dynamics-based adaptive sliding mode control for a wheeled inverted pendulum with parametric friction and uncertain dynamics compensation.” Transactions of the Institute of Measurement and Control 37.1 (2014): 91–99.
[30]	Jouini, Marwa, S. Dhahri, and A. Sellami. "Combination of integral sliding mode control design with optimal feedback control for nonlinear uncertain systems." Transactions of the Institute of Measurement and Control (2018).
[31]	Wang, J. Yuan, and Y. Pan. “Adaptive second-order sliding mode control: A unified method.” Transactions of the Institute of Measurement and Control 40.6 (2017): 1927–1935.
[32]	Lo, Ji Chang, and Y. H. Kuo. "Decoupled fuzzy sliding-mode control." IEEE Transactions on Fuzzy Systems 6.3 (1998): 426-435.
[33]	Han. “nonlinear tracking-differentiator.” Journal of Systems Science and Mathematical Sciences 14.2 (1994).
[34]	Mao, Wei. Li, and X. L. Feng. “Nonlinear tracking differentiator design based on hyperbolic tangent.” Computer applications 36. z1 (2016).
[35]	Marks, G., et al. "Effects of High Order Sliding Mode Guidance and Observers On Hit-to-Kill Interceptions." Aiaa Guidance, Navigation, & Control Conference & Exhibit 2006.
[36]	Wang, W., et al. "Design of a stable sliding-mode controller for a class of second-order underactuated systems." IEE Proceedings-Control Theory and Applications 151.6 (2004): 683-0.

Cite This Article

Plain Text BibTeX RIS

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

Copy | Download

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

Copy | Download

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

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

Download PDF

Sections

Plain Text BibTeX RIS

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

Copy | Download

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

Copy | Download

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