0
Technical Brief

Approximation-Free Output-Feedback Control of Uncertain Nonlinear Systems Using Higher-Order Sliding Mode Observer

[+] Author and Article Information
Jang-Hyun Park

Professor
Department of Electrical and Control Engineering,
Mokpo National University,
Cheonnam 58554, South Korea
e-mail: jhpark72@mokpo.ac.kr

Seong-Hwan Kim

Professor
Department of Electrical and Control Engineering,
Mokpo National University,
Cheonnam 58554, South Korea
e-mail: shkim@mokpo.ac.kr

Tae-Sik Park

Associate Professor
Department of Electrical and Control Engineering,
Mokpo National University,
Cheonnam 58554, South Korea
e-mail: tspark@mokpo.ac.kr

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received September 10, 2017; final manuscript received June 20, 2018; published online July 23, 2018. Assoc. Editor: Hashem Ashrafiuon.

J. Dyn. Sys., Meas., Control 140(12), 124502 (Jul 23, 2018) (5 pages) Paper No: DS-17-1454; doi: 10.1115/1.4040664 History: Received September 10, 2017; Revised June 20, 2018

A novel output-feedback controller for uncertain single-input single-output (SISO) nonaffine nonlinear systems is proposed using high-order sliding mode (HOSM) observer, which is a robust exact finite-time convergent differentiator. The proposed controller utilizes (n + 1)th-order HOSM observer to cancel the uncertainty and disturbance where n is the relative degree of the controlled system. As a result, the control law has an extremely simple form of linear in the differentiator states. It is required no separate sliding-mode controller or universal approximators such as neural networks (NNs) or fuzzy logic systems (FLSs) that are adaptively tuned online. The proposed controller guarantees finite time stability of the output tracking error.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Wang, W.-Y. , Chan, M.-L. , Hsu, C.-C. J. , and Lee, T.-T. , 2002, “ H Tracking-Based Sliding Mode Control for Uncertain Nonlinear Systems via an Adaptive Fuzzy-Neural Approach,” IEEE Trans. Syst., Man, Cybern.-Part B, 32(4), pp. 483–492. [CrossRef]
Park, J.-H. , Huh, S.-H. , Kim, S.-H. , Seo, S.-J. , and Park, G.-T. , 2005, “ Direct Adaptive Controller for Nonaffine Nonlinear Systems Using Self-Structuring Neural Networks,” IEEE Trans. Neural Networks, 16(2), pp. 414–422. [CrossRef]
Park, J.-H. , Park, G.-T. , Kim, S.-H. , and Moon, C.-J. , 2005, “ Direct Adaptive Self-Structuring Fuzzy Controller for Nonaffine Nonlinear Systems,” Fuzzy Sets Syst., 153(3), pp. 429–445. [CrossRef]
Park, J.-H. , Kim, S.-H. , and Moon, C.-J. , 2009, “ Adaptive Neural Control for Strict-Feedback Nonlinear Systems Without Backstepping,” IEEE Trans. Neural Networks, 20(7), pp. 1204–1209. [CrossRef]
Na, J. , Ren, X. , and Zheng, D. , 2013, “ Adaptive Control for Nonlinear Pure-Feedback Systems With High-Order Sliding Mode Observer,” IEEE Trans. Neural Networks Learn. Syst., 24(3), pp. 370–382. [CrossRef]
Shen, Q. , Zhang, T. , and Lim, C.-C. , 2014, “ Novel Neural Control for a Class of Uncertain Pure-Feedback Systems,” IEEE Trans. Neural Networks Learn. Syst., 86(5), pp. 912–922.
Wang, H. , Chen, B. , Lin, C. , and Sun, Y. , 2016, “ Observer-Based Adaptive Neural Control for a Class of Nonlinear Pure-Feedback Systems,” Neurocomputing, 171, pp. 1517–1523. [CrossRef]
Levant, A. , 2003, “ Higher-Order Sliding Modes, Differentiation and Output-Feedback Control,” Int. J. Control, 76(9–10), pp. 924–941. [CrossRef]
Levant, A. , 2005, “ Homegeneity Approach to High-Order Sliding Mode Design,” Automatica, 41(5), pp. 823–830. [CrossRef]
Levant, A. , and Alelishvil, L. , 2007, “ Integral High-Order Sliding Modes,” IEEE Trans. Autom. Control, 52(7), pp. 1278–1282. [CrossRef]
Dinuzzo, F. , and Ferrara, A. , 2010, “ Higher Order Sliding Mode Controllers With Optimal Reaching,” IEEE Trans. Autom. Control, 54(9), pp. 2126–2136. [CrossRef]
Feng, Y. , Han, F. , and Yu, X. , 2014, “ Chattering Free Full-Order Sliding-Mode Control,” Automatica, 50(4), pp. 1310–1314. [CrossRef]
Dadras, S. , and Momeni, H. R. , 2014, “ Fractional-Order Dynamic Output Feedback Sliding Mode Control Design for Robust Stabilization of Uncertain Fractional-Order Nonlinear Systems,” Asian J. Control, 16(2), pp. 1–9. [CrossRef]
Ding, S. , Levant, A. , and Li, S. , 2016, “ Simple Homogeneous Sliding-Mode Controller,” Automatica, 67, pp. 22–32. [CrossRef]
Incremona, G. P. , Rubagotti, M. , and Ferrara, A. , 2017, “ Sliding Mode Control of Constrained Nonlinear System,” IEEE Trans. Autom. Control, 62(6), pp. 2965–2972. [CrossRef]
Song, J. , Niu, Y. , and Zou, Y. , 2017, “ Finite-Time Stabilization via Sliding Mode Control,” IEEE Trans. Autom. Control, 62(3), pp. 1478–1483. [CrossRef]
Oliveira, T. R. , Estrada, A. , and Fridman, L. M. , 2017, “ Global and Exact Differentiator With Dynamic Gains for Output-Feedback Sliding Mode Control,” Automatica, 81, pp. 156–163. [CrossRef]
Levant, A. , and Livne, M. , 2012, “ Exact Differentiation of Signals With Unbounded Higher Derivatives,” IEEE Trans. Autom. Control, 57(4), pp. 1076–1080. [CrossRef]
Khalil, H. K. , 1992, Nonlinear Systems, Macmillan Publishing, New York.
Hunter, J. D. , 2007, “ Matplotlib: A 2D Graphics Environment,” Comput. Sci. Eng., 9(3), pp. 90–95. [CrossRef]

Figures

Grahic Jump Location
Fig. 3

Trajectories of tracking errors for L = 10, 25, and 40

Grahic Jump Location
Fig. 4

Trajectories of control inputs for L = 10, 25, and 40

Grahic Jump Location
Fig. 6

Simulation result using the controller in Ref. [9]: (a) y and yd, (b) tracking error, and (c) control input

Grahic Jump Location
Fig. 1

Block diagram of the overall control system

Grahic Jump Location
Fig. 2

Trajectories of (a) y and yd, (b) tracking error e1, and (c) control input u

Grahic Jump Location
Fig. 5

Trajectories of (a) y and yd and (b) tracking error e1

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In