Research Papers

Neural Network Adaptive Output Feedback Control of Flexible Link Manipulators

[+] Author and Article Information
A. Farmanbordar

Department of Electrical Engineering,
Islamic Azad University,
Borujerd Branch, 6915136111, Iran
e-mail: a.farmanbordar@gmail.com

S. M. Hoseini

Department of Electrical Engineering,
Malek Ashtar University of Technology,
Esfahan, 115-83145, Iran
e-mail: sm_hoseini@iust.ac.ir

Contributed by the Dynamic Systems Division of ASME for publication in the Journal of Dynamic Systems, Measurement, and Control. Manuscript received October 15, 2011; final manuscript received August 18, 2012; published online November 7, 2012. Assoc. Editor: Warren E. Dixon.

J. Dyn. Sys., Meas., Control 135(2), 021009 (Nov 07, 2012) (9 pages) Paper No: DS-11-1319; doi: 10.1115/1.4007701 History: Received October 15, 2011; Revised August 18, 2012

This paper presents an adaptive output-feedback control method based on neural networks for flexible link manipulator which is a nonlinear nonminimum phase system. The proposed controller comprises a linear, a neuro-adaptive, and an adaptive robustifying parts. The neural network is designed to approximate the matched uncertainty of the system. The inputs of the neural network are the tapped delays of the system input–output signals. In addition, an appropriate reference signal is proposed to compensate the unmatched uncertainty inherent in the internal system dynamics. The adaptation laws for the neural network weights and adaptive gains are obtained using the Lyapunov’s direct method. These adaptation laws employ a linear observer of system dynamics that is realizable. The ultimate boundedness of the error signals are analytically shown using Lyapunov's method.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Seshagiri, S., and Khalil, H., 2000, “Output Feedback Control of Nonlinear Systems Using RBF Neural Networks,” IEEE Trans. Neural Networks, 11, pp. 69–79. [CrossRef]
Hovakimyan, N., Nardi, F., and Calise, A. J., 2002, “A Novel Error Observer Based Adaptive Output Feedback Approach for Control of Uncertain Systems,” IEEE Trans. Automat. Control, 47, pp. 1310–1314. [CrossRef]
Ge, S. S., and Zhang, T., 2003, “Neural Network Control of Non-Affine Nonlinear With Zero Dynamics by State and Output Feedback,” IEEE Trans. Neural Networks, 14, pp. 900–918. [CrossRef]
Shang, F., and Liu, Y. G., 2010, “Adaptive Output-Feedback Stabilization for a Class of Uncertain Nonlinear Systems,” Acta Automatica Sin., 36, pp. 92–100. [CrossRef]
Wu, Y., Yu, J., and Zhao, Y., 2012, “Output Feedback Regulation Control for a Class of Cascade Nonlinear Systems and Its Application to Fan Speed Control,” Nonlinear Anal., 13, pp. 1278–1291. [CrossRef]
Ding, Z., 2005, “Semi-Global Stabilisation of a Class of Non-Minimum Phase Nonlinear Output-Feedback System,” IEE Proc.: Control Theory Appl., 152, pp. 460–464. [CrossRef]
Karagiannis, D., Jiang, Z. P., Ortega, R., and Astolfi, A., 2005, “Output-Feedback Stabilization of a Class of Uncertain Non-Minimum Phase Nonlinear Systems,” Automatica, 41, pp.1609–1615. [CrossRef]
Isidori, A., 2000, “A Tool for Semilobal Stabilization of Uncertain Non-Minimum Phase Nonlinear Systems via Output Feedback,” IEEE Trans. Autom. Control, 45, pp. 1817–1827. [CrossRef]
Lan, W., and Chen, B. M., 2008, “Explicit Construction of H Control Law for a Class of Nonminimum Phase Nonlinear Systems,” Automatica, 44, pp. 738–774. [CrossRef]
Chen, S. C., and Chen, W. L., 2003, “Output Regulation of Nonlinear Uncertain System With Non-Minimum Phase via Enhances RBFN Controller,” IEEE Trans. Syst. Man Cybern., Part A. Syst. Humans, 33, pp. 265–270. [CrossRef]
Lee, C. H., 2004, “Stabilization of Nonlinear Nonminimum Phase Systems: Adaptive Parallel Approach Using Recurrent Fuzzy Neural Network,” IEEE Trans. Syst., Man, Cybern., Part B: Cybern., 34, pp. 1075–1088. [CrossRef]
Hoseini, S. M., and Farrokhi, M., 2009, “Neuro-Adaptive Output Feedback Control for Class of Nonlinear Non-Minimum Phase Systems,” J. Intell. Robotic Syst., 56, pp. 487–511. [CrossRef]
Gopalswamy, S., and Hedrick, J. K., 1993, “Tracking Nonlinear Non-Minimum Phase Systems Using Sliding Control,” Int. J. Control, 57, pp. 1141–1158. [CrossRef]
Lee, Y., Kouvaritakis, B., and Cannon, M., 2008, “Input–Output Feedback Linearization for Non-Minimum Phase Nonlinear Systems Through Periodic Use of Synthetic Outputs,” Syst. Control Lett., 57, pp. 626–630. [CrossRef]
Hauser, J., Sastry, S., and Meyer, G., 1992, “Nonlinear Control Design for Slightly Non-Minimum Phase Systems: Application to V/STOL Aircraft,” Automatica, 28, pp. 665–679. [CrossRef]
Doyle, F., Allgower, F., Oliveria, S., Gilles, E., and Moran, M., 1992, “On Nonlinear Systems With Poorly Behaved Zero Dynamics,” Proceedings of the American Control Conference, pp. 2571–2575.
Sadegh, N., 1993, “A Perceptron Network for Functional Identification and Control of Nonlinear Systems,” IEEE Trans. Neural Networks, 4, pp. 982–988. [CrossRef]
Hoseini, S. M., Farrokhi, M., and Koshkouei, A. J., 2010, “Adaptive Neural Network Output Feedback Stabilization of Nonlinear Non-Minimum Phase Systems,” Int. J. Adapt. Control Signal Process., 24, pp. 65–82. [CrossRef]
Polycarpou, M. M., 1996, “Stable Adaptive Neural Control Scheme for Nonlinear Systems,” IEEE Trans. Autom. Control, 41, pp. 447–451. [CrossRef]
Lewis, F. L., Liu, K., and Yesildirek, A., 1995, “Neural Net Robot Controller With Guaranteed Tracking Performance,” IEEE Trans. Neural Networks, 6, pp. 703–715. [CrossRef]
Yesildirek, A., and Lewis, F., 1994, “Feedback Linearization Using Neural Networks,” Proceedings ofIEEE International Conference on Neural Networks, pp. 2539–2544. [CrossRef]
Gutierrez, L. B., Lewis, F. L., and Lowe, J. A., 1998, “Implementation of a Neural Network Tracking Controller for a Single Flexible Link: Comparison With PD and PID Controllers,” IEEE Trans. Ind. Electron., 45, pp. 307–318. [CrossRef]
Zhang, Y., Yang, T., and Sun, Z., 2009, “Neuro-Sliding-Mode Control of Flexible-Link Manipulators Based on Singularly Perturbed Model,” Tsinghua Sci. Technol., 14, pp. 444–451. [CrossRef]
Rigatos, G. G., 2009, “Model-Based and Model-Free Control of Flexible-Link Robots: A Comparison Between Representative Methods,” Appl. Math. Model., 33, pp. 3906–3925. [CrossRef]
Arciniegas, J. I., Eltimsahy, A., and Cios, K. J., 1993, “Fuzzy Inference and the Control of Flexible Robotic Manipulators,” Proceedings of the IEEE International Symposium on Intelligent Control, pp. 250–254. [CrossRef]
Wedding, D. K., and Eltimsahy, A., 2000, “Flexible Link Control Using Multiple Forward Paths, Multiple RBF Neural Networks in a Direct Control Application,” Proceedings of theIEEE International Conference on Systems, Man, and Cybernetics, pp. 2619–2624. [CrossRef]
Wu, L., Sun, Z., and Sun, F., 2001, “Neural Networks Control Structure for Manipulators With Flexible Last Link,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 2404–2408. [CrossRef]
Maeda, Y., 2002, “Real-Time Control and Learning Using Neuro-Controller via Simultaneous Perturbation for Flexible Arm System,” Proceedings of the American Control Conference, ACC, pp. 2583–2588. [CrossRef]
Talebi, H. A., Patel, R. V., and Khorasani, K., 2005, “A Neural Network Controller for a Class of Nonlinear Non-Minimum Phase Systems With Application to a Flexible-Link Manipulator,” ASME J. Dyn. Sys., Meas., Control, 127, pp. 289–294. [CrossRef]
Lavertsky, E., Calise, A. J., and Hovakimyan, N., 2003, “Upper Bounds for Approximation of Continuous-Time Dynamics Using Delayed Outputs and Feedforward Neural Networks,” IEEE Trans. Autom. Control, 48, pp. 1606–1610. [CrossRef]
Wang, D., and Vidiasagar, M. T., 1991, “Transfer Function for Single Flexible Link,” Int. J. Robot. Res., 10, pp. 540–549. [CrossRef]
Khalil, H., 2002, Nonlinear Systems, Prentice-Hall, Englewood Cliffs, NJ.


Grahic Jump Location
Fig. 1

Flexible link manipulator

Grahic Jump Location
Fig. 2

Block diagram of the augmented plant

Grahic Jump Location
Fig. 3

Block diagram of the proposed controller

Grahic Jump Location
Fig. 4

Response of the FLM closed-loop system without parameters uncertainty. Dotted line: linear optimal controller, solid line: the proposed controller.

Grahic Jump Location
Fig. 5

Response of the FLM system with parameters uncertainty. Dashed line: linear optimal controller, solid line: the proposed controller.

Grahic Jump Location
Fig. 6

Response of the FLM system with parameter uncertainty. (a) Matched uncertainty cancellation, (b) validation of unmatched uncertainty bound, (c) errors of estimation ξ˜, and (d) normalized norm of adaptive weights.

Grahic Jump Location
Fig. 7

Response of the FLM system with parameters uncertainty. Solid line: the proposed controller, dotted line: proposed control without unmatched uncertainty cancellation (yd = 0).



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