A Neural Network Controller for a Class of Nonlinear Non-Minimum Phase Systems with Application to a Flexible-Link Manipulator

[+] Author and Article Information
H. A. Talebi

Department of Electrical Engineering,  AmirKabir University, Tehran, Iran 15914alit@aut.ac.ir

R. V. Patel

Department of Electrical and Computer Engineering,  University of Western Ontario, London, Ontario N6A 5B9, Canadarajni@eng.uwo.ca

K. Khorasani

Department of Electrical and Computer Engineering,  Concordia University, Montreal, Quebec H3G 1M8, Canadakash@ece.concordia.ca

J. Dyn. Sys., Meas., Control 127(2), 289-294 (Aug 09, 2004) (6 pages) doi:10.1115/1.1898232 History: Received June 13, 2002; Revised August 09, 2004

This paper investigates the problem of controlling a nonlinear nonminimum phase system. An output re-definition strategy is first introduced to guarantee stable zero dynamics. This output re-definition scheme is applicable to a class of open-loop stable nonlinear systems whose input–output maps contain nonlinear terms in the output and linear terms in the input. No explicit knowledge about the nonlinearities of the system is required. The nonlinearities of the system are identified by a neural network. The identified neural network model is then used in modifying the zero dynamics of the system. A stable∕anti-stable factorization is performed on the zero dynamics of the system. The new output is re-defined using the neural identifier and the stable part of the zero dynamics. A controller is then designed based on the new output whose zero dynamics are stable and can be inverted. An experimental setup of a single-link flexible manipulator is considered as a practical case study of a nonlinear nonminimum phase system. Experimental results are presented to illustrate the advantages and improved performance of the proposed tracking controller over both linear and nonlinear conventional controllers in the presence of unmodeled dynamics and parameter variations.

Copyright © 2005 by American Society of Mechanical Engineers
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Figure 1

Structure of the inverse dynamics controller using the output re-definition approach

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Figure 2

Structure of the proposed neural network controller. The neural controller and the feedthrough compensator are realized according to 10,9, respectively

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Figure 3

Experimental results for the step inputs using the PD controller with different gains: (a) and (d) actual tip positions, (b) and (e) elastic deflections, (c) and (f) torque input commands

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Figure 4

Experimental results for the step and sinusoidal inputs using the proposed approach: (a) and (c) actual tip positions, (b) and (d) elastic deflections; (the dashed lines correspond to the desired trajectory)




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