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TECHNICAL PAPERS

# Output Feedback Neural Network Adaptive Robust Control With Application to Linear Motor Drive System

[+] Author and Article Information
J. Q. Gong

School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907

Bin Yao

School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907byao@purdue.edu

J. Dyn. Sys., Meas., Control 128(2), 227-235 (Jun 01, 2006) (9 pages) doi:10.1115/1.2199860 History:

## Abstract

In this paper, neural networks (NNs) and adaptive robust control design method are integrated to design a performance oriented control law with only output feedback for a class of single-input-single-output $n$th order nonlinear systems in a normal form. The nonlinearities in the system include repeatable unknown nonlinearities and nonrepeatable unknown nonlinearities such as external disturbances. In addition, unknown nonlinearities can exist in the control input channel as well. A high-gain observer is employed to estimate the states of system. All unknown but repeatable nonlinear functions are approximated by the outputs of multilayer neural networks with the estimated states as inputs to achieve a better model compensation. All NN weights are tuned on-line. In order to avoid possible divergence of on-line tuning, discontinuous projections with fictitious bounds are used in the weight adjusting law to make sure that all the weights are adapted within a prescribed range. Theoretically, the resulting controller achieves a guaranteed output tracking transient performance and a guaranteed final tracking accuracy in general. Certain robust control terms is then constructed to effectively attenuate various model uncertainties and estimate errors. Furthermore, if all the states are available and the unknown nonlinear functions are in the functional ranges of the neural networks, an asymptotic output tracking is also achieved to retain the perfect learning capability of NNs in the ideal situation provided that the ideal NN weights fall within the prescribed range. The output feedback neural network adaptive robust control is then applied to the control of a linear motor drive system. Experiments are carried out to show the effectiveness of the proposed algorithm and the excellent output tracking performance.

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## Figures

Figure 1

Experimental setup

Figure 2

NN structure for estimating −Fa∕M

Figure 3

Position, velocity, and acceleration of the desired trajectory

Figure 4

Position error

Figure 5

NN output under output feedback NNARC (no filter)

Figure 6

NN output (with filter 50∕(s+50)) for the segment of t=25.8248s to t=38.9052s

Figure 7

Fa versus position (constant velocity 0.017m∕s)

Figure 8

Estimate of velocity and “true” velocity

Figure 9

Control input

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