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.
A Neural Network Controller for a Class of Nonlinear Non-Minimum Phase Systems with Application to a Flexible-Link Manipulator
Talebi, H. A., Patel, R. V., and Khorasani, K. (August 9, 2004). "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. June 2005; 127(2): 289–294. https://doi.org/10.1115/1.1898232
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