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Research Papers

On the Generalized Frequency Response Functions of Volterra Systems

[+] Author and Article Information
Xingjian Jing1

Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield S1 3JD, UKxingjian.jing@googlemail.com

Ziqiang Lang

Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield S1 3JD, UKz.lang@shef.ac.uk

1

Corresponding author. Also at ISVR, University of Southampton, Southampton, SO17 1BJ, UK.

J. Dyn. Sys., Meas., Control 131(6), 061002 (Nov 09, 2009) (8 pages) doi:10.1115/1.3211088 History: Received May 10, 2008; Revised November 26, 2008; Published November 09, 2009; Online November 09, 2009

The generalized frequency response function (GFRF) for Volterra systems described by the nonlinear autoregressive with exogenous input model is determined by a new mapping function based on its parametric characteristic. The nth-order GFRF can now be directly determined in terms of the first order GFRF, which represents the linear component of the system, and model parameters, which define system nonlinearities. Some new properties of the GFRFs are therefore developed. These results can analytically reveal the linear and nonlinear effects on system frequency response functions, and also demonstrate the relationship between convergence of system Volterra series expansion and model parameters.

Copyright © 2009 by American Society of Mechanical Engineers
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