Abstract
Model reference techniques are successfully used in many control system designs, particularly in the field of model reference adaptive control systems. In this paper for a linear single-input, single-output time-invariant system, a method for modeling transfer functions of reference model using the basic performance specifications is presented. A set of non-linear equations is constructed from the definitions of the performance specifications and the unknown coefficients of a transfer function. Improved Newton-Raphson method and optimal linear model are applied to solve the non-linear equations. The proposed method constructs approximate representations of the desired transfer functions to ensure more rapid convergence of the numerical method. First, improved Newton-Raphson method is developed. Second, a optimal linearization technique is explained to obtain optimal linear model of nonlinear equations. Finally, simulation with four specifications is carried out to obtain a second-order transfer function model and demonstrate our method.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Huang, C.J., Shieh, L.S.: Modelling large dynamical systems with industrial specifications. Int. J. Systems Sci. 7(3), 241–256 (1976)
Shieh, L.S., Datta-Barua, M., Yates, R.E.: A method for modelling transfer functions using dominant frequency-response data and its applications. Int. J. Systems Sci. 10(10), 1097–1114 (1979)
Dabney, J.B., Harman, T.L.: Mastering SIMULINK 2. Prentice-Hall, Englewood Cliffs (1998)
Teixeira, M.C.M., Zak, S.H.: Stabilizing controller design for uncertain nonlinear systems using fuzzy models. IEEE Trans. on Fuzzy Syst. 7, 133–142 (1999)
Rao, S.S.: Optimization:Theory and Applications, pp. 292–300. John Wiley Sons, New York (1984)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Park, JJ., Choi, GS., Park, IK. (2011). Control System Design Using Improved Newton-Raphson Method and Optimal Linear Model of Nonlinear Equations. In: Kim, Th., et al. Multimedia, Computer Graphics and Broadcasting. MulGraB 2011. Communications in Computer and Information Science, vol 262. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27204-2_31
Download citation
DOI: https://doi.org/10.1007/978-3-642-27204-2_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-27203-5
Online ISBN: 978-3-642-27204-2
eBook Packages: Computer ScienceComputer Science (R0)