Abstract
We propose algorithms to compute the well known Bode, Nyquist, and Nichols frequency response plots for nonrational transfer functions. The proposed algorithms are very widely applicable—the magnitude and phase functions need to be only bounded and continuous in frequency. The proposed algorithms guarantee that the magnitude and phase plots are reliably computed to a prescribed accuracy, in a finite number of iterations. Through several practical nonrational examples, we demonstrate the superior performance of the proposed algorithm over the widely used routines in MATLAB's control system toolbox and over the conventional gridding method.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bhattacharyya, S. P., Chapellat, H., and Keel, L. H.: Robust Control—The Parametric Approach, Prentice Hall, New York, 1995.
Bode, H. W.: Network Analysis and Feedback Design, Van Nostrand, New York, 1945.
Chen, Y. L. and Han, K. W.: Stability Analysis of a Nonlinear Reactor Control System, IEEE Transactions on Nuclear Science NS-18 (1971), pp. 18–25.
D'Azzo, J. J. and Houpis, C. H.: Linear Control System Analysis and Design, 4th edition, McGraw-Hill, New York, 1995.
Doebelin, E. O.: Control System Principles and Design, John-Wiley and Sons, New York, 1985.
Grace, A., Laub, A. J., Little, J. N., and Thompson, C. M.: Control System Toolbox for Use with MATLAB: User Guide, MA, 2002.
Horowitz, I. M.: Synthesis of Feedback Systems, Academic Press, New York, 1963.
Kearfott, R. B.: Abstract Generalized Bisection and a Cost Bound, Mathematics of Computation 49(179) (1987), pp. 187–202.
Kearfott, R. B.: Some Tests of Generalized Bisection, ACM Transactions on Mathematical Software 13(3) (1987), pp. 197–220.
Klatte, R., Kulisch, U., Neaga, M., Ratz, D., and Ullrich, Ch.: PASCAL–XSC Language Reference with Examples, Springer-Verlag, Berlin, Heidelberg, 1993.
Malek-Zavarei, M. and Jamshidi, M.: Time Delay Systems: Analysis, Optimization and Application, North-Holland, 1987.
MATLAB User Guide, version 6.1, The MathWorks Inc., MA, 2002.
Moore, R. E.: Interval Analysis, Prentice Hall, Englewood Cliffs, 1966.
Moore, R. E.: Methods and Applications of Interval Analysis, SIAM, Philadelphia, 1979.
Nataraj, P. S. V. and Sheela, S.: A New Subdivision Strategy for Range Computations, Reliable Computing 8(1) (2002), pp. 83–92.
Ogunnike, B. A. and Ray, W. H.: Process Dynamics, Modelling and Control, Oxford University Press, New York, 1994.
Rump, S. M.: INTLAB—Interval Laboratory, in: Csendes, T. (ed.), Developments in Reliable Computing, Kluwer Academic Publishers, 1999.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Nataraj, P.S.V., Barve, J.J. Reliable Computation of Frequency Response Plots for Nonrational Transfer Functions to Prescribed Accuracy. Reliable Computing 9, 373–389 (2003). https://doi.org/10.1023/A:1025131214469
Issue Date:
DOI: https://doi.org/10.1023/A:1025131214469