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Construction of bode envelopes using REP based range finding algorithms

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Abstract

The frequency domain analysis of systems is an important topic in control theory. Powerful graphical tools exist in classic control, such as the Nyquist plot, Bode plots, and Nichols chart. These methods have been widely used to evaluate the frequency domain behavior of system. A literature survey shows that various approaches are available for the computation of the frequency response of control systems under different types of parametric dependencies, such as affine, multi-linear, polynomial, etc. However, there is a lack of tools in the literature to construct the Bode envelopes for the general nonlinear type of parametric dependencies. In this paper, we address the problem of computation of the envelope of Bode frequency response of a non-rational transfer function with nonlinear parametric uncertainties varying over a box. We propose two techniques to compute the Bode envelopes: first, based on the natural interval extensions (NIE) combined with uniform subdivision and second, based on the existing Taylor model combined with subdivision strategy. We also propose the algorithms to further speed up both methods through extrapolation techniques.

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Authors and Affiliations

  1. IDP in Systems and Control Engineering, Indian Institute of Technology Bombay, Mumbai, India

    P. S. V. Nataraj

  2. Vivekanand Education Society’s Institute of Technology, Mumbai, India

    Shanta Sondur

Authors
  1. P. S. V. Nataraj
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  2. Shanta Sondur
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Correspondence to P. S. V. Nataraj.

Additional information

P. S. V. Nataraj received the Ph.D. degree from IIT Madras, India in process dynamics and control in 1987. He then worked in the CAD center at IIT Bombay, India for about one and half years before joining the Faculty of the Systems and Control Engineering Group at IIT Bombay in 1988. He received an NASA/US Navy commendation and memento for the Best Applied Research Paper awarded at the International Symposium on Air Breathing Engines (ISOABE), Cleveland, Ohio, September 2003, and the “Best Paper of Session” award for the paper improved robust feedback synthesis for nonlinear integro-differential equations (NIDE) models in the IETE International Conference on Quality, Reliability, and Control, Mumbai, December 2001.

His research interests include robust stability and control especially using quantitative feedback theory (QFT) techniques, nonlinear system analysis and control, and reliable computing using interval analysis techniques.

Shanta Sondur received the B. Eng. degree in instrumentation engineering from the Marathawada University, India in 1989, M.Eng. degree in electronics and telecommunication engineering from Pune University, and Ph.D. degree in systems and controls, from Indian Institute of Technology, Bombay, India in 1997 and 2008, respectively. In 1994, she was a faculty member at Pune University. Currently, she is a professor at the Department of Information Technology at Mumbai University, India, and also a professor at the Department of Information Technology, Vivekanand Education Society’s Institute of Technology, Mumbai, India. She is a member of ISOI, ISA, and ISTE.

Her research interests include process control, automation, optimization, and iterative learning control.

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Nataraj, P.S.V., Sondur, S. Construction of bode envelopes using REP based range finding algorithms. Int. J. Autom. Comput. 8, 112–121 (2011). https://doi.org/10.1007/s11633-010-0562-0

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  • DOI: https://doi.org/10.1007/s11633-010-0562-0

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