ANALYTICAL ALGORITHM FOR COMPUTING GAIN AND PHASE MARGINS FOR DISCRETE TIME SYSTEM

Year 2018, Volume: 1 Issue: 2, 47 - 55, 30.12.2018

Esmat Bekir

Abstract

This note describes an algorithm
for computing the gain and phase margins for single input single output
discrete time systems. It converts the complex computations into real
computations. It results into Chebyshev polynomials from which we compute the
desired margins. The algorithm is simple, easy to implement and devoid of
complex computations.

Keywords

Gain margin, phase margin, control system stability, discrete time system, Chebyshev polynomials

References

• 1. Bourles H and Kosmidou O. Gain and phase margins of the discrete-time guaranteed cost regulator. Proceeding of the 33rd IEEE Conference on Decision and Control; 33rd IEEE Conference on Decision and Control; 1994 Dec 14-16; USA. Florida: IEEE Control Systems Society; 1994. p. 3837-3839.
• 2. Eriksson L and Koivo H. Tuning of discrete time PID controllers in sensor network based control systems. Proceedings 2005 IEEE International Symposium on Computational Intelligence in Robotic and Automation; CIRA2005; 2005 June 27-30; Finland. Espoo: IEEE; 2005. p. 359-364.
• 3. Ogata K. Modern control engineering. New Jersey: Prentice Hall, Englewood Cliffs; 1970.
• 4. Driels M. Linear control systems engineering. New York: McGraw-Hill; 1996.
• 5. Astrom KJ and Murray RM. Feedback systems: an introduction for scientists and engineers. New Jersey: Princeton University Press; 2008.
• 6. Margin. Mathworks [Document on the internet]. Mathworks Documentation; 2018 [cited 2018 September 1]. Available from: https://www.mathworks.com/help /control/ref/margin.html
• 7. Mason J. Chebyshev polynomials. Florida: Chapman & Hall/CRC, Boca Raton; 2003.
• 8. Arden BW and Astill KN. Numerical algorithms. Massachusetts: Addison Wesley, Reading; 1970.