Comparison of the Existing Methods in Determination of the Characteristic Polynomial

This paper presents comparison among methods of determination of the characteristic polynomial coefficients. First, the resultant systems from the methods are compared based on frequency criteria such as the closed loop bandwidth, gain and phase margins. Then the step responses of the resultant systems are compared on the basis of the transient behavior criteria including overshoot, rise time, settling time and error (via IAE, ITAE, ISE and ITSE integral indices). Also relative stability of the systems is compared together. Finally the best choices in regards to the above diverse criteria are presented.

Authors:

• Mohammad Saleh Tavazoei
• Mohammad Haeri

Keywords:

• Characteristic Polynomial
• Transient Response
• Filters
• Stability.

References:

[1] F. H. Imlay, "A Theoretical Study of Lateral Stability with an Automatic
Pilot", NACA, TR 693, Washington, 1940.
[2] D. Graham and R.C. Lathrop, "The synthesis of "optimum" transient
response: criteria and standard forms", AIEE Transactions, vol. 72, pt.
II, pp. 273-288, 1953.
[3] C. Kessler, "Ein Beitrag zur Theorie Mehrschleifiger Regulungen",
Regelungst., vol. 8, no. 8, pp. 261-266, 1960.
[4] S. Manabe, "Coefficient Diagram Method", 14th IFAC Symposium on
Automatic Control in Aerospace, Seoul, 1998.
[5] P. Naslin, Essentials of Optimal Control, Boston Technical, Boston,
MA, 1969.
[6] Y. C. Kim, L.H. Keel and S. P. Bhattacharyya, Transient Response
Control via Characteristic Ratio Assignment, IEEE Transactions on
Automatic Control, 2003, vol. 48, no. 12, pp. 2238-2244.
[7] S. Winder, Analog and Digital Filter Design, 2nd Ed., Newnes, 2002.
[8] S. Manabe, "Brief Tutorial and Survey of Coefficient Diagram Method",
4th Asian Control Conference, Singapore, 2002.