The analytic method for plotting root loci is examined. The basic equation for this method, originally published by Bendrikov and Teodorchik4 in 1959, is derived in a very simple way. A second equation, which complements the original Bendrikov equation, is also derived. An example of how these two equations may be used to plot root loci using Mathematica is presented.
Get full access to this article
View all access options for this article.
References
1.
EvansW. R., ‘Graphical analysis of control systems’. Trans. AIEE, 67, pp. 547–51 (1948)
2.
PowerH. M. and SimpsonR. J., Introduction to Dynamics and Control, McGraw-Hill (1978)
3.
DransfieldP. and HaberD. F., Introducing Root Locus, Cambridge (1973)
4.
BendrikovG.A. and TeodorchikK. F., “The analytic theory of constructing root loci”, Automation and Remote Control, 20, pp. 340–344 (1959)
5.
LehnigkS.H., Stability Theorems for Linear Motions, Prentice Hall (1966)
6.
HarleyM.H. and PowerH. M., ‘Analytic equations for geometrical construction of some common root loci’, Int. J. Elec. Enging. Educ., 11, pp. 45–59 (1973)
7.
WojcikC.K., ‘Analytical representation of the root locus’, Trans. ASME, ser. D, J. Basic Eng., 86, pp. 37 43 (March 1964)
8.
Mathematica Version 2.2.3., Wolfram Research Inc., Champaign, Illinois (1994)
9.
ShawW.T. and TiggJ., Applied Mathematica, Addison Wesley (1994)