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An analytical approach to root loci

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1 Author(s)
K. Steiglitz ; New York University, Morristown, NJ, USA

The general algebraic equations of root loci for real K are found in polar and Cartesian coordinates. A synthesis method is then suggested which leads to linear equations in the coefficients of the open-loop transfer function when closed-loop poles and their corresponding gains are specified. Equations are also found for the gain corresponding to a given point on the root locus. A superposition theorem is presented which shows how the root loci for two open-loop functions place constraints on the locus for their product. With a knowledge of the simple lower-order loci, this theorem can be used in sketching and constructing root loci.

Published in:

IRE Transactions on Automatic Control  (Volume:6 ,  Issue: 3 )