Root Locus Determination by the Use of Real Roots

In the usual application of root locus techniques, points are found by a method of trial and error according to a number of standard rules,
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or by the use of some additional aids for more accuracy.
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With either method, the determination is often cumbersome and laborious, To facilitate the construction of the root locus, this paper presents a procedure for determining a pair of root loci in the complex region by the other loci, especially by those on the real axis that usually can be found easily. The gain of each root locus is expressed by a curve, a method that has been found to be more rational than the ordinary plotting of gain values on each locus. Three illustrative examples are presented to demonstrate the relative simplicity of the described method, as well as the accuracy of its results.