The main properties of the root loci of linear delayed systems are found, including the equations of the loci and formulas for the free parameter, whereby the root loci can be plotted (geometrically and analytically) and the value of the free parameter determined at any point of the locus. Examples are considered, showing how the main properties of the loci of systems of different classes may be used to find the regions of stability, the variation in the magnitude and nature of the degree of stability, the critical values of the frequency and free parameter, and the transients in the system.
Department of Oscillation Physics
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