Investigation of systems with pure time delay by root locus method

There is considered the application of the root locus method of a characteristic equation for the investigation of linear and harmonically linearized control systems with pure time delay. There are formulated general geometric properties of the root loci of time delay systems which makes it possible to approximately plot the root loci and thus qualitatively investigate systems. There are obtained correlations which allow to analytically plot the loci and determine the quantitative characteristics of a system. The method is illustrated with an example of a 5th order time delay system.