Research on the Root-Locus' Properties as Time Lag Varies

For the single-loop SISO system which has pure time delay in its feedback loop, several properties of the root-locus as time lag τ varies were studied, including the symmetry of the loci, τ → 0 + and τ +∞ points, loci and breakaway points on the real axis and intersections with the imaginary axis, etc. The effect on the system stability while time lag varies was also investigated on the basis of previous conclusions. Finally, a scanning method that can be employed on computer to get the root-locus was provided at the end of this paper.