The concept of root locus is used to determine the stability and performance of a closed-loop control system. The complete root locus is the set of all possible locations of closed-loop poles as a function of a parameter such as the gain of the system.

Asymptotes of Root Locus:

The root locus consists of branches that start at the open-loop poles and end at the open-loop zeros. The branches move towards the asymptotes as the gain of the system increases. The asymptotes are straight lines that approach the branches of the root locus as the gain tends to infinity. The asymptotes provide an estimate of the behavior of the root locus at high gain values.

Number of Intersection of Asymptotes:

The number of asymptotes of the root locus is equal to the number of poles of the open-loop transfer function that are not canceled by zeros. The asymptotes intersect at a point known as the centroid of the poles. The number of intersection points of the asymptotes is equal to the number of poles that are not canceled by zeros.

In the case of a single-input, single-output (SISO) system, the number of intersection points is equal to the number of poles of the open-loop transfer function that are not canceled by zeros. Therefore, the answer to the given question is option 'D', which states that there is only one intersection point of the asymptotes in the complete root locus.

Conclusion:

In conclusion, the number of intersection points of the asymptotes of the complete root locus is equal to the number of poles that are not canceled by zeros. For a SISO system, there is only one intersection point of the asymptotes in the complete root locus.