Root locus Equation

Introduce Root locus

The root locus analysis is graphical representation to test if the roots of the system will varies with the change of system's parameter. (The root locus system is usually use in a feed back system) The analysis is created by Walter R. Evans because he wants to determine the stability of the system. The root locus plots has different poles which use closed loop function as the gain parameter,

The use of root locus system is determining the stability of the system, which included design the damping ratio and natural frequency of a feedback system. Lines of constant damping ratio can be drawn radially from the origin and lines of constant natural frequency can be drawn as arcs whose center points coincide with the origin. We can do so by selecting a point along the root locus that coincides with a desired damping ratio and natural frequency a gain. The K can be calculated and implemented in the controller. There are more techniques you can learn from the Matlab tutorial in extra resources. For both pole location and root locus.

Damping ratio and natural frequency mean overall feedback system is well approximated by a second order system.

Practice Problems
Practice problem for root locus Example and include practice problem

Extremely useful matlab practice problem

Website practice problem for root locus

Extra Resources
Matlab tutorial for Root Locus equation

Understand drawing of root locus: Part 1, Part 2,