Recall from the Introduction: Root Locus Controller Design page. a root locus plot shows all possible closed-loop pole locations as a parameter (usually a proportional gain K) is varied from 0 to infinity. We will employ the root locus to design our controller to place our system's closed-loop poles in locations that will result in behavior that satisfies our given requirements. Recall from the Aircraft Pitch: System Analysis page. how pole locations directly affect the character of the system's response to a step reference.
We will specifically use MATLAB's SISO Design Tool to modify the system's root locus to design a compensator to place the system's closed-loop poles to achieve the given design requirements. More specifically, we will use the root locus to design for the requirements on transient response. We will assume the following unity-feedback architecture.