Fig. 2 summarizes the above relationships and
illustrates how the corresponding root migration plots
influence one another, ultimately yielding the closedloop
transfer functions, as well as closed-loop stability
and performance levels. The compensator matrix K(s)
in Eq. (2) has five "degrees of freedom": k k11, t12,
k 1, and k 2 , aside from the freedom available within
each compensation term nk..(s). In Fig. 2 for root
locus design applications, lJthese parameters are
reformulated in terms of the five "degrees of freedom"
G21k2, 4 116 1, 42Ik11, and specification of any
single /$ value.