Nyquist theory - Control system - Stability
Not really an answer, more of a caution.
(In the following I am assuming that things are 'nice', such as \$gh\$ is proper, \$1+g(\infty)h(\infty) \neq 0\$, etc.)
With the transfer function \$h_{CL}={gh \over 1+gh}\$ note that the poles of \$h_{CL}\$ are exactly the zeros of \$1+gh\$. (there is no cancellation and if \$p\$ is a pole of \$gh\$ then \$h_{CL}(p) = 1\$).
Hence it is sufficient to (Nyquist) plot \$gh\$ (or \$1+gh\$ if you prefer) to determine stability.
However, if you add dynamics to the feedback path this is no longer true.
We now have \$h_{CL}={gh \over 1+bgh}\$ and we are interested in the poles of \$h_{CL}\$.
If \$b\$ does not cancel a \$gh\$ pole, then the poles of \$h_{CL}\$ are exactly the zeros of \$1+bgh\$, so you can use Nyquist again.
However, if there is a cancellation more care is needed. For example, with
\$g(s)h(s)= {s+2 \over s-1 } \$, \$b(s)= {s-2 \over s+1 } \$ we get
\$1+b(s)g(s)h(s) = { 2s+3 \over x+1}\$ and
\$h_{CL}(s) = {(s+1) (s+2) \over (s-1) (2s+3) } \$, so a Nyquist plot will suggest
that all is good, but there is an unstable pole in the closed loop dynamics.
In the latter case, one needs to check the cancelled open loop poles. (The lesson here is broadly to stay away from non minimum phase cancellations :-).)
As an aside, the Nyquist plot gives some nominally useful information (you can read off phase &amp; gain margins and look for unusual features) but if stability is a concern I would prefer a state space approach which has the added advantage of being easier to simulate.