This topic is relevant to Problem 6.1, parts (d) and (e), where:
You are asked to discuss the effects of replacing
your original expressions for Q(s) and M(s) with more
complicated polynomial expressions in 's'.
For part (d), you are asked about the steady-state error.
Just use the same analytic techniques
(discussed on previous pages) by which you derived you
answer to 6.1, part (b) [ss error to a step response, for the original
system...].
For part (e), you asked about potential effects on the
Gain Margin.
Recall that the gain margin depends
upon where/if the open-loop system phase has dropped
below -180 degrees.
The phase in turn depends on the location of poles in
the open-loop system.
Do these new polynomials change and/or add system poles?
If so, how? Would this then affect gain margin?
(Justify why or why not...)
Make sure you understand qualitatively why the steady-state
error and gain margin (each) do or do not depend on these
higher order dynamics in the system.
(Hint: Think about effects on the system type. Does this
change the number of 'free integrators'?)