A unity negative feedback loop has the loop transfer function We know from the underlying physics of

Question:

A unity negative feedback loop has the loop transfer function

We know from the underlying physics of the problem that the parameter a can vary only between 0 (a) The steady-state tracking error due to a negative unit step input (i.e., R(s) = -1/s ) versus the parameter a.
(b) The maximum percent initial undershoot (or overshoot) versus parameter a.
(c) The gain margin versus the parameter a.
(d) Based on the results in parts (a)-(c), comment on the robustness of the system to changes in parameter a in terms of steady-state errors, stability, and transient time response.