I am studying control systems, and I am studying the lead and lag compensator.
I have seen than if I use a lead compensatpr in the following way:
consider a closed loop transfer function:
$T(s)=\frac{s+2}{(s+1)(s+8)}$
and I design a lead compensator as:
$lead(s) = \frac{3s+1}{0.1s+1}$
and I use it as a precompensator, so the lead compensator is outside the loop:
$lead(s)\cdot T(s)$
and plot the frequency response, I see that I have a frequency respose I have that there is a reasonance peak, which increases as I decrease the frequency at which the zero is present:
in this case, the red line is a lead compensator defined as:
$\frac{3s+1}{0.1s+1}$
and the green line is the system in which I have used the following compensator:
$\frac{6s+1}{0.1s+1}$
can somebody explain to me why?