Design a controller using Matlab

[PhysicoRaj]

Homework Statement

For the plant:
$G(s)=\frac{1}{s(s+2)(0.4s+1)}$
Design a controller in Matlab such that $K_v=4$ , phase margin = $60^o$ and zero steady state error for step input.

Homework Equations

$e_{ss} = Lim_{s->0} \frac{s R(s)}{1+D(s)G(s)}$
Lead/Lag compensator structure: $D(s) = K\frac{(\alpha s + 1)}{(\beta s + 1)}$

The Attempt at a Solution

From the data that $e_{ss}=0$ for step input and finite non zero velocity error for ramp reference, the system desired is type-1. The plant already has a pole at $s=0$, hence the controller need not add poles at $s=0$ .
I chose the lead/lag compensator to tune the phase margin.
Using MATLAB I found the plant has a phase margin of $65.7499^o$ at phase crossover of $0.4777 rad s^{-1}$.
To find the controller gain K:
using $R(s) = \frac{1}{s^2}$ (for ramp input) and $e_{ss} = \frac{1}{4}$ in the steady state error equation, I got $K = 8$ .
So my compensator becomes:
$D(s) = 8\frac{(\alpha s + 1)}{(\beta s + 1)}$

I loaded the plant in the Matlab sisotool and tried adjusting the phase margin to 60 degrees but its not going beyond 46 degrees:

While with controller gain K around 2, the pm can be adjusted to 60 degrees:

Is my choice of controller or controller gain wrong? Or have i missed anything in this route? Are other assumptions and calculations right? How do I proceed further?
Also, how would I verify the steady state error of the closed loop system after design (from the ramp response? [attachment3]) .

Thank you.

 

[PhysicoRaj]

I finally solved it. I assumed the controller gain $K = 8$ to be the inherent gain of the plant and for that plant designed a restructured controller of the form:
$D(s) = \frac{(\alpha_1 s+1)(\alpha_2 s+1)}{(\beta_1 s+1)(\beta_2 s+1)}$
leaving with two poles and two zeros.

Closed loop characteristics were satisfactory.

Thanks.