For the figure below, $G_c(s)$ is a PID controller and the $G(s)$ is given as

$G(s)=\frac{1}{s(s+1)(s+6)}$

a$)$ Obtain the $K_p,K_1$ and $K_d$ values of PID controller by using the $2^{nd}$ Ziegler Nichols Method. Show added zeros and a pole on the S plane. What kind of root$-$locus curve do you expect?

b$)$ Do you expect a good step response? $.$ How could you improve the performance further?