A unity negative feedback closed loop system has a plant with the transfer function $\text{G}(s)=\frac{1}{s^{2}+2 s+2}$ and a controller $\text{G}_{c}(s)$ in the feedforward path. For a unit step input, the transfer function of the controller that gives minimum steady state error is
- $\text{G}_{c}(s)=\frac{s+1}{s+2}$
- $\text{G}_{c}(s)=\frac{s+2}{s+1}$
- $\text{G}_{c}(s)=\frac{(s+1)(s+4)}{(s+2)(s+3)}$
- $\text{G}_{c}(s)=1+\frac{2}{s}+3 s$