For the control system shown in Fig.3.20:

(a) design a PID control $G_{c}(s)$ such that the dominant closed-loop poles located at $s=-1$ $\pm j 1$.

(b) select $a=0.6$ for the PID controller and find the values of $K$ and $b$

(c) root-locus plot using MATLAB.

Fig. P 3. 20

R(s) + K PID controller (s +a)(s +b) S Ge(s) Plant G(s) 1 C(s) (s +0.8)