List of top Control Systems Questions on Tuning of PID controllers and sizing of control valves asked in GATE IN

Consider a unity feedback configuration with a plant and a PID controller as shown in the figure. \( G(s) = \dfrac{1}{(s+1)(s+3)} \text{  and  } C(s) = \dfrac{K(s+3-j)(s+3+j)}{s} \) with \( K \) being scalar. The closed loop is