The open-loop transfer function of a control system that includes a negative unity feedback is as follows:

The uncontrolled closed-loop system response has the overshoot and settling time of \(16 \%\) and 3.32 seconds, respectively. Design a proportional-derivative (PD) controller (with the format of \(G_{c}(s)=s+z_{c}\) ), so that, without changing the overshoot of the system response, a threefold reduction happens in its settling time.

G(s) k s(x+4)(s+6)