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e$)$ A PID controller is designed with coefficients in the form of $F(s)=K_p+K_{d}s+\frac{K_i}{s}$ and with the gain values $K_p=12\mathrm{.}7,K_i=20,K_d=2\mathrm{.}2,$ and connected to the system as shown in the below. Find the resulting closed$-$loon svstem and its characteristic equation. $($Use feedback$()$ command for finding closed loop transfer function.$)$

f$)$ Find the overshoot, settling time, and peak time values of the closed$-$loop system. Plot the unit step response. $($Use stepinfo$()$ and $[y,t]=$ step$()-$commands.$)$