Consider the car's cruise control problem discussed in previous sections. The openloop and closed-loop transfer functions were found to be

\[\begin{align*}& H_{o l}(s)=K G(s)=\frac{b K}{m s+b} \tag{4.60}\\& H_{c l}(s)=\frac{K G(s)}{1+K G(s)}=\frac{\frac{b K}{m s+b}}{1+\frac{b K}{m s+b}}=\frac{b K}{m s+b+b K} \tag{4.61}\end{align*}\]

Compare the sensitivity of the open-loop and closed-loop systems with respect to the controller gain \(K\).