How does the gain affect the transient and steady$-$state response? $($a$)$ Derive the closed$-$loop poles and steady$-$state gain as a function of the proportional controller gain kp$.($b$)$ Use the Final Value Theorem to determine the steady$-$state reference tracking error, ess, for a constant reference $($R$($s$)=$c$1$ s $).($c$)$ Summarize what can and cannot be done with proportional$-$only control