$3(8$ points$)/$ Figure $3$ shows the block diagram of the speed control of an Hybrid Vehicle

Assume the speed controller is given as $G_{sc}(S)=K_{p_{sc}}.$ Find the gain, $K_{P_{sc}},$ that yields a steady$-$state error, $e_{\text{s}\text{t}\text{e}\text{p}}()=1\%.$

Now assume that in order to reduce the steady$-$state error for step inputs, integration is added to the controller yielding $G_{sc}(s)=K_{P_{sc}}+(\frac{K_{l_{sc}}}{s})=100+(\frac{K_{lsc}}{s}).$ Find the value of the integral gain, $K_{lsc},$ hat results in a steady$-$state crror, $e_{\text{r}\text{a}\text{m}\text{p}}()=2\mathrm{.}5\%.$