Consider a $4-$stroke SI engine modeled as a first order system without time delay according to the transfer function $G_p(s)=\frac{K_M}{{}_{M}s+1}.$ The parameters $K_M$ and ${}_M$ are nominally equal to $1,$ but both can vary from $0\mathrm{.}5$ to $2$ depending on operating conditions. Determine the gain $K_P$ of a proportional controller so that despite these variations, the steady state error for a unit step input does not exceed $10\%,$ and the system time constant $($closed$-$loop$)$ stays below $0\mathrm{.}2$ s $.$ Assume unity feedback.

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