A feedback control system is shown in Figure P7.18. The filter $G_c(s)$ is often called a compensator, and the design problem involves selecting the parameters $\alpha$ and $\beta$. Using the root locus method, determine the effect of varying the parameters. Select a suitable filter so that the time to settle (to within $2 \%$ of the final value) is less than 4 seconds and the damping ratio of the dominant roots is greater than 0.60 .