(Solved): A unity negative feedback control system with G(s)=K(s+2)/[s(1+ts)(1+2s)] has two parameters to be s ...

3. (15 pts total) A unity negative feedback control system with $\mathrm{G}(\mathrm{s})=\mathrm{K}(\mathrm{s}+2)/$ $[s(1+?s)(1+2s)]$ has two parameters to be selected. $(K,?>0)$ (a) Determine and plot the regions of stability for this system. (b) Select $?$ and $\mathrm{K}$ so that the steady state error to a ramp input is less than or equal to $25\%$ of the input magnitude. (c) Determine the percentage overshoot for a step input for the design selected in part (b).