(Solved): Consider the feedback control system shown helom. a) (10) Calculate the closed-loop transfer functi ...

Consider the feedback control system shown helom. a) (10) Calculate the closed-loop transfer function: (Symbolic) $G(s)=\frac{Y(s)}{R(s)}$ b) (10) Determine the values of the control gains $K_1$ and $K_2$ such that the closed-loop satisfies the following criteria simultaneously: (Numeric) - The system is critically damped. - The undamped natural frequency of the system is ${?}_n=1\mathrm{rad}/\mathrm{s}$ c) (5) Using the values of the gains obtained in part b), determine the closed-loop syster state error $e_{ss}={\lim }_{t??}(r(t)?y(t))$ to a unit-ramp input. (Numeric) d) (5) Determine the closed-loop system's time response $y(t)$ to unit-impulse input $r(t)$. (Numeric) (5) Is the response obtained in part d) stable? Explain.