(Solved): 1. (20 points) A feedback system with negative unity feedback has a loop transfer function \[ L(s) ...

1. (20 points) A feedback system with negative unity feedback has a loop transfer function \[ L(s)=G_{c}(s) G(s)=\frac{2(s+8)}{s(s+4)} \] (a) Determine the closed-loop transfer function \( T(s)=Y(s) / \) \( R(s) \cdot(5 \) points \( ) \) (b) Find the time response, \( \mathrm{y}(\mathrm{t}) \), for a step input \( r(t)= \) A for \( t>0 \). (5 points) (c) Determine the percent overshoot of the response. (5 points) (d) Using the final-value theorem, determine the steady-state value of \( y(t) \) (5 points)