3 This is a design problem where you will use the root locus tool in MATLAB to design a proportional controller K(s) = K for the plant given G(s) in the feedback loop from Problem 2. The objectives are for the rise time Tr1 to be 0.21 seconds and the overshoot to be equal to 12%. Follow the steps below to produce this controller design. s + 10 G(s) S2 + 2s (a) Find the poles and zeros of G(s) and classify stability of G(s). (b) Use the second order performance approximations to find ( and wn for the closed loop system GCl(s) to meet the performance objectives. (c) With the values you found for 5 and Wn to determine desired pole locations for the closed loop system Gcl(s). (d) Use the root locus tool in MATLAB to find the gain (e) Find the closed loop transfer function Gcl(s) with this value of K and estimate the rise time and percent overshoot. R(S) K(s) G(s) Y(s) 3 This is a design problem where you will use the root locus tool in MATLAB to design a proportional controller K(s) = K for the plant given G(s) in the feedback loop from Problem 2. The objectives are for the rise time Tr1 to be 0.21 seconds and the overshoot to be equal to 12%. Follow the steps below to produce this controller design. s + 10 G(s) S2 + 2s (a) Find the poles and zeros of G(s) and classify stability of G(s). (b) Use the second order performance approximations to find ( and wn for the closed loop system GCl(s) to meet the performance objectives. (c) With the values you found for 5 and Wn to determine desired pole locations for the closed loop system Gcl(s). (d) Use the root locus tool in MATLAB to find the gain (e) Find the closed loop transfer function Gcl(s) with this value of K and estimate the rise time and percent overshoot. R(S) K(s) G(s) Y(s)