4. Pl controller design Consider a unity gain feedback system with the following open loop transfer function (forward path): G₂(s) = 2 apl s² + bp1s+ CPI PIS (a) Find the value of K₁ so that the ramp-error constant Kv is 14. (b) Sketch the root locus of the characteristic equation 0 ≤ Kp > ∞. (c) Find the values of Kp such that the damping ratio of the controlled system is (=0.1. If there is more than one choice, state which value you recommend and provide rational for the value you select. d) Find the roots of the characteristic equation. d) Using MATLAB, demonstrate that the damping ratio requirement is met for the close loop controlled system.