Consider the below unity feedback closed-loop control system: R(s) K(s 1 30) s(s + 20s +100) Y(s) a. Do a basic sketch of the rough locus of the poles of the closed-loop system as a function of K. [5 pts] b. Determine the values of K for which the system is stable. [5 pts] d. c. Determine what value of K, if any, will yield a velocity error eramp (0) 1/10- [5 pts] Refine the root locus by precisely determining all its relevant points, angles, asymptotes, jw-axis crossings, etc. [5 pts] e. If K = 10, using the refined root locus plot the precise location of the poles of the system and characterize the step-response of the system. [5 pts] f. If K = 10, determine the relevant parameters of the system's step-response, namely, the wn, Ts, and %OS. [5 pts] g. Determine a value of K so the system has a step-response with 10% overshoot. [5 pts]