You want to design a lead compensator such that the above system has the following nse time and settling time values: Rise time: 0.2012 sec; settling time (1%) = 0.575 sec a) Obtain the desired dominant poles of the closed loop system, such that the above response specification is met. b) Selecting an appropriate location for the compensator’s pole, obtain the compensator’s zero using the phase property of the root locus. c) What is the root locus gain? What is the compensator’s gain? d) Write the transfer function of the lead compensator. e) What segments of the real axis (if any) contain parts of the root locus? f) How many asymptotes does the root locus have? What are their orientation angles? What is their centroid? g) Obtain the angles at which the root locus branches depart from the plant poles. h) Sketch the root locus of the closed-loop system. Make sure to label your sketch clearly (pole locations, zero locations, asymptotes, etc.).