Problem 1 Consider the following system as shown in figure 1: (a) Draw the root locus of the system. (b) Determine the gain value for which two complex poles have a real part of -.6. (c) Design a lead compensator for the system such that the closed-loop system has a maximum overshoot of and a settling time of 5 sec. (d) For the value of K = 10 determine the frequency of oscillations and the percent of overshoot in a response to unit step input