Consider the control system shown in Figure CP10.6. Design a lag compensator using root locus methods to meet the following specifications: (1) steady state error less than 10% for a step input, (2) phase margin greater than 45°, and (3) settling time (with a 2% criterion) less than 5 seconds for a unit step input. (a) Design a lag compensator utilizing root locus methods to meet the design specifications. Develop a set of m-file scripts to assist in the design process. (b) Test the controller developed in part (a) by simulating the closed-loop system response to unit step input. Provide the time histories of the output y(t). (c) Compute the phase margin using the margin function.