I. Investigate the stability of the closed loop system in Figure 1. Use both the Routh stability criterion and root locus tools. 2. Investigate the steady state tracking error for a step input when the actuator gain is Knee is 500. 3. Provide the root-loci for the closed loop system as function of Kan. In the mat-locus plot. indicate the region for a damping ratio such that 0.7 < ( < 0.9 and a damped natural frequency of 10 < cod < 20 irad/secl. 4. Design a Lead•Lag compensator H(s) for this system as indicated in Figure 2. to achieve the following design requirements for the closed loop: (a) The 2" order poles are located in the region of the root locus plot you indicated above. (address this trquirentent with the lead compensation) (b) The steady state error of the system to a step input is reduced to less than 10%. (use the lag-compensation to meet this trtitiirtintsit) Figure 2 R(8)