This could represent the dynamics of an Industrial Remote Inspection System, which is essentially a remote-controlled robot for high radiation fields. Our goal is to design a proper compensator C(s). (a) (7 points) Design a compensator C(s) such that the gain crossover frequency become ωg = 10 rad/sec, and a minimum phase margin of 35 degrees is achieved (Note: tan−1 (10) = 84.3 ◦ , and tan−1 (3.33) = 73.3 ◦ And don’t forget to account for, say, 5◦ additional margin so once you modify your compensator in the next part, you would still meet your minimum phase margin of 35◦ ). (b) (1 point) Find the velocity constant Kv for the compensated system you designed in Part (a). What would be the steady-state tracking error of the closed-loop system ess for a ramp input r(t) = tu(t)? (c) (4 points) Now, modify your compensator in order to further reduce the steadystate ramp tracking error to less than 0.001 while still trying to preserve the same gain crossover frequency and the same phase margin as Part (a). (d) (2 points) How would you propose to modify your compensator in Part (a) if, instead of the 0.001 tracking error requirement in Part (c), your objective was actually to completely eliminate the steady-state error in tracking a ramp input?