Consider a third-order servo system with a plant transfer function of = 50,000 + + 50) . assuming a unity feedback configuration, use bode plots to design a lead compensator that results in a phase margin of pm ≥ 50∘ and a closed-loop bandwidth greater than 20 rad/sec. [hint: you do not have to satisfy any steady-state error specification. therefore, you may use gain to you meet the bandwidth specification. gain can be less than 1, if necessary. also, note that closed-loop bandwidth is never less than the open-loop gain crossover frequency.]