TUTORIAL 12 – ROOT LOCUS DESIGN Objective • Integrate material from all previous lectures into a practical problem. • Practice for the Final exam. You are to design compensation for a servo aircraft pitch dynamics placed in a unity feedback system. The system is pictured below. Control Elevator servo Aircraft dynamics FIGURE 1: AIRCRAFT PITCH DYNAMICS You are provided transfer functions . (s) Elevator servo, 45 — — 10 ec(s) s + 10 0(s) 3 Aircraft dynamics,6,(s)— s2 + 3s + 4 1. Design a gain compensator that will produce closed loop system having damping ratio of 0.42 (desired poles approximately at -1.2±2.6i). Calculate the settling time for a step input, and the steady state error for a step input. 2. Design a new compensator that will eliminate the steady state error to a step input, while retaining % overshoot with similar step input settling time to gain compensation. Estimate the new settling time. 3. Design a new compensator that will decrease the step input settling time to one half of the value found for gain compensation, but with same % overshoot