ELE 302 Lecture Notes - Lecture 40: Damping Ratio, Pid Controller
19 Oct 2017
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The two complex conjugate poles are at: 4. 52 j 5. 04. Note that since we have not changed the proportional gain, = 40. 78, the frequency remains the same, 6. 67 rad/seconds (the conjugate poles were at: 3. 5 j 5. 79). The damping ratio went up from 0. 59 for = 0,0245, to 0. 67 for = 0. 05. The new estimates of the po and settling time are now: The stepeval shows the actual values, very close to the predicted from the. 5. 96 0. 6246 0. 4565 0. 3003 tsettle(2%) tsettle(5%) wd tring ess(in %) 0. 7 is still there, but the dominant complex poles moved from 4. 52 j 5. 04 to 4. 18 j 4. 9. The damping ratio went down from 0. 67, for = The slight drop in damping is the effect of an integrator, and will cause the overshoot to go up slightly. 5. 68 0. 6446 0. 4805 0. 3163 tsettle(2%) tsettle(5%) wd tring ess(in %) For = 0. 05 the system under pid control has this closed loop transfer function: 2. 04 0. 7 20.
