Question

1 Gc(s) R(S) Gp(s) Y(S) Given the system above, determine the gain K for a lead/lag compensator so the system meets the desired responses: Settles at about 2 seconds . Has a percent overshoot of about 33% The plant has a transfer function of: Gp (S+18)/((s+1) (s+8)) Assume that the pole of the lead/lag compensator has a pole at s =-5.

Given the system above, determine the gain K for a lead/lag compensator so the system meets the desired responses:

• Settles at about 2 seconds
• Has a percent overshoot of about 33%
• The plant has a transfer function of: Gp = (s+18) / ( (s+1)*(s+8) )
• Assume that the pole of the lead/lag compensator has a pole at s = -5.

Answer 1

Given Block diogxam R(S) Gp(s) s+1.8 Given Gp (s) , = 's at s=-5 Leod /lag Co tvern pole s+5 2 sec. Noue Settling Trno 2 Also % overshoot 33% 0.332 0.33 e. L..5 Tkon O.332 funchon Now ovexall Thonsfer 4(s) = G s) Ge(s) : Stia . Keras) chavacte stic equation, fut Nous Choracterstic equabion, fut a (lood compenuahi)

Abus Gnal s cand ondo equaton s2.Co Hevo It is ko value = 4.5 [By compa ing 40+90 K = 45) 2 -' 10K96.25 40 K = 0.55 8 ured valua This is tho ensato