Question

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Problem 3: (15 points) The feedback control system shown has the closed loop transfer function R(S) + Y(s) Gc(s) G(s) 169 Ge(s)G(s) 1 + Gc(s)G(s) (s+85)(s2 + s + 1.69) If the system starts at rest and is subjected to a unit step input, determine estimates for the following aspects of the system response: a) Percent overshoot b) Final value of y c) 2% settling time

Answer 1

-85, Given closed loop to ans fer function, T(S) - 169 5+85) (Sa+s+1-69) Poles = oist 1.22 As we can see poles of second order of second order is more closer to origin than first order... So they dominates and we can approximate transfer function to lower order 'S' by neglecting in (st 85) or Put sro in ea+85² T(S) = 16 85 (5²+2 +1.69) 1.98 s²+8+1-69 characteristic equation: s² t st1.69 compare it with s²+2&wnston w2=1-69 Wh=1-3 2 & wn - 1 я = L 2x1-3 al 0:38

a) Percentage overshoot, M= evo-92 Xloo 8 = 27.52 E E=0.38) (6) Y() (1.98 5²+5+169 R (s) unit step r(t) = R (3) -11 Y(s) $ 645 . 1.98 S (5²+ St1-69 = s-o = final value of y lim & YGS) lim sxl (1.98 S (5²+571-69 17 (1) 2% settling time, ts & wn 4 0.38 X1.3 4 taa 8.1 sec.