Question

Question 13 For the control system shown below the input signal is x(C) and the output signal in ), the fransfer function is 10s +50 s +12s+ 100 10s +50 o HCs)--S-10s + 150 10s +50 s2 + 22s 101 10s+50 H(s) HS)2 + 22s 150 50 O H(s)- s2 +22s 150

Answer 1

For negative feedback TF = G (s)/1 + G (s) H (s) for positive f/B TF = G (s)/1 - G (s) H (s) Therefore closed log Transfer function is H (s) = y (s)/x (s) = (10 s + 50/s^2 + 12 s + 100)/1 + 10 s + 50/s^2 + 12 s + 100 H (s) = (10 s + 50/s^2 + 12 s + 100)/(s^2 + 12 s + 100 + 10 s + 50/s^2 + 12 s + 100) H (s) = 10 s + 50/s^2 + 22 s + 150 \r\n H (s) = y (s)/x (s) = (1/s + 1) (1/s + 1)/1 + 1/s 1/(s + 1)^2 H (s) = 1/(s + 1)^2/1 + 1/s (s + 1)^2 H (s) = 1/s (s + 1)^2 + 1 H (s) = 1/s (s^2 + 2 s + 1) + 1 H (s) = 1/s^3 + 2 s^2 + s + 1 Standard 2nd