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a) Using the Routh-Hurwitz array, prove that the critical gain Kcr = 72 and Wer = V11 rad/s. b) Using the Ziegler-Nichols met

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ANSWER0 Given Equation GLS)= 8 +93 H) (+5) a ) The chagact@gristic Equation is ItG(S) =0 k 1+ (5795:1) (9+) к + S3 +25+5+58 +105+55-03 (s= (6) ka=72, Q1 f = Si i se f = 0 211 f 3316 21 f = 0.59185 T= Т. 0:52185 T= 1.8944 P.F!- Kp = 0.45X KG kp=0.45X72 kp=(3) GPID(S) = KP[1+ tis + T3 8 Kp = 0.6ka =>06172) Kp = 43.2 Tp =0.5 P Q = 2.9+ TP = 0 51-5166) TP = 0. 941116 Td = 0.125 PG

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