Question

1 Passive-circuit realization 30 pts Identify and realize the following compensators with passive networks. As- sume the value of capacitor is 10μF. s 0.1 s +0.01 s + 2 8+6 s 0.1 (s + 1 s + 0.01/s+10

Answer 1

S + 0.1/s + 0.01 compare the above given transfer function with (1 + tau_s/1 + Alpha tau_s) TF = s + 0.1/s + 0.01 = 0.1[10s + 1]/0.01[100s + 1] Right Double Arrow [1 + tau_s/1 + Alpha tau_s] times Alpha TF = 10[1 + 10s]/[1 + 100s] Alpha [1 + tau_s]/[1 + Alpha tau_s] on comparing Alpha = 10 & tau = 10 Alpha > 1 Right Double Arrow Lag compensator. [Alpha - is called lag constant]. circuit is as follows. Alpha = R_1 + R_2/R_2 tau = Lag time constant = R_2 C_2 Given that C_2 = 10 mu F tau = 10 Right Double Arrow 10 = R_2 times 10 mu F Right Double Arrow R_2 = 10^6 Ohm = 1 mu Ohm R_2 = 1 mu Ohm Alpha = R_1 + R_2/R_2 = 10 Right Double Arrow 10 = R_1 + 10^6/10^6 Right Double Arrow 10^4 = R_1 + 10^6 R_1 = 10(10^6) - 10^6