Question

Consider a control system with the open loop transfer function is Gol =Kc e^{-0.36S}/12S+1 the pre factor S in minutes and Kc, is the gain of the controller. The frequency for phase. margin of 30° is 4.04 rad/min; find the value of the gain of the controller for a gain margin of 2. °

Answer 1

$Phase \space margin\\ \pi-\frac{\pi}{4}= 2 tan^{-1}(-0.5 w)+ (-\frac{\pi}{2})\\ \frac{\pi}{2}-\pi-\frac{\pi}{4}= 2 tan^{-1}(-0.5 w)\\ \frac{+2 \pi -4 \pi-\pi}{4}= 2 tan^{-1}(-0.5 w)\\ \implies w= 4.83 rad/sec$

The value of the gain of the controller  = $4.83(1+0.25*9.83)=10.66$