Answer to Question #233462 in Chemical Engineering for Lok

Question #233462

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. °


1
Expert's answer
2021-09-07T23:53:28-0400

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

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


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