Anesthesia is used in surgery to induce unconsciousness
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Anesthesia is used in surgery to induce unconsciousness

Problem 12.7

Anesthesia is used in surgery to induce unconsciousness. One problem with drug-induced unconsciousness is differences in patient responsiveness. Furthermore, the patient response changes during an operation. A model of drug-induced anesthesia control is shown in the figure below. The proxy for unconsciousness is the arterial blood pressure.

(a) Obtain the Bode plot and determine the gain margin and the phase margin when T = 0.05s.

(b) Repeat part (a) when T = 0.1s. Describe the effect of the 100% increase in the time delay T.

(c) Using the phase margin, predict the percent overshoot for a step input for parts (a) and (b).


Hint
EngineeringThe gain margin is the factor by which the gain must be multiplied at the phase crossover to have the value 1. The phase crossover occurs at 0.010 Hz and so the gain margin is 1.00/0.45=2.22. The phase margin is the number of degrees by which the phase angle is smaller than −180° at the gain crossover. Greater will the gain margin greater will be the stability of the system. It refers t...
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