Consider a lead compensator of the form K(s) = (1 + s/a) / (1 + s/(βa)), β 1, a 0. The frequency at which this compensator produces maximum phase lead is 4 rad/s. At this frequency, the gain amplification provided by the controller, assuming asymptotic Bode-magnitude plot of K(s), is 6

Question

Consider a lead compensator of the form K(s) = (1 + s/a) / (1 + s/(βa)), β > 1, a > 0. The frequency at which this compensator produces maximum phase lead is 4 rad/s. At this frequency, the gain amplification provided by the controller, assuming asymptotic Bode-magnitude plot of K(s), is 6 dB. The values of a, β, respectively, are

Accepted Answer

2, 4. The correct option is right because it satisfies the conditions for maximum phase lead and gain amplification at the specified frequency. The values of a and β must be chosen such that the compensator's phase lead reaches its peak at 4 rad/s while providing a gain of 6 dB, which is achieved with a = 2 and β = 4.

Solution

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