An open loop transfer function of a unity negative feedback control system is given by-Gs-Kss-as-bIf the gain margin of the system is 32 dB for K - 2- then the value of K required to get the gain margin of 25 dB will be

The gain margin of the system can be given as, GM=20log_101|G(jω_pc)| ω_pc is independent of the value of K. So, nbsp; nbsp; nbsp; nbsp; nbsp; ...

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Basics on Gain Margin

An open loop ...

Question

An open loop transfer function of a unity negative feedback control system is given by,
$G (s) = \frac{K}{s (s + a) (s + b)}$
If the gain margin of the system is 32 dB for K = 2, then the value of K required to get the gain margin of 25 dB will be

4.48

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38.1

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1.12

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6.38

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Solution

The correct option is A 4.48
The gain margin of the system can be given as,

$G M = 20 {log}_{10} \frac{1}{| G (j ω_{p c}) |}$

$ω_{p c}$ is independent of the value of K.

So, $G M = C - 20 l o g_{10} (K)$

Where, C is a term independent of "K".

For K = 2, $G M = 32 d B$
So, $C = 32 + 20 l o g_{10} (2)$

When GM = 25 dB,
$25 = C - 20 {log}_{10} (K)$
$25 = 32 + 20 {log}_{10} (2) - 20 l o g_{10} (K)$
$20 {log}_{10} (K) = 7 + 20 {log}_{10} (2) = 13.02$

$K = 10^{(13.02 / 20)} = 4.48$

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An open loop transfer function of a unity negative feedback control system is given by, G(s)=Ks(s+a)(s+b) If the gain margin of the system is 32 dB for K = 2, then the value of K required to get the gain margin of 25 dB will be

An open loop transfer function of a unity negative feedback control system is given by,
$G (s) = \frac{K}{s (s + a) (s + b)}$
If the gain margin of the system is 32 dB for K = 2, then the value of K required to get the gain margin of 25 dB will be