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Consider the control system closed-loop represented such a block diagram below:

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Given that: G_C(s) = K and G(s) = 1/s

a) Determine the values of K which the closed-system loop is stable.

b) Suppose that the disturbance d(s) be sinusoidal with amplitude A and frequency w. The exactly value of w is unknown, but know itself 0 leq w leq 10 rad/s

Is it possible to choose a value of K such that, in steady state, the amplitude of the output value is less than or equal to 1% of the value A?

If your answer is “YES”, so compute the value of K that guarantees this attenuation.

If your answer is “NO”, so show that there is no value of K that guarantees this attenuation.


However my question is very similar, i have some doubts about the letter b)

dfrac{y(s)}{d(s)}=dfrac{1}{1+KG(s)}Rightarrow bigg|dfrac{y(s)}{d(s)}bigg|_{s=jomega}=0.1

frac{1}{|1+Kfrac{1}{j10}|} = 0.1Rightarrow 10 = sqrt{1+frac{K^2}{100}}Rightarrow 100 = 1+frac{K^2}{100}implies ,,,,boxed{K = 10sqrt{99}}

Is this correct?