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Consider the following closed loop system. yₛₚy

G_cK_cG _f10 / 0.1 s1 G_{p}1 / (0.1 s1)^2

G_c'G_f' andGₚare the transfer functions of the controller, the final control element and the process, respectively. yandy ₛₚare the response and its set point, respectively. For a gain margin of 1.6, the design value of K_C is _____(correct up to one decimal place).

Options

none

Answer

0.5

Solution

T.FA.R = G_{ope} = G_{CG}_{fG}_pG_m

.

T.FA.R = /frac{10/mathrm{Kc}}{((0.1s+1)^3)}

A.R_2 = 10K^ᶜ_3

[(0.1)^2w^2+1]^2

.

w = 17.3

A.R_w_{=}_w_c_o = 10K^ᶜ_3

[(0.1)^2 /times (17.3)^2+1]^2

A.R = 10K^ᶜ

7.97

GM = /frac{1}{ARw} = w_0

7.921.6 = 10K_C

K_C = /frac{7.97}{(10 /times 1.6)}

K = 0.5

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Source PDF: GATE CH 2020 (with Solutions).pdf

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