GATE Electrical Engineering (EE) 2021 Solved Papers

Question : 55 of 65

Marks: +1, -0

Consider a closed-loop system as shown.

G_{p}(s)=\;{14.4}/{s(100.1 s)}

is the plant transfer function and

G_{c}(s)=

1 is the compensator. For a unit-step input, the output response has damped oscillations. The damped natural frequency is ________ rad/s. (Round off to 2 decimal places.)

Your Answer:

Validate

Solution:

1+G_{c}(a) G_{p}(s) H(s)=1

1+1 × \;{14.4}/{s(1+0.1 s)}=0

0.1 s^{2}+s+14.4=0

{s}^{2}+10 {s}+144=0

2 ξ ω_{ {n}}=10

ω_{ {n}}^{2}=144

2 ξ × 12=10

ξ=\;{10}/{24}=\;{5}/{12}

So,

ω_{ {d}}=ω_{ {n}} √{1-ξ^{2}}=12 √{1-\;{25}/{144}}=√{119}=10.91

rad/sec

Go to Question:

Prev Question

Next Question