1
GATE EE 2023
MCQ (Single Correct Answer)
+2
-0.67

Consider a lead compensator of the form

$$K(s) = {{1 + {s \over a}} \over {1 + {s \over {\beta a}}}},\beta > 1,a > 0$$

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 $$a,\beta$$, respectively, are

A
1, 16
B
2, 4
C
3, 5
D
2.66, 2.25
2
GATE EE 2022
MCQ (Single Correct Answer)
+2
-0.67

An LTI system is shown in the figure where $$G(s) = {{100} \over {{s^2} + 0.1s + 100}}$$. The steady state output of the system, to the input r(t), is given as y(t) = a + b sin(10t + $$\theta$$). The values of a and b will be

GATE EE 2022 Control Systems - Polar Nyquist and Bode Plot Question 8 English

A
a = 1, b = 10
B
a = 10, b = 1
C
a = 1, b = 100
D
a = 100, b = 1
3
GATE EE 2022
MCQ (Single Correct Answer)
+2
-0.67

The open loop transfer function of a unity gain negative feedback system is given as

$$G(s) = {1 \over {s(s + 1)}}$$

The Nyquist contour in the s-plane encloses the entire right half plane and a small neighbourhood around the origin in the left half plane, as shown in the figure below. The number of encirclements of the point ($$-$$1 + j0) by the Nyquist plot of G(s), corresponding to the Nyquist contour, is denoted as N. Then N equals to

GATE EE 2022 Control Systems - Polar Nyquist and Bode Plot Question 7 English

A
0
B
1
C
2
D
3
4
GATE EE 2016 Set 1
MCQ (Single Correct Answer)
+2
-0.6
Consider the following asymptotic Bode magnitude plot ($${\omega \,\,}$$ is in $$rad/s$$) GATE EE 2016 Set 1 Control Systems - Polar Nyquist and Bode Plot Question 22 English

Which one of the following transfer functions is best represented by the above Bode magnitude plot?

A
$${{2s} \over {\left( {1 + 0.5s} \right){{\left( {1 + 0.25} \right)}^2}}}$$
B
$${{4\left( {1 + 0.5s} \right)} \over {s\left( {1 + 0.25s} \right)}}$$
C
$${{2s} \over {\left( {1 + 2s} \right)\left( {1 + 4s} \right)}}$$
D
$${{4s} \over {\left( {1 + 2s} \right){{\left( {1 + 4s} \right)}^2}}}$$
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