1
GATE EE 2023
MCQ (Single Correct Answer)
+1
-0.33

Consider a unity-gain negative feedback system consisting of the plant G(s) (given below) and a proportional-integral controller. Let the proportional gain and integral gain be 3 and 1, respectively. For a unit step reference input, the final values of the controller output and the plant output, respectively, are

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

A
$$\infty,\infty$$
B
$$1,0$$
C
$$1,-1$$
D
$$-1,1$$
2
GATE EE 2023
MCQ (Single Correct Answer)
+2
-0.67

The magnitude and phase plots of an LTI system are shown in the figure. The transfer function of the system is

GATE EE 2023 Control Systems - Polar Nyquist and Bode Plot Question 5 English

A
$$2.51{e^{ - 0.032s}}$$
B
$${{{e^{ - 2.514s}}} \over {s + 1}}$$
C
$$1.04{e^{ - 2.514s}}$$
D
$$2.51{e^{ - 1.047s}}$$
3
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
4
GATE EE 2023
Numerical
+2
-0

Consider the state-space description of an LTI system with matrices

$$A = \left[ {\matrix{ 0 & 1 \cr { - 1} & { - 2} \cr } } \right],B = \left[ {\matrix{ 0 \cr 1 \cr } } \right],C = \left[ {\matrix{ 3 & { - 2} \cr } } \right],D = 1$$

For the input, $$\sin (\omega t),\omega > 0$$, the value of $$\omega$$ for which the steady-state output of the system will be zero, is ___________ (Round off to the nearest integer).

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