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# GATE : Control Systems Champion Quiz 3

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Question 1

If the closed-loop transfer functions of a control system is given as , then its is

Question 2

Consider the feedback system shown in the figure. The Nyquist plot G(s) of is also shown. Which one of the following conclusions is correct?

Question 3

In the AC equivalent circuit shown in the figure, if the input current is very large, the type of feedback is

Question 4

Consider two real valued signals, x(t) band-limited to [-500 Hz, 500 Hz] and y(t) band-limited to the [-1 kHz, 1 kHz]. For z(t) = x(t) . y(t), the Nyquist sampling frequency (in kHz) is ______

Question 5

An analog signal is band-limited to 4 kHz, sampled at the Nyquist rate and the samples are quantized into 4 levels. The quantized levels are assumed to be independent and equally probable. If we transmit two quantized samples per second, the information rate is

Question 6

The number of open right half plane poles of is

Question 7

The feedback configuration and the pole-zero locations of are shown below. The root locus for negative values of k, i.e. for –∞< k < 0, has breakaway/break in points and angle of departure at pole P (with respect to the positive real axis) equal to

Question 8

Four voice signals each limited to 4 KHz and sampled at Nyquist rate, are converted into binary PCM signal using 256 quantization levels. The bit transmission rate for the time division multiplexing signal will be

Question 9

Consider the feedback control system shown below which is subjected to a unit step input. The system is stable and has the following parameters kP = 4, ki = 10, ω = 500 and ξ = 0.7.

The steady state value of z is

Question 10

Consider a continuous-time signal defined as

Where ‘*’ denotes the convolution operation and t is in seconds. The Nyquist sampling rate In samples/sec) for x (t) is_________.
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