GATE EC 2017 Question Paper (05-Feb-2017) (Shift 2)

A unity feedback control system is characterized by the open-loop transfer function

$G\left(s\right)=\frac{2\left(s+1\right)}{s^3+k{s}^2+2s+1}$

The value of k for which the system oscillates is _________

A second-order LTI system is described by the following state equations.

$\frac{d}{dt}{x}_1\left(t\right)-x_2\left(t\right)=0$

$\frac{d}{dt}{x}_2\left(t\right)+2x_1\left(t\right)+3x_2\left(t\right)=r\left(t\right)$

where x₁(t) and x₂(t) are the two state variables and r(t) denotes the input. The output c(t) = x₁(t). The system is

A unity feedback control system is characterized by the open-loop transfer function

$G\left(s\right)=\frac{10K\left(s+2\right)}{s^3+3s^2+10}$

The Nyquist path and the corresponding Nyquist plot of G(s) are shown in the figures below.





If 0 < K < 1, then the number of poles of the closed-loop transfer function that lie in the right-half of the s-plane is

The signal x(t) = sin (14000 πt), where t is in seconds, is sampled at a rate of 9000 samples per second. The sampled signal is the input to an ideal low pass filter with frequency response H(f) as follows:

H≤ft( f ) = ≤ft\{ {*20c 1,&≤ft| f | ≤slant 12kHz \\ 0,&≤ft| f | > 12kHz } ..

What is the number of sinusoids in the output and their frequencies in kHz?

The unmodulated carrier power in an AM transmitter is 5 kW. This carrier is modulated by a sinusoidal modulating signal. The maximum percentage of modulation is 50%. If it is reduced to 40%, then the maximum unmodulated carrier power (in kW) that can be used without overloading the transmitter is _________