PYQs Based Test - 05 : Control Systems

Consider an even polynomial p(s) given by

p(s) = s⁴ + 5s² + 4 + K

where K is an unknown real parameter. The complete range of K for which p(s) has all its roots on the imaginary axis is ________.

The block diagram of a closed-loop control system is shown in the figure. R(s), Y(s), and D(s) are the Laplace transforms of the time-domain signals r(t), y(t), and d(t), respectively. Let the error signal be defined as e(t) = r(t) − y(t). Assuming the reference input r(t) = 0 for all t, the steady-state error e(∞), due to a unit step disturbance d(t), is _________ (rounded off to two decimal places).

For an LTI system, the Bode plot for its gain is as illustrated in the figure shown. The number of system poles N ₚand the number of system zeros N ${}_z$ in the frequency range 1 Hz ≤ f ≤ 10 ⁷Hz is

For the unity feedback control system shown in the figure, the open-loop transfer function G(s) is given as

$\mathrm{G}\left(\mathrm{s}\right)=\frac{2}{\mathrm{s}\left(\mathrm{s}+1\right)}$

The steady-state error eₛₛ due to a unit step input is

The root-locus plot of a closed-loop system with unity negative feedback and transfer function KG(s) in the forward path is shown in the figure. Note that K is varied from 0 to ∞.

Select the transfer function G(s) that results in the root-locus plot of the closed-loop system as shown in the figure.