The Nyquist stability criterion and the Routh criterion both are powerful analysis tools for
determining the stability of feedback controllers. Identify which of the following statements
is FALSE.
A
The closed-loop frequency response for a unity feedback system cannot be obtained
from the Nyquist plot.
B
The Routh criterion is not applicable in the condition of transport lag, which can be
readily handled by the Nyquist criterion.
C
The general shape of the Nyquist plot is readily obtained from the Bode magnitude plot
for all minimum-phase systems.
D
Both the criteria provide information relative to the stable gain range of the system.
2
GATE ECE 2018
MCQ (Single Correct Answer)
+1
-0.33
Consider p(s) = s3 + $${a_2}$$s2 + $${a_1}$$s + $${a_0}$$ with all real coefficients. It is known that its
derivative p'(s) has no real roots. The number of real roots of p(s) is
A
0
B
1
C
2
D
3
3
GATE ECE 2018
Numerical
+2
-0
For a unity feedback control system with the forward path transfer function
$$G(s) = {K \over {s\left( {s + 2} \right)}}$$
The peak resonant magnitude Mr
of the closed-loop frequency response is 2. The
corresponding value of the gain
K
(correct to two decimal places) is _________.
Your input ____
4
GATE ECE 2018
Numerical
+2
-0
The logic gates shown in the digital circuit below use strong pull-down nMOS transistors for
LOW logic level at the outputs. When the pull-downs are off, high-value resistors set the
output logic levels to HIGH (i.e. the pull-ups are weak). Note that some nodes are
intentionally shorted to implement “wired logic”. Such shorted nodes will be HIGH only if
the outputs of all the gates whose outputs are shorted are HIGH.
The number of distinct values of X3X2X1X0 (out of the 16 possible values) that give
𝑌 = 1 is _______.
