GATE ECE 2022 | Stability Question 1 | Control Systems

GATE ECE 2022

MCQ (Single Correct Answer)

-0.33

Consider an even polynomial p(s) given by

$$p(s) = {s^4} + 5{s^2} + 4 + K$$

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 __________.

$$ - 4 \le K \le {9 \over 4}$$

$$ - 3 \le K \le {9 \over 2}$$

$$ - 6 \le K \le {5 \over 4}$$

$$ - 5 \le K \le 0$$

GATE ECE 2018

MCQ (Single Correct Answer)

-0.33

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.

The closed-loop frequency response for a unity feedback system cannot be obtained from the Nyquist plot.

The Routh criterion is not applicable in the condition of transport lag, which can be readily handled by the Nyquist criterion.

The general shape of the Nyquist plot is readily obtained from the Bode magnitude plot for all minimum-phase systems.

Both the criteria provide information relative to the stable gain range of the system.

GATE ECE 2018

MCQ (Single Correct Answer)

-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

GATE ECE 2016 Set 1

MCQ (Single Correct Answer)

-0.3

Match the inferences X, Y, and Z, about a system, to the corresponding properties of the elements of first column in Routh's Table of the system characteristic equation.

X: The system is stable …
Y: The system is unstable …
Z: The test breaks down …

P: … when all elements are positive
Q: … when any one element is zero
R: … when there is a change in sign of coefficients

X→P, Y→Q, Z→R

X→Q, Y→P, Z→R

X→R, Y→Q, Z→P

X→P, Y→R, Z→Q