GATE EC || CONTROL SYSTEM || ROUTH HURWITZ || PYQS (2000-2025)

The system shown in the figure remains stable When

For unbypassed [Tex]R_E[/Tex]:

[Tex]R_i = \beta r_e + (1 + \beta) R_E \text{ (Increases)}[/Tex]

[Tex]A_v = \frac{A_I R_L}{R_i} \text{ (Decreases)}[/Tex]

( GATE 2002 || EC || MCQ ||2 MARK)

For the polynomial [Tex]P(s) = s^5 + s^4 + 2s^3 + 2s^2 + 3s + 15[/Tex], the number of roots which lie in the right half of the s-plane is
( GATE 2004 || EC || MCQ ||2 MARK)

The positive values of "K" and "a" so that the system shown in the figure below oscillates at a frequency of 2 rad/sec, respectively, are

( GATE 2006 || EC || MCQ ||2 MARK)

If the closed-loop transfer function of a Control system is given as [Tex]T(s) = \frac{s - 5}{(s + 2)(s + 3)}[/Tex], then it is

( GATE 2007 || EC || MCQ ||2 MARK)

The feedback system shown below oscillates at 2 rad/s when

( GATE 2007 || EC || MCQ ||2 MARK)

Consider a transfer function

[Tex]G_p(s) = \frac{ps^2 + 3ps - 2}{s^2 + (3 + p)s + (2 - p)}[/Tex]

with [Tex]p[/Tex] a positive real parameter. The maximum value of [Tex]p[/Tex] until which [Tex]G_p[/Tex] remains stable is ______.

(GATE 2014 || EC || MCQ ||2 MARK)

A plant transfer function is given as

[Tex]G(s) = \left( K_p + \frac{K_i}{s} \right) \frac{1}{s(s + 2)}[/Tex]

When the plant operates in a unity feedback configuration, the condition for the stability of the closed-loop system is

( GATE 2015 || EC || MCQ ||2 MARK)

The characteristic equation of an LTI system is given by

[Tex]F(s) = s^5 + 2s^4 + 3s^3 + 6s^2 - 4s - 8[/Tex]. The number of roots that lie strictly in the left half of the s-plane is

( GATE 2015 || EC || NAT ||2 MARK)

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.

List-I

X. The system is stable…

Y. The system is unstable…

Z. The test breaks down …

List -II

P.... when all elements are positive

Q....when any one element is zero

R....when there is a change in sign of coefficients

( GATE 2016 || EC || MCQ||2 MARK)

The transfer function of a linear time-invariant system is given by

[Tex]H(s) = 2s^4 - 5s^3 + 5s - 2[/Tex]

The number of zeroes in the right half of the s-plane is

( GATE 2016 || EC || NAT||2 MARK)